**Eco. 131 Online Quiz/Discussion (Sampling and other issues)—1-3-2023**

**QUESTION ONE**

**The following yields (kg) were obtained from plots in a soyabean field given two sprays of pesticides.**

**22, 20, 19, 25, 22, 17, 28, 20, 22, 23, 17**

**18, 24, 25, 22, 20, 23, 25, 22, 28, 19, 22**

**25, 27, 23, 24, 17, 18, 22, 19, 22, 23, 24**

**Compute the table as follows:**

**The class interval using sturge rule****Mid-point****Frequency****Cumulative Frequency****Relative Frequency****Relative Cumulative Frequency**

**QUESTION TWO**

**Write a brief note on the following:**

**Sample****Population****Continuous Variable****Discrete variable****Statistics****Data**

1a. Class Interval

17-18

19-20

21-22

23-24

25-26

27-28

1b. Frequency

5

6

8

7

4

3

33

1c. Midpoint

17.5

19.5

21.5

23.5

25.5

27.5

1d. Cumulative frequency

5

11

19

26

30

33

1e. Relative frequency

15.2

18.2

24.2

21.2

12.1

9.1

1f. Relative Cumulative frequency

15.2

33.3

57.5

78.7

90.9

100

2a. Sample: This is defined as part or portion of a population and it is taken from the population as a representation of it. For example; height of of students in the faculty of social sciences taken to represent the height of students in the department.

b. Population: This is the entire collection of items or individuals which one wishes to examine at a particular time. It is also defined as the entire group about which information is desired. It is described as a largest collection of entities for which we have an interest at a particular time; an entire set of objects, observations, or scores that have something in common.

c. Continuous variable: A continuous variable is one for which, within the limits the variable ranges, any value is possible. Continuous variables can take any value between a certain set of real numbers. The value given to an observation for a continuous variable can include as small as the instrument of measurement allows.

d. Discrete variable: Discrete variables or data are also categorical variables. They are variables or data that exist only as whole numbers and are not divisible. A discrete variable can take on a finite number of numerical values, categories or codes.

e. Statistics: The word ‘ Statistics’ refers to numerical facts such as the number of events occuring in time or the number of people living in a particular area. It also involves the the study of ways of collecting, analyzing and interpreting numerical facts or numerical data.

f. Data: This is a numerical statement of facts in a specific field of enquiry or simply numbers which may result from taking measurements. Examples; recording heights, weights or temperature measurements.

NWANKWO ESTHER CHIOMA

ECONOMICS DEPT

2021/244120

1. Using Sturge rule formula =k= 1 + 3.322 logN

Where N= Total number of observations.

K= 1 + 3.322 log33

K= 1 + 3.322(1.5185)

K= 1 + 5.0445

K= 6.0445

K~=6

Range=Highest value – Lowest value

Range= 28 – 17 = 11

Class interval = 11/6

=1.83

~= 2

Class Interval Mid-point Frq. C.F. R.F. R.C.F

17 – 18 17.5 5 5 15.15 15.15

19 – 20 19.5 6 11 18.18 33.33

21 – 22 21.5 8 19 24.24 57.57

23 – 24 23.5 7 26 21.21 78.78

25 – 26. 25.5 4 30 12.12 90.90

27 – 28 27.5 3 33 9.09 100

Total=33

2.a SAMPLE

It is the portion of the population (which must be a representative of the population in all ramifications) that is being drawn out for conclusions since it is usually difficult to examine all members of the population due to time, cost and other constraints.

Sampling is a procedure by which one or more members of a population are selected from the population.

b. POPULATION

It is the entire group of individuals that we’re interested in making a statement about. It is the entire group about which information is desired.

It can also be described as the largest collection of entities for which we have an interest at a particular time; an entire set of objects, observations, or scores that have something in common.

c. CONTINUOUS VARIABLE

A continuous variable is one for which, within the limits the variable changes, any value is possible.

A variable is said to be continuous if it can assume an infinite number of real values within a given interval. For instance, consider the height of a student. The height can’t take any values. It can’t be negative and it can’t be higher than three metres.

d. DISCRETE VARIABLES

Discrete variables or data are also known as categorical variables. They are variables which exist only as whole numbers and are not divisible. A discrete variable can take on a finite number of numerical values, categories or codes.

e. STATISTICS

Statistics, in itself, is the collation and analysis of numerical data to arrive at specific inference. This academic discipline finds application in various other branches of studies, such as Economics. Any study about Economics and Statistics involves the validation of theories with quantified data sets.

Statistics concerns the collection, processing, compilation, dissemination, and analysis of economic data. It is closely related to business statistics and econometrics.

f. DATA

Data are raw facts or unprocessed information that has been collected for use. The collection may include numbers, words, measurements, observations or even descriptions of things.

They are the raw material from which econometric analysis is constructed. Just as a building is no stronger than the wood or steel used in its framework, an econometric study is only as reliable as the data used in its analysis. Many econometricians over the years have written about problems with data.

(1) the class interval using sturge rule formula=k=1+3.322logn

k=1+3.322log33

k=1+3.322(1.5185)

k=6.0445

k=6

class interval=range/1+13.322logn

range=28-17=11

class interval=11/6=1.83=2

(1a) class interval midpoint=

17-18

19-20

21-22

23-24

25-26

27-28

(1c) frequency

5

6

8

7

4

2

(1d) cumulative frequency

5

11

19

26

30

32

Relative cumulative frequency

4.1

8.9

15.5

21.1

24.4

26.02

NAME: ONOJA KINGSLEY CHISOM

REG. NO: 2021/247636

DEPARTMENT: COMBINE SOCIAL SCIENCE (ECONOMICS & PSYCHOLOGY)

EMAIL: onojakingsley2000@gmail.com

Question One.

1. The class interval using sturge rule:

Sturge rule formula= k= 1 + 3.322 logN

Where N= Total number of observations.

K= 1 + 3.322 log33

K= 1 + 3.322(1.5185)

K= 1 + 5.0445

K= 6.0445

K= 6~

Class interval= Range/1 + 3.322 logN

Range=Highest value – Lowest value

Range= 28 – 17 = 11

Class interval= 11/ 1+3.322log33

= 11/6

=1.83

= 2~

C.I M F. C.F. R.F. R.C.F

17 – 18 17.5 5 5 15.15 15.15

19 – 20 19.5 6 11 18.18 33.33

21 – 22 21.5 8 19 24.24 57.57

23 – 24 23.5 7 26 21.21 78.78

25 – 26 25.5 4 30 12.12 90.90

27 – 28 27.5 3 33 9.09 100

Total= 33

where:

C.I. is the Class Interval

M. is the Midpoint

Fr. is the Frequency

R. Fr. is the Relative Frequency

C. Fr. is the Cumulative Frequency

R. C. Fr. is the Relative Cumulative Frequency

Question Two.

1. Sample: A sample is a subset of fraction of the population selected as a representative of the population for study. It is also defined as a part of fraction of the population selected from the population in order to study it and use the result obtained from it to make generalization about the population from where it is drawn.

2. Population: Population is a set of existing units (usually people objects or events). Population can also be defined as the totality of all the observations of a particular variable having similar characteristics that a researcher or investigator has chosen for study at a particular point or period of time.

3. Continuous Variable: A continuous variable is one for which, within the limits the variable ranges, any value is possible. Continuous variable can take any value between a certain set of real numbers. The value given to an observation for a continuous variable can include values as small as the instrument of measurement allows.

4. Discrete variable: These types of variables or data exist only as whole numbers, and are not divisible. A discrete variable is a variable that takes on distinct, countable values. It can take on a finite number of numerical values, categories or codes. There are five classes of discrete variables: Norminal, Ordinal, Dummy, Preference, and Multiple response variables. Norminal variables: they’re said to be measured only on Norminal scale. Ordinal variables: they are said to be measured only on ordinal scale. Dummy variables: In regression analysis, a dummy variable is one that takes the values 0 or 1 to indicate the absence or presence of some categorical effect that may be expected to shift the outcome. Preference variable: these are the variables whose values are either in increasing or decreasing order. Multiple response variables: they’re those which can assume more than one value. As opposed to a continuous variable, a discrete variable can assume only a finite number of real values within a given interval.

5. Statistics: The word ‘statistics’ refers to numerical facts such as the number of events occurring in a particular time. It is the scientific method of collecting, organizing, summarizing, presenting and analyzing data. It is also the theory and methods of collecting, organizing, presenting, analyzing and interpreting data sets so as to determine their essential characteristics.

It is the development and application of methods to the collection, analysis, and interpretation of observed data from planned investigations.

6. Data: Data is a numerical statement of facts in a specific field of enquiry or simply numbers which may result from taking measurement. It could also be qualitative i.e. data that deals with description. Data are required for empirical analysis and other forms of analysis. Data are of two types: primary data which are data collected originally for the first time by a person who secures them by survey for his own personal use, and secondary data which are data collected by someone else from a person that originally collected them and which are processed to some extent.

Question One.

1. The class interval using sturge rule:

Sturge rule formula= k= 1 + 3.322 logN

Where N= Total number of observations.

K= 1 + 3.322 log33

K= 1 + 3.322(1.5185)

K= 1 + 5.0445

K= 6.0445

K= 6~

Class interval= Range/1 + 3.322 logN

Range=Highest value – Lowest value

Range= 28 – 17 = 11

Class interval= 11/ 1+3.322log33

= 11/6

=1.83

= 2~

C.I M F. C.F. R.F. R.C.F

17 – 18 17.5 5 5 15.15 15.15

19 – 20 19.5 6 11 18.18 33.33

21 – 22 21.5 8 19 24.24 57.57

23 – 24 23.5 7 26 21.21 78.78

25 – 26 25.5 4 30 12.12 90.90

27 – 28 27.5 3 33 9.09 100

Total= 33

where:

C.I. is the Class Interval

M. is the Midpoint

Fr. is the Frequency

R. Fr. is the Relative Frequency

C. Fr. is the Cumulative Frequency

R. C. Fr. is the Relative Cumulative Frequency

Question Two.

1. Sample: A sample is a subset of fraction of the population selected as a representative of the population for study. It is also defined as a part of fraction of the population selected from the population in order to study it and use the result obtained from it to make generalization about the population from where it is drawn.

2. Population: Population is a set of existing units (usually people objects or events). Population can also be defined as the totality of all the observations of a particular variable having similar characteristics that a researcher or investigator has chosen for study at a particular point or period of time.

3. Continuous Variable: A continuous variable is one for which, within the limits the variable ranges, any value is possible. Continuous variable can take any value between a certain set of real numbers. The value given to an observation for a continuous variable can include values as small as the instrument of measurement allows.

4. Discrete variable: These types of variables or data exist only as whole numbers, and are not divisible. A discrete variable is a variable that takes on distinct, countable values. It can take on a finite number of numerical values, categories or codes. There are five classes of discrete variables: Norminal, Ordinal, Dummy, Preference, and Multiple response variables. Norminal variables: they’re said to be measured only on Norminal scale. Ordinal variables: they are said to be measured only on ordinal scale. Dummy variables: In regression analysis, a dummy variable is one that takes the values 0 or 1 to indicate the absence or presence of some categorical effect that may be expected to shift the outcome. Preference variable: these are the variables whose values are either in increasing or decreasing order. Multiple response variables: they’re those which can assume more than one value. As opposed to a continuous variable, a discrete variable can assume only a finite number of real values within a given interval.

5. Statistics: The word ‘statistics’ refers to numerical facts such as the number of events occurring in a particular time. It is the scientific method of collecting, organizing, summarizing, presenting and analyzing data. It is also the theory and methods of collecting, organizing, presenting, analyzing and interpreting data sets so as to determine their essential characteristics.

It is the development and application of methods to the collection, analysis, and interpretation of observed data from planned investigations.

6. Data: Data is a numerical statement of facts in a specific field of enquiry or simply numbers which may result from taking measurement. It could also be qualitative i.e. data that deals with description. Data are required for empirical analysis and other forms of analysis. Data are of two types: primary data which are data collected originally for the first time by a person who secures them by survey for his own personal use, and secondary data which are data collected by someone else from a person that originally collected them and which are processed to some extent.

Name. Nwankwo chinecherem benedictha.

Reg number.2021/243695.

Department. Economics

Question 1

1.The class interval using sturge rule:

Sturge rule formula= k= 1 + 3.322 logN

Where N= Total number of observations.

K= 1 + 3.322 log33

K= 1 + 3.322(1.5185)

K= 1 + 5.0445

K= 6.0445

K= 6~

Class interval= Range/1 + 3.322 logN

Range=Highest value – Lowest value

Range= 28 – 17 = 11

Class interval= 11/ 1+3.322log33

= 11/6

=1.83

= 2~

Class Interval Mid-point F. C.F. R.F. R.C.F

17 – 18 17.5 5 5 15.15 15.15

19 – 20 19.5 6 11 18.18 33.33

21 – 22 21.5 8 19 24.24 57.57

23 – 24 23.5 7 26 21.21 78.78

25 – 26 25.5 4 30 12.12 90.90

27 – 28 27.5 3 33 9.09 100

Total= 33.

Question 2

1 SAMPLE refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observation.

2.A POPULATION is the complete set group of individuals. Whether that group comprises a nation or a group of people with a common characteristics. In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study

3. CONTINUOUS VARIABLES-

This type of variable can take on any value within a range. Continuous variable represent measurable amounts such as volume, weight etc. It can take on uncountable of infinite sets of values which can be represented in whole numbers, fractions or decimals. The range of numbers here is incomplete and it can assume any value between two values. Examples of these variables are weight of baby elephants, height of students in a class etc.

4. A discrete variable is a variable whose value is obtained by counting. Examples: number of students present. number of red marbles in a jar. number of heads

5. STATISTICS-

Statistics is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data. It can also be defined as the collation and analysis of numerical data to arrive at a specific inference. The two categories of statistics are descriptive and inferential statistics.

6. DATA-

Data is the information used for calculation, analysis, or planning. It is the collection of fact or raw and unorganized information such as words, numbers, symbols etc. The two categories of data include qualitative data (i.e data that deal with description) and quantitative data (i.e data that deals with numbers

NAME: TOCHUKWU ADAORAH DESTINY

DEPARTMENT: ECONOMICS

REG. NUMBER: 2021/249145

1.Using the Sturges’ rule, the number of classes can be calculated as 1 + log2(n), where n is the number of data points. In this case, n = 33, so the number of classes is 1 + log2(33) ≈ 5.24, which rounds up to 6.

Class interval using Sturges’ rule:

Range: 11 (28 – 17)

Class interval: 11/6 ≈ 1.83, rounded up to 2

So the class intervals are:

17-18

19-20

21-22

23-24

25-26

27-28

Mid-point:

17.5, 19.5, 21.5, 23.5, 25.5, 27.5

Frequency:

Class interval Frequency

17-18 2

19-20 3

21-22 7

23-24 5

25-26 3

27-28 2

Cumulative Frequency:

Class interval Frequency Cumulative Freq.

17-18 2 2

19-20 3 5

21-22 7 12

23-24 5 17

25-26 3 20

27-28 2 22

Relative Frequency:

Class interval Freq. Relative Freq.

17-18 2 2/33 ≈ 0.061

19-20 3 3/33 ≈ 0.091

21-22 7 7/33 ≈ 0.212

23-24 5 5/33 ≈ 0.152

25-26 3 3/33 ≈ 0.091

27-28 2 2/33 ≈ 0.061

Relative Cumulative Frequency:

Class int. Freq. Rel. Freq. Rel. Cum. Freq.

17-18 2 0.061 0.061

19-20 3 0.091 0.152

21-22 7 0.212 0.364

23-24 5 0.152 0.515

25-26 3 0.091 0.606

27-28 2 0.061 0.667

2. a). Sample: A sample is a subset of a population, which is selected to represent the entire population. The purpose of taking a sample is to estimate the characteristics of the entire population with less cost and time.

b). Population: A population refers to a group of individuals, objects, or events that share some common characteristics. It can be finite or infinite and can be used to make inferences about the entire group.

c). Continuous Variable: A continuous variable is a type of variable that can take on any value within a certain range or interval. Examples include age, weight, and height.

d). Discrete Variable: A discrete variable is a type of variable that can only take on specific values within a certain range or set. Examples include the number of siblings a person has or the number of cars in a parking lot.

e). Statistics: Statistics is the science of collecting, analyzing, interpreting, and presenting data. It involves the use of mathematical and statistical methods to draw conclusions from data.

f). Data: Data refers to any collection of facts, figures, or information. It can be in numerical or non-numerical form and can be collected from various sources, such as surveys, experiments, or observations. The analysis of data can provide insights and information that can be used to make informed decisions.

An Assignment on Eco 131 (Introduction to Economic Statistics)

Name: OGBONNA ISAIAH CHEKWUBE.

Reg. Number: 2021/246041

Department: Economics.

The following yields (kg) were obtained from plots in a soya bean field given two sprays of pesticides.

22, 20, 19, 25, 22, 17, 28, 20, 22, 23, 17

18, 24, 25, 22, 20, 23, 25, 22, 28, 19, 22,

25, 27, 23, 24, 17, 18, 22, 19, 22, 23, 24.

Compute the table as follow;

The class interval using Sturges rule.

Mid- point.

Frequency.

Cumulative frequency.

Relative frequency.

Relative cumulative frequency.

Solutions

Using sturge’s rule;

Range (R). = XG(Greatest value in set ) XL ( least value in set)

XG = 28, XL = 17

R = 28 17

= 11

Therefore the number of classes K = 1 + 3.3log10n. Where n = 33 (number of observation)

K = 1 + 3.3log33

K = 6.01109600159…

K = 6

The class width C = range/ K

= 11/6

= 1.83333

= 2

Table of values:

Class interval

Mid-point (x)

L1+L2/ 2

Frequency (F)

Cumulative frequency (Cf)

Relative frequency (R.F) = fi/∑fi

Relative Cumulative frequency (RCF )

17 – 18

17.5

5

5

0.15

0.15

19 – 20

19.5

6

11

0.18

0.33

21 – 22

21.5

8

19

0.24

0.57

23 – 24

23.5

7

26

0.21

0.78

25 – 26

25.5

4

30

0.12

0.90

27 – 28

27.5

3

33

0.09

0.99

∑f = 33

∑Rf= 0.99 = 1

Note: the variable are arranged in the other listed in the sub headings/ table of value

Write a brief note on the following;

Sample.

Population.

Continuous variable.

Discrete variable.

Statistics.

Data.

Solution

Sample: Sample is a subset of units containing only a finite number of unit from population. In other words sample is a smaller representative of a population.

The finite number of units is called the sample size often denoted by n.

Population: This is the totality of all units with identical characteristics of interest. Population used in statistics refers to any well defined class of people, animals plants, objects , etc. A complete enumeration of the entire units in a population during a survey is called census.

Continuous variable: This is a specific kind of quantitative variable used in statistic to describe data measurable in a way that may assume an infinite values between any two value of reference. For instance using 3 and 4 as reference, there is and infinite number of decimals between them such as 3, 3.1, 3.2, 3.3, 3.4, 3.5, 3.51, 3.52, 3.53, …

Discrete variable: A discrete variable is a type of statistical variable that can assume only fixed number of distinct values and lacks an inherent order. It is also known as categorical variable because it exist in between the categories that can either be finite or countable infinite. These are variable that exist only as whole numbers and able to count the sets of items.

Statistics: Statistic is the scientific method for collecting, organizing, summarizing, presenting and analyzing data as well as drawing valid conclusions and making reasonable decision on the basis of such analysis.

In other words statistics is the body of decisions in the face of uncertainty or incomplete information. Statistics is used to denote data and members defined from the data such as averages.

In another context, the term statistics denotes a discipline: the art and science of making inference from the particular to the general.

It is an art because it designs an effective research project and to decide an appropriate assumption upon which a proposed analysis rests.

It is a science because it draws sound conclusion from results obtained within the framework of proper assumptions through observation, establishment of hypothesis and empiricism.

Data: this comprises of numeric measurements taken from observed phenomena. Such measurement which have not been organized, arranged or treated in any manner is term raw data. Data can be obtain from both primary(obtain from first hand) and secondary source.

Name: Ajah Helminna Sama

Dept: Economics

Reg: 2021/243688

Question one:

1, class interval using surge’s rule

K=1+3.3logN

Where k=class interval

N=number of observations:33

K=1+3.3log33= 1+3.3(1.5185)

=6.01= 6 intervals

CLASS INTERVAL:

17-18

19-20

21-22

23-24

25-26

27-28

MIDPOINT

17+18/2=17.5

19+20/2=19.5

21+22/2=21.5

23+24/2=23.5

25+26/2=25.5

27+28/2=27.5

FREQUENCY

5

6

8

7

4

3

TOTAL= 33//

CUMULATIVE FREQUENCY

to find cumulative frequency

Formula= CF = F + CF

5

11

19

26

30

33

RELATIVE FREQUENCY

RF= FREQUENCY/TOTAL FREQUENCY×100/1

RF= 5/33 ×100=15.15

= 6/33 × 100=18.18

= 8/33×100 =24.24

=7/33 ×100=21.21

= 4/33×100= 12.12

= 3/33×100=9.09

RELATIVELY CUMULATIVE FREQUENCY

RCF= CUMULATIVE FREQUENCY/TOTAL FREQUENCY ×100/1

= 5/33×100= 15.15

=11/33× 100=33.33

=19/33×100=57.57

=26/33×100=78.78

=30/33×100=90.90

=33/33×100=100

Question 2

1) Sample means a subgroup of the members of population chosen for participation in the study. It Include Only a handful of units of population, we can also say it is a subset of the population.

2)Population refers to the collection of all elements possessing common characteristics, that comprises universe. It includes all the units in that group.

3) continues variable alludes to the a variable which assumes infinite number of different values.

4)Discrete variable refers to the variable that assumes a finite number of isolated values

5) statistics is a scientific method of collecting, organising, summarizing, analysing and presentation of data as well as drawing inference

Or making valid conclusion on the basis of such analysis

6) Data could be seen as a collection of facts, such as numbers, words, measurements, observations or even just discription of things. The are information in raw and unorganized

NAME : MUOEMENAM CHIBUGO FAVOUR

DEPARTMENT : ECONOMICS

REG NO: 2021/243694

1) 17,717, 18, 18, 19, 19, 19, 20, 20, 20, 22, 22, 22, 22, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 25, 25, 25, 25, 27, 28,28

Class mid frequency cumulative relative RCF

interval point frequency frequency

17-18 17.5 5 5 15.24.9

19-20 19.5 6 11 18.2 10.8

22-23 22.5 12 23 36.2 22.5

24-25 24.5 7 30 21.2 29.4

27-28 27.5 3 33 9.09 32.4

33 102

Determine the number of intervals by applying the stunges rule where :

K=1+3.3logN

N=33

K=1+3.3log(33)

K=6.01 ~6

With Stunges rule we have 6 intervals

2) SAMPLE

A sample is a specific group that you will collect data from. The size of the sample is always less than the total size of the population.

In research, a population doesn’t always refer to people. It can mean a group containing elements of anything you want to study, such as objects, events, organizations, countries, species, organisms, etc.

POPULATION

It includes all the elements from the data set and measurable characteristics of the population such as mean and standard deviation are known as a parameter. For example, All people living in India indicate the population of India.

There are different types of populations. They are:

FINITE POPULATION

The finite population is also known as a countable population in which the population can be counted. In other words, it is defined as the population of all the individuals or objects that are finite. For statistical analysis, the finite population is more advantageous than the infinite population. Examples of finite populations are employees of a company and potential consumers in a market.

INFINITE POPULATION

The infinite population is also known as an uncountable population in which the counting of units in the population is not possible. An example of an infinite population is the number of germs in the patient’s body is uncountable.

EXISTING POPULATION

The existing population is defined as the population of concrete individuals. In other words, the population whose unit is available in solid form is known as the existent population. Examples are books, students, etc.

HYPOTHETICAL POPULATION

The population in which whose unit is not available in solid form is known as the hypothetical population. A population consists of sets of observations, objects, etc that all have something in common. In some situations, the populations are only hypothetical. Examples are the outcome of rolling the dice, and the outcome of tossing a coin.

CONTINUOS VARIABLE

A continuous variable is defined as a variable that can take an uncountable set of values or an infinite set of values. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range. Thus, the range of real numbers between x and y with x, y ∈ R and x ≠ y; is said to be uncountable and infinite.

DISCRETE VARIABLE

A discrete variable is a variable that takes on distinct, countable values. In theory, you should always be able to count the values of a discrete variable.

Examples of discrete variables include:

•Years of schooling

•Number of goals made in a soccer match

•Number of red M&M’s in a candy jar

•Votes for a particular politician

•Number of times a coin lands on heads after ten coin tosses

All of these variables take a finite number of values that you can count. They are examples of discrete variables.

STATISTICS

Statistics is a branch that deals with every aspect of the data. Statistical knowledge helps to choose the proper method of collecting the data and employ those samples in the correct analysis process to effectively produce the results. In short, statistics is a crucial process that helps to make decisions based on the data.

DATA

Data is numerical statements of facts in a specific field of inquiry or simply numbers that may result from taking measures recording height weight and temperature measurements.

1) 17,717, 18, 18, 19, 19, 19, 20, 20, 20, 22, 22, 22, 22, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 25, 25, 25, 25, 27, 28,28

Class mid frequency cumulative relative RCF

interval point frequency frequency

17-18 17.5 5 5 15.2 4.9

19-20 19.5 6 11 18.2 10.8

22-23 22.5 12 23 36.2 22.5

24-25 24.5 7 30 21.2 29.4

27-28 27.5 3 33 9.09 32.4

33 102

Determine the number of intervals by applying the stunges rule where :

K=1+3.3logN

N=33

K=1+3.3log(33)

K=6.01 ~6

With Stunges rule we have 6 intervals

2) SAMPLE

A sample is a specific group that you will collect data from. The size of the sample is always less than the total size of the population.

In research, a population doesn’t always refer to people. It can mean a group containing elements of anything you want to study, such as objects, events, organizations, countries, species, organisms, etc.

POPULATION

It includes all the elements from the data set and measurable characteristics of the population such as mean and standard deviation are known as a parameter. For example, All people living in India indicate the population of India.

There are different types of populations. They are:

FINITE POPULATION

The finite population is also known as a countable population in which the population can be counted. In other words, it is defined as the population of all the individuals or objects that are finite. For statistical analysis, the finite population is more advantageous than the infinite population. Examples of finite populations are employees of a company and potential consumers in a market.

INFINITE POPULATION

The infinite population is also known as an uncountable population in which the counting of units in the population is not possible. An example of an infinite population is the number of germs in the patient’s body is uncountable.

EXISTING POPULATION

The existing population is defined as the population of concrete individuals. In other words, the population whose unit is available in solid form is known as the existent population. Examples are books, students, etc.

HYPOTHETICAL POPULATION

The population in which whose unit is not available in solid form is known as the hypothetical population. A population consists of sets of observations, objects, etc that all have something in common. In some situations, the populations are only hypothetical. Examples are the outcome of rolling the dice, and the outcome of tossing a coin.

CONTINUOS VARIABLE

A continuous variable is defined as a variable that can take an uncountable set of values or an infinite set of values. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range. Thus, the range of real numbers between x and y with x, y ∈ R and x ≠ y; is said to be uncountable and infinite.

DISCRETE VARIABLE

A discrete variable is a variable that takes on distinct, countable values. In theory, you should always be able to count the values of a discrete variable.

Examples of discrete variables include:

•Years of schooling

•Number of goals made in a soccer match

•Number of red M&M’s in a candy jar

•Votes for a particular politician

•Number of times a coin lands on heads after ten coin tosses

All of these variables take a finite number of values that you can count. They are examples of discrete variables.

STATISTICS

Statistics is a branch that deals with every aspect of the data. Statistical knowledge helps to choose the proper method of collecting the data and employ those samples in the correct analysis process to effectively produce the results. In short, statistics is a crucial process that helps to make decisions based on the data.

DATA

Data is numerical statements of facts in a specific field of inquiry or simply numbers that may result from taking measures recording height weight and temperature measurements.

Name: Tse Mnedoo Rita

Reg No: 2021/241334

Dept.: Economics

Question 1

1. The class interval using sturge rule:

Sturge rule formula= k= 1 + 3.322 logN

Where N= Total number of observations.

K= 1 + 3.322 log33

K= 1 + 3.322(1.5185)

K= 1 + 5.0445

K= 6.0445

K= 6~

Class interval= Range/1 + 3.322 logN

Range=Highest value – Lowest value

Range= 28 – 17 = 11

Class interval= 11/ 1+3.322log33

= 11/6

=1.83

= 2~

Class Interval Mid-point F. C.F. R.F. R.C.F

17 – 18 17.5 5 5 15.15 15.15

19 – 20 19.5 6 11 18.18 33.33

21 – 22 21.5 8 19 24.24 57.57

23 – 24 23.5 7 26 21.21 78.78

25 – 26 25.5 4 30 12.12 90.90

27 – 28 27.5 3 33 9.09 100

Total=

33

Question 2

1. Sample:

A sample is a subset of fraction of the population selected as a representative of the population for study. It is also defined as a part of fraction of the population selected from the population in order to study it and use the result obtained from it to make generalization about the population from where it is drawn.

2. Population:

Population is a set of existing units (usually people objects or events). Population can also be defined as the totality of all the observations of a particular variable having similar characteristics that a researcher or investigator has chosen for study at a particular point or period of time.

3. Continuous Variable:

A continuous variable is one for which, within the limits the variable ranges, any value is possible. Continuous variable can take any value between a certain set of real numbers. The value given to an observation for a continuous variable can include values as small as the instrument of measurement allows.

4. Discrete Variable:

Discrete variables or data are also known as categorical variables.They are variables or data that exist only as whole numbers and are not divisible. A discrete variable can take an finite number of numerical values, categories or codes.

5. Statistics:

The word ‘Statistic’ refers to numerical facts such as the number of events occurring in time or the number of people living in a particular area. It also involves the study of ways of collecting analysing and interpreting numerical facts or numerical data. Statistic is broadly divided into two main branches which are; descriptive and inferential statistic. Descriptive statistics studies a body of numerical information (data) without using the results obtained to make inference or generalization about the population from where they are drawn. It involves the use of charts; diagrams etc to study a set of data. While inferential statistics study a body statistical data with the intent of using the result obtained to make generalization or inference about the population where they are gotten. It is the science of using sample results to make generalization about the population data.

6. Data:

Data are raw facts, sets of numbers, figures or symbols obtained from enumerations or measurements. Data are unprocessed information often in the form of facts of figure obtained from surveys or experiments, used as a basis to making calculation or drawing conclusions. They could be in form of numbers, texts, images, symbols, and sounds, in form that is suitable for processing and storage.

Question 1)

CLASS INTERVAL MID POINT F CF RF RCF

17 – 18 17.5 5 5 15.15 4.03

19 – 20 19.5 6 11 18.18 8.87

21 – 22 21.5 8 19 24.24 15.32

23 – 24 23.5 7 26 21.21 20.97

25 – 26 25.5 4 30 12.12 24.19

27 – 28 27.5 3 33 9.09 26.61

= 33 =124 = 99.93 =99.99

Question 2)

SAMPLE refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observation.

POPULATION is a set of existing units (usually people objects or events). Population can also be defined as the totality of all the observations of a particular variable having similar characteristics that a researcher or investigator has chosen for study at a particular point or period of time.

A CONTINUOUS VARIABLE is defined as a variable which can take an uncountable set of values or infinite set of values. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range.

A DISCRETE VARIABLE is also known as categorical variables. This is in the case of a variable that can only be counted and represents in a whole number. They exist only as whole numbers and are not divisible. A discrete variable can take on a finite number of numerical values or codes.

STATISTICS can be referred to as numerical facts such as numbers of events occurring at a particular time etc and it can be further defined as the study which involves the collecting, analyzing of numerical data or facts.

DATA can be defined as a systematic record of a particular quantity. It is the different values of that quantity represented together in a set. It is a collection of facts and figures to be used for a specific purpose such as a survey or analysis. When arranged in an organized form, can be called information.

NAME: UMEH CHINAZA LUCY

REG NO: 2018/246901

DEPARTMENT:EDU/ECONOMICS

EMAIL: umehchinazalucy@gmail.com

COURSE CODE: ECO 131

SOLUTION

(1) To determine the class interval using Sturges rule, we first need to find the number of classes (k) using the formula:

k = 1 + log2(n)

where n is the number of observations. In this case, n = 33, so:

k = 1 + log2(33) ≈ 6.6

We can’t have a fractional number of classes, so we round up to 7. Therefore, the class interval will be:

Class interval = range/number of classes ≈ (28-17)/7 ≈ 1.6

To make it easier to work with, we can round this to 2. So our class intervals will be:

17-19, 19-21, 21-23, 23-25, 25-27, 27-29

Now we can construct the frequency table:

Class Interval Mid-point Frequency Cumulative Frequency Relative Frequency Relative Cumulative Frequency

17-19 18 3 3 0.091 0.091

19-21 20 6 9 0.182 0.273

21-23 22 12 21 0.364 0.636

23-25 24 8 29 0.242 0.879

25-27 26 2 31 0.061 0.939

27-29 28 2 33 0.061 1.000

To calculate the mid-point, we simply take the average of the lower and upper limits of each class interval. For example, for the first interval, the mid-point is (17+19)/2 = 18.

The frequency is the number of observations that fall within each class interval. For example, there are 3 observations between 17 and 19.

The cumulative frequency is the sum of the frequencies up to that point. For example, the cumulative frequency for the second interval (19-21) is 3+6=9.

The relative frequency is the frequency divided by the total number of observations (33 in this case). For example, the relative frequency for the first interval is 3/33 = 0.091.

The relative cumulative frequency is the cumulative frequency divided by the total number of observations. For example, the relative cumulative frequency for the second interval is 9/33 = 0.273.

(2)BRIEF NOTE ON THE FOLLOWING

Sample

Population

Continuous Variable

Discrete variable

Statistics

Data

•Sample: A sample is a subset of a population that is selected for analysis in order to draw conclusions about the entire population. It is often impractical or impossible to study the entire population, so researchers use samples to infer information about the larger group.

•Population: A population refers to the entire group of individuals or objects that share a particular characteristic of interest. In statistics, researchers use population data to make inferences about the characteristics of a larger group.

•Continuous Variable: A continuous variable is a type of numerical variable that can take on an infinite number of values within a given range. Examples of continuous variables include height, weight, and time.

•Discrete Variable: A discrete variable is a type of numerical variable that can only take on specific values, usually whole numbers. Examples of discrete variables include the number of children in a family, the number of cars in a parking lot, and the number of pets in a household.

•Statistics: Statistics is the practice of collecting, analyzing, and interpreting data. It involves using mathematical methods to describe and summarize data, make inferences about populations, and test hypotheses.

•Data: Data refers to the information that is collected and analyzed in order to draw conclusions or make decisions. Data can be numerical, such as the results of a survey or the measurements of a physical property, or it can be non-numerical, such as text or images.

Name; Chimezie Temple Chimereze

Reg No:10844834HE

Question1

Class interval Midpoint F CF RF RCF

17_18 17.5 5 5 15.5 15.15

19_20 19.5 6 11 18.18 3.3

21_22 21.5 8 19 24.24 57.57

23_24 23.5 7 26 21.21 78.78

25_26 25.5 4 30 12.12 90.90

27_28 27.5 3. 33 9.09 100

Total 33

Question 2:

1: Samples are used to make inferences about populations. Samples are easier to collect data from because they are practical, cost-effective, convenient, and manageable.

2: Populations are used when a research question requires data from every member of the population. This is usually only feasible when the population is small and easily accessible.

3: A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range.

4: A discrete variable is a variable whose value is obtained by counting. Examples: number of students present. number of red marbles in a jar. number of heads …

5:statistics, the science of collecting, analyzing, presenting, and interpreting data.

6:In computing, data is information that has been translated into a form that is efficient for movement or processing. Relative to today’s computers and transmission media, data is information converted into binary digital form. It is acceptable for data to be used as a singular subject or a plural subject.

NAME:. Nwachukwu Emmanuel Ginikachi

REG no : 19754367BJ

DEPT. : Economics

QUESTION ONE

n= 33

Using sturge rule for the class interval

K=1+3, 3.22 Log N

K=1+3, 3.22 Log 33= 6.04

K= 6 Class intervals

Class interval Midpoint. F. CF RF. RCF

17- 22. 19.5. 18. 18 0.6. 40

23- 28 25. 5. 12. 30. 0.4 60

30. 48

QUESTION TWO

A). SAMPLE

A sample refers to a smaller, manageable version of a larger group

It is a subset containing the characteristics of a larger population. Testing when population sizes are too large for the test to include all possible members or observations..

B). POPULATION

A population is a set of similar items or event’s, which is of interest for some questions or experiment. It can be seen as a group of existing objects or a hypothetical and potentially infinite group of objects conceived as a generalization from experience.

C). CONTINUOUS VARIABLE

A quantitative variable may be Continuous or discrete. If they are typically obtained by measuring or counting respectively. If it can take on two particular real values, such that it can also take on all real values between them, the variable is Continuous in that interval.

D). DISCRETE VARIABLE

A discrete variable is a variable that takes on distinct countable values.

E). STATISTICS

Statistics is the collection, organization, analysis, interpretation and presentation of data.

F). DATA

Data are facts and statistics collection together for reference or analysis. Data is above processed information or raw information

Utility can be defined as the total quantity of satisfaction derived from consumption of goods and services. Production is not complete untill it gets to the final consumer utility is measured in utiles, we have five types of utility

Place utility:is a type of satisfaction derived from comsumption of good and services at a particular place eg using fan during rainy season.

Form utility: lts a utility derived from consumption of goods and services derived from consumption of goods by converting it to a particular form eg converting floor to bread.

Time utility: lt is a satisfaction derived from consumption at a particular time.

Possession utility: lt is a satisfaction derived from consumption of good or service you own eg satisfaction from the car you bought for yourself.

2

Cardinal school of thought. Ordinal school of thought

1 Cardinal school of thought: Cardinal school of thought assumes that utility can be measured using a number ranging from one to infinity,it also assume that consumer can be rational it assumes that income can be held constant.

Ordinal school of thought ordinal school of thought assume that utility can can be ranked in ordinal school of thought two commodity are being considered xandy it requires a consumer to draw a scale of preference the criticism is that commodity are not divisible

2 .Labour productivity

If labour productivity increases, firms will demand more labour at each wage rate and the firm’s demand for labour itself will increase. This would shift the labour demand curve outwards.

Changes in technology

Changes in technology can cause the demand for labour to increase and decrease depending on the situation.

If technological changes make labour more productive relative to the other factors of production (such as capital), firms would demand an increased amount of workers and substitute the other factors of production with new labour.

For example, the production of computer chips will require a certain amount of skilled software and hardware engineers. Thus, the demand for such workers would increase. This would shift the labour demand curve outwards.

However, with the production and subsequent competition from other firms, we could assume that chip development could become automated. The subsequent result would be a replacement of labour with machines. This would shift the labour demand curve inwards.

Changes in the number of firms

Changes in the number of firms operating in the industry can have an immense effect on the overall labour market. This is because demand for a certain factor can be determined by the number of firms currently utilising that factor.

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Eco. 131 Online Quiz/Discussion (Sampling and other issues)—1-3-2023

Tony Orji by Tony Orji March 1, 2023Reading Time: 1 min read

A A

Eco. 131 Online Quiz/Discussion (Sampling and other issues)—1-3-2023

QUESTION ONE

The following yields (kg) were obtained from plots in a soyabean field given two sprays of pesticides.

22, 20, 19, 25, 22, 17, 28, 20, 22, 23, 17

18, 24, 25, 22, 20, 23, 25, 22, 28, 19, 22

25, 27, 23, 24, 17, 18, 22, 19, 22, 23, 24

Compute the table as follows:

The class interval using sturge rule

Mid-point

Frequency

Cumulative Frequency

Relative Frequency

Relative Cumulative Frequency

QUESTION TWO

Write a brief note on the following:

Sample

Population

Continuous Variable

Discrete variable

Statistics

Data

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Comments 0

Ugwuanyi Dumebi Dominic Your comment is awaiting moderation

3 days ago

NAME:

UGWUANYI DUMEBI DOMINIC

REG NO:

2021/241948

DEPARTMENT:

ECONOMICS

DATE:

10/03/2023

1

CLASS INTERVAL USING STURGES RULE= K=1-+3.3LOG (N) =N=EF WHICH IS = 33 ; CLASS

INTER VAL=1+3.3LOG(33) =1+5.01=6.01=6

RELATIVE FREQUENCY=F/N MUITIPLED BY 100/1

RELATIVE CUMULATIVE FREQUENCY=CF/ECF MUITIPLED BY100/1

AGE

M.P

FREQ

CF

RF

RCF

17-18

17.5=17+18/2 5

1

ST FREQ=5 15.15=

4.03

19-20

19.5=19+20/2 6

6+5=11

18.18

8.87

21-22

21.5=21+22/2 8

11+8=19

24.24

15.32

23-24

23.5=23+24/2 7

19+7=26

21.21

20.97

25-26

25.5=25+26/2 4

26+4=30

90.91

24.19

27-28

27.5=27+28/2 3

33

100

26.61

EF=33

ECF=124

2

SAMPLE: IT IS USUALLY DIFFCULT TO EXAMINE AII MEMBERS OF A POPULATION DUE TO TIME

,COSTAND OTHER CONSTRAINTS .SO WE EXAMINE ONLY A PORTION OF THE POPULATION AND

TRY TO DRAW CONCLUSIONS ABOUT THE WHOLE USING SAMPLE ESTIMATES .THE PROCESS OF

GENERALISING THE RESULTS IN OUR SAMPLE TO THAT OF THE ENTIRE POPULATION IS KNOWN

AS STATISTICAL INFERENCE.

POPULATION: THIS IS THE ENTIRE GROUP OF INDIVIDUALS WE ARE INTERESTED IN MAKING A

STATEMENT ABOUT;IT CAN BE DEFINED AS THE ENTIRE GROUP ABOUT WHICH INFORMATION IS

DESIRED.

A CONTINUOUS VARIABLE: IS ONE FOR WHICH ,WITHIN THE LIMTS THE VARIABLE RANGES,ANY

VALUE IS POSSIBLE,IT CAN TAKE ANY VALUE BETWEEN A CERTAIN SET OF REAL NUMBERS,THE

VALUE GIVEN TO AN OBSERATION FOR CONTINUOUS VARIABLE CAN VALUES AS SMALL AS THE

INTRUMENT OF MEASUREMENT ALLOWS.

DISCRETE VARIABLES: DISCRETE VARIABLES OR DATA ARE KNOWN AS CATEGORICAL

VARIABLES.THEY ARE VARIABLES OR DATA THAT EXIST ONLY AS WHOLE NUMBERS AND NOT

DIVISIBLE. A DISCRETE VARIABLE CAN ON A FINITE NUMBER OF NUMERICAL

VALUES,CATEGORIES OR CODES.

STATISTICS: IT CAN BE DEFINED AS A FIELD OF STUDY CONCERNING THE LAYOUT OF

EXPERIMENT,COLLECTION,CALCULATIONS,SUMMARIZATION AND ANALYSIS OF DATA.IT AISO

INVOLUES INTERPRETATION OF RESULTS OR DRAWING OF INFERENCE.

DATA: IS A NUMERICALSTATEMENT OF FACTS IN A SPECIFIC SPEED OF ENQUIRY OR SIMPLY

NUMBERS WHICH MAY RESULT FROM TAKING

MEASUREMENTS;EG=RECORDING,HEIGHTS,WEIGHT OR TEMPERATURE MEASUREMENTS.SSS

Reply

Ugwuanyi Dumebi Dominic Your comment is awaiting moderation

3 days ago

NAME:

UGWUANYI DUMEBI DOMINIC

REG NO:

2021/241948

DEPARTMENT:

ECONOMICS

DATE:

10/03/2023

1

CLASS INTERVAL USING STURGES RULE= K=1-+3.3LOG (N) =N=EF WHICH IS = 33 ; CLASS

INTER VAL=1+3.3LOG(33) =1+5.01=6.01=6

RELATIVE FREQUENCY=F/N MUITIPLED BY 100/1

RELATIVE CUMULATIVE FREQUENCY=CF/ECF MUITIPLED BY100/1

AGE

M.P

FREQ

CF

RF

RCF

17-18

17.5=17+18/2 5

1

ST FREQ=5 15.15=

4.03

19-20

19.5=19+20/2 6

6+5=11

18.18

8.87

21-22

21.5=21+22/2 8

11+8=19

24.24

15.32

23-24

23.5=23+24/2 7

19+7=26

21.21

20.97

25-26

25.5=25+26/2 4

26+4=30

90.91

24.19

27-28

27.5=27+28/2 3

33

100

26.61

EF=33

ECF=124

2

SAMPLES IT IS USUALLY DIFFCULT TO EXAMINE AII MEMBERS OF A POPULATION DUE TO TIME

,COSTAND OTHER CONSTRAINTS .SO WE EXAMINE ONLY A PORTION OF THE POPULATION AND

TRY TO DRAW CONCLUSIONS ABOUT THE WHOLE USING SAMPLE ESTIMATES .THE PROCESS OF

GENERALISING THE RESULTS IN OUR SAMPLE TO THAT OF THE ENTIRE POPULATION IS KNOWN

AS STATISTICAL INFERENCE.

POPULATION: THIS IS THE ENTIRE GROUP OF INDIVIDUALS WE ARE INTERESTED IN MAKING A

STATEMENT ABOUT;IT CAN BE DEFINED AS THE ENTIRE GROUP ABOUT WHICH INFORMATION IS

DESIRED.

A CONTINUOUS VARIABLE: IS ONE FOR WHICH ,WITHIN THE LIMTS THE VARIABLE RANGES,ANY

VALUE IS POSSIBLE,IT CAN TAKE ANY VALUE BETWEEN A CERTAIN SET OF REAL NUMBERS,THE

VALUE GIVEN TO AN OBSERATION FOR CONTINUOUS VARIABLE CAN VALUES AS SMALL AS THE

INTRUMENT OF MEASUREMENT ALLOWS.

DISCRETE VARIABLES: DISCRETE VARIABLES OR DATA ARE KNOWN AS CATEGORICAL

VARIABLES.THEY ARE VARIABLES OR DATA THAT EXIST ONLY AS WHOLE NUMBERS AND NOT

DIVISIBLE. A DISCRETE VARIABLE CAN ON A FINITE NUMBER OF NUMERICAL

VALUES,CATEGORIES OR CODES.

STATISTICS: IT CAN BE DEFINED AS A FIELD OF STUDY CONCERNING THE LAYOUT OF

EXPERIMENT,COLLECTION,CALCULATIONS,SUMMARIZATION AND ANALYSIS OF DATA.IT AISO

INVOLUES INTERPRETATION OF RESULTS OR DRAWING OF INFERENCE.

DATA: IS A NUMERICALSTATEMENT OF FACTS IN A SPECIFIC SPEED OF ENQUIRY OR SIMPLY

NUMBERS WHICH MAY RESULT FROM TAKING

MEASUREMENTS;EG=RECORDING,HEIGHTS,WEIGHT OR TEMPERATURE MEASUREMENTS.SSS

Reply

Ugwuanyi Dumebi Dominic Your comment is awaiting moderation

3 days ago

NAME:

UGWUANYI DUMEBI DOMINIC

REG NO:

2021/241948

DEPARTMENT:

ECONOMICS

DATE:

10/03/2023

1

CLASS INTERVAL USING STURGES RULE= K=1-+3.3LOG (N) =N=EF WHICH IS = 33 ; CLASS

INTER VAL=1+3.3LOG(33) =1+5.01=6.01=6

RELATIVE FREQUENCY=F/N MUITIPLED BY 100/1

RELATIVE CUMULATIVE FREQUENCY=CF/ECF MUITIPLED BY100/1

kg

M.P

FREQ

CF

RF

RCF

17-18

17.5=17+18/2 5

1

ST FREQ=5 15.15=

4.03

19-20

19.5=19+20/2 6

6+5=11

18.18

8.87

21-22

21.5=21+22/2 8

11+8=19

24.24

15.32

23-24

23.5=23+24/2 7

19+7=26

21.21

20.97

25-26

25.5=25+26/2 4

26+4=30

90.91

24.19

27-28

27.5=27+28/2 3

33

100

26.61

EF=33

ECF=124

2 this is basically on some terms

SAMPLES IT IS USUALLY DIFFCULT TO EXAMINE AII MEMBERS OF A POPULATION DUE TO TIME

,COSTAND OTHER CONSTRAINTS .SO WE EXAMINE ONLY A PORTION OF THE POPULATION AND

TRY TO DRAW CONCLUSIONS ABOUT THE WHOLE USING SAMPLE ESTIMATES .THE PROCESS OF

GENERALISING THE RESULTS IN OUR SAMPLE TO THAT OF THE ENTIRE POPULATION IS KNOWN

AS STATISTICAL INFERENCE.

POPULATION: THIS IS THE ENTIRE GROUP OF INDIVIDUALS WE ARE INTERESTED IN MAKING A

STATEMENT ABOUT;IT CAN BE DEFINED AS THE ENTIRE GROUP ABOUT WHICH INFORMATION IS

DESIRED.

A CONTINUOUS VARIABLE: IS ONE FOR WHICH ,WITHIN THE LIMTS THE VARIABLE RANGES,ANY

VALUE IS POSSIBLE,IT CAN TAKE ANY VALUE BETWEEN A CERTAIN SET OF REAL NUMBERS,THE

VALUE GIVEN TO AN OBSERATION FOR CONTINUOUS VARIABLE CAN VALUES AS SMALL AS THE

INTRUMENT OF MEASUREMENT ALLOWS.

DISCRETE VARIABLES: DISCRETE VARIABLES OR DATA ARE KNOWN AS CATEGORICAL

VARIABLES.THEY ARE VARIABLES OR DATA THAT EXIST ONLY AS WHOLE NUMBERS AND NOT

DIVISIBLE. A DISCRETE VARIABLE CAN ON A FINITE NUMBER OF NUMERICAL

VALUES,CATEGORIES OR CODES.

STATISTICS: IT CAN BE DEFINED AS A FIELD OF STUDY CONCERNING THE LAYOUT OF

EXPERIMENT,COLLECTION,CALCULATIONS,SUMMARIZATION AND ANALYSIS OF DATA.IT AISO

INVOLUES INTERPRETATION OF RESULTS OR DRAWING OF INFERENCE.

DATA: IS A NUMERICALSTATEMENT OF FACTS IN A SPECIFIC SPEED OF ENQUIRY OR SIMPLY

NUMBERS WHICH MAY RESULT FROM TAKING

MEASUREMENTS;EG=RECORDING,HEIGHTS,WEIGHT OR TEMPERATURE MEASUREMENTS.SSS

Reply

Ugwuanyi Dumebi Dominic Your comment is awaiting moderation

3 days ago

NAME:

UGWUANYI DUMEBI DOMINIC

REG NO:

2021/241948

DEPARTMENT:

ECONOMICS

DATE:

10/03/2023

1the class interval using the

CLASS INTERVAL USING STURGES RULE= K=1-+3.3LOG (N) =N=EF WHICH IS = 33 ; CLASS

INTER VAL=1+3.3LOG(33) =1+5.01=6.01=6

RELATIVE FREQUENCY=F/N MUITIPLED BY 100/1

RELATIVE CUMULATIVE FREQUENCY=CF/ECF MUITIPLED BY100/1

kg

M.P

FREQ

CF

RF

RCF

17-18

17.5=17+18/2 5

1

ST FREQ=5 15.15=

4.03

19-20

19.5=19+20/2 6

6+5=11

18.18

8.87

21-22

21.5=21+22/2 8

11+8=19

24.24

15.32

23-24

23.5=23+24/2 7

19+7=26

21.21

20.97

25-26

25.5=25+26/2 4

26+4=30

90.91

24.19

27-28

27.5=27+28/2 3

33

100

26.61

EF=33

ECF=124

2 this is basically on some terms

SAMPLES IT IS USUALLY DIFFCULT TO EXAMINE AII MEMBERS OF A POPULATION DUE TO TIME

,COSTAND OTHER CONSTRAINTS .SO WE EXAMINE ONLY A PORTION OF THE POPULATION AND

TRY TO DRAW CONCLUSIONS ABOUT THE WHOLE USING SAMPLE ESTIMATES .THE PROCESS OF

GENERALISING THE RESULTS IN OUR SAMPLE TO THAT OF THE ENTIRE POPULATION IS KNOWN

AS STATISTICAL INFERENCE.

POPULATION: THIS IS THE ENTIRE GROUP OF INDIVIDUALS WE ARE INTERESTED IN MAKING A

STATEMENT ABOUT;IT CAN BE DEFINED AS THE ENTIRE GROUP ABOUT WHICH INFORMATION IS

DESIRED.

A CONTINUOUS VARIABLE: IS ONE FOR WHICH ,WITHIN THE LIMTS THE VARIABLE RANGES,ANY

VALUE IS POSSIBLE,IT CAN TAKE ANY VALUE BETWEEN A CERTAIN SET OF REAL NUMBERS,THE

VALUE GIVEN TO AN OBSERATION FOR CONTINUOUS VARIABLE CAN VALUES AS SMALL AS THE

INTRUMENT OF MEASUREMENT ALLOWS.

DISCRETE VARIABLES: DISCRETE VARIABLES OR DATA ARE KNOWN AS CATEGORICAL

VARIABLES.THEY ARE VARIABLES OR DATA THAT EXIST ONLY AS WHOLE NUMBERS AND NOT

DIVISIBLE. A DISCRETE VARIABLE CAN ON A FINITE NUMBER OF NUMERICAL

VALUES,CATEGORIES OR CODES.

STATISTICS: IT CAN BE DEFINED AS A FIELD OF STUDY CONCERNING THE LAYOUT OF

EXPERIMENT,COLLECTION,CALCULATIONS,SUMMARIZATION AND ANALYSIS OF DATA.IT AISO

INVOLUES INTERPRETATION OF RESULTS OR DRAWING OF INFERENCE.

DATA: IS A NUMERICALSTATEMENT OF FACTS IN A SPECIFIC SPEED OF ENQUIRY OR SIMPLY

NUMBERS WHICH MAY RESULT FROM TAKING

MEASUREMENTS;EG=RECORDING,HEIGHTS,WEIGHT OR TEMPERATURE MEASUREMENTS.SSS

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Dr Anthony Orji is a Ph.D holder in Economics and a lecturer at the Department of Economics, University of Nigeria Nsukka.

He obtained his B.Sc, Msc and Ph.D Degrees from the University of Nigeria, Nsukka and a Post Graduate Diploma in Sustainable Local Economic Development (SLED) from Erasmus University, Rotterdam Netherlands.

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1. Using sturge rule

K = 1+3.3Log (N)

K= 1+3.3Log 33

K = 6.0

2. Midpoint:- 17.5, 19.5, 21.5, 23.5, 25.5, 27.5

Calculations:- 17- 18 (17+18/2= 17.5) 19-20(19+20/2= 19.5). The rest calculated in that manner.

3. Frequency:-5,6,8,7,4,3 =33

4. Cumulative frequency:- 5,11,19,26,30,33 =124

Calculations:- 5 being a constant, then 5 +6=11, 8+11=19. The rest calculated in that manner.

5. Relative frequency:- 0.15,0.18,0.24,0.21,0.12,0.09

Calculations:- (5/33= 0.15, 6/33=0.18) the rest calculated in that manner

6. Relative cumulative frequency:- 0.15,0.33,0.57,0.78,0.9,0.99

2. Sample:- it is a part or portion of the population on which further analysis is sought.

Population:- This is a group or collection of items of the same nature which are under study e.g group of consumers, number if retired workers in a country.

Continuous variable:- It is a variable which can take an uncountable set of value or infinite set of values. E.g the height of a student. The height of a student can be considered any value.

Discrete variable:- it is a quantitative variable that are typically obtained by measuring or counting respectively. e.g, the score given by a judge to a gymnast in a competition. The range is 0 to 10 and the score is always given to a decimal ( e.g a score of 8.5)

Statistics:- it is a science or study of collecting, analyzing, presenting and interpreting data.

Data:- is an information in it’s original form. They can also be stated as fact and statistics collected together for reference or analysis.

1. K=1+3.3logn

=1+3.3log33

=6.0110

Class interval m.p f cf rf crf

17-18 17.5 5 5 15% 15%

19-20 19.5 6 11 18% 33%

21-22 21.5 8 19 24% 57%

23-24 23.5 7 26 21% 78%

25-26 25.5 4 30 12% 90%

27-28 27.5 3 33 9% 99%

2.a Sample: A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations

B. Population: This is the total number of people (including children, the disabled, beggars and other persons) living within a geographical area or country at a particular time.

C. Continuous variable: A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values.a continuous variable has two types which are the instant variable and ratio variable

D. Discrete variable: A discrete variable is a variable that takes on distinct, countable values. In theory, you should always be able to count the values of a discrete variable.

E. Statistics: Statistics deals with collection, organisation, analysis, interpretation and presentation of data. Statistics plays a vital role in understanding economic data

F. Data: Data is a systematic record of a particular quantity. It is the different values of that quantity represented together in a set

1) CLASS INTERVAL MID POINT F CF RF RCF

17 – 18 17.5 5 5 15.15 4.03

19 – 20 19.5 6 11 18.18 8.87

21 – 22 21.5 8 19 24.24 15.32

23 – 24 23.5 7 26 21.21 20.97

25 – 26 25.5 4 30 12.12 24.19

27 – 28 27.5 3 33 9.09 26.61

= 33 =124 = 99.93 =99.99

2) i, Sample ;

A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations.

ii, Population

population is any complete group with at least one characteristic in common. Populations are not just people. Populations may consist of, but are not limited to, people, animals, businesses, buildings, motor vehicles, farms, objects or events. Thus, any selection of individuals grouped by a common feature can be said to be a population

iii, Continuous variable

A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range. There are two types : Instant variable, Ratio variable.

Instant variable : A variable can be defined as the distance or level between each category that is equal and static. For example, what is the average day time temperature in Bangalore during the summer?

Ratio variable : Ratio variable is another type of continuous variable. This type of variable has only one variation from an interval variable. The only difference is that the ratio between the scores gives information regarding the relationship between the responses.

iv) Discrete Variable :

Discrete variables are countable in a finite amount of time. For example, you can count the change in your pocket. You can count the money in your bank account. You could also count the amount of money in everyone’s bank accounts.

Discrete variables may be further subdivided into:

Dichotomous variables.

Categorical variables (or nominal variables)

Ordinal variables.

v) Statistics :

the practice or science of collecting and analysing numerical data in large quantities, especially for the purpose of inferring proportions in a whole from those in a representative sample.

vi)Data :

. Data are measurements or observations that are collected as a source of information used to analyze something or make decisions. There are a variety of different types of data, and different ways to represent data.

C-I MP F CF RF RCF

17-18 17.5 5 5 15.15 4.03

19-20 19.5 6 11 18.18 4.83

21-22 21.5 8 19 24.24 6.45

23-24 23.5 7 26 21.21 5.64

25-26 25.5 4 30 12.12 3.22

27-28 27.5 3 33 9.09 2.41

33 124

SAMPLE refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observation.

A POPULATION is the complete set group of individuals. Whether that group comprises a nation or a group of people with a common characteristics. In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study.

CONTINUOUS VARIABLE is defined as a variable which can take an uncountable set of values or infinite set of values. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range.

A DISCRETE VARIABLE is a variable that take on distinct countable values. It has values that are counted.

STATISTICS is the study of the collection, analysis, interpretation, presentation, and organization of data. It is a mathematical discipline to collect and summarize data.

I

DATA inform about the values of the variables measured for the statistical units of a population or a subset of a people and cover a broad range of data types defined by different criteria.

Name Odinkonigbo febechukwu Anthony

Reg no 2021/247449

Question1

Class interval Midpoint F CF RF RCF

17_18 17.5 5 5 15.5 15.15

19_20 19.5 6 11 18.18 3.3

21_22 21.5 8 19 24.24 57.57

23_24 23.5 7 26 21.21 78.78

25_26 25.5 4 30 12.12 90.90

27_28 27.5 3. 33 9.09 100

Total 33

Question 2:

1: Samples are used to make inferences about populations. Samples are easier to collect data from because they are practical, cost-effective, convenient, and manageable.

2: Populations are used when a research question requires data from every member of the population. This is usually only feasible when the population is small and easily accessible.

3: A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range.

4: A discrete variable is a variable whose value is obtained by counting. Examples: number of students present. number of red marbles in a jar. number of heads …

5:statistics, the science of collecting, analyzing, presenting, and interpreting data.

6:In computing, data is information that has been translated into a form that is efficient for movement or processing. Relative to today’s computers and transmission media, data is information converted into binary digital form. It is acceptable for data to be used as a singular subject or a plural subject.

Name: Godspower chinecherem Mercy

Reg no:2021/244131

Faculty: social sciences

Department: Economics

Assignment

Number 1 answer

Class interval

Midpoint

Frequency

Cumulative frequency

Relative frequency

Cumulative relative frequency

17-19

18

7

7

21.21%

21.21%

20-22

21

11

18

33.33%

54.54%

23-25

24

12

30

36.36%

90.9%

26-28

27

3

33

9.09%

99.99%

Total

33

99.99%

Number 2 answer

i, Sample: this is defined as a part of population observed.it is also defined as the largest collection of entities for which we have an interest at a particular time.types of sampling are; Random, systematic, convenience, cluster and stratified sampling.

ii, Population: This is the entire group of individuals that we are interested in making a statement about.

iii, Continuous variable: This the type of variable for which writing the limits the variable ranges, any value is possible. This means that it can take any value between s certain set of real numbers.

iv, Descrete variable: These are the variables or data that exist only as whole number and are not divisible. It is also known as categorical variables.

v, Statistics: This can be defined as the study of ways of collecting, analysing and interpreting numerical facts or data.it also shows the deriving, summarizing, presenting and analysing of data .

vi, Data: This can be defined as a collection of facts.It can be seen as information in raw or unorganized state.It can be qualitative or quantitative.

Name: Godspower chinecherem Mercy

Reg no:2021/244131

Faculty: social sciences

Department: Economics

Assignment

Number 1 answer

Class interval

Midpoint

Frequency

Cumulative frequency

Relative frequency

Cumulative relative frequency

17-19

18

7

7

21.21%

21.21%

20-22

21

11

18

33.33%

54.54%

23-25

24

12

30

36.36%

90.9%

26-28

27

3

33

9.09%

99.99%

Total

33

99.99%

Number 2 answer

i, Sample: this is defined as a part of population observed.it is also defined as the largest collection of entities for which we have an interest at a particular time.types of sampling are; Random, systematic, convenience, cluster and stratified sampling.

ii, Population: This is the entire group of individuals that we are interested in making a statement about.

iii, Continuous variable: This the type of variable for which writing the limits the variable ranges, any value is possible. This means that it can take any value between s certain set of real numbers.

iv, Descrete variable: These are the variables or data that exist only as whole number and are not divisible. It is also known as categorical variables.

v, Statistics: This can be defined as the study of ways of collecting, analysing and interpreting numerical facts or data.it also shows the deriving, summarizing, presenting and analysing of data .

vi, Data: This can be defined as a collection of facts.It can be seen as information in raw or unorganized state.It can be qualitative or quantitative.

Reg no:2021/244131

Faculty: social sciences

Department: Economics

Assignment

Number 1 answer

Class interval

Midpoint

Frequency

Cumulative frequency

Relative frequency

Cumulative relative frequency

17-19

18

7

7

21.21%

21.21%

20-22

21

11

18

33.33%

54.54%

23-25

24

12

30

36.36%

90.9%

26-28

27

3

33

9.09%

99.99%

Total

33

99.99%

Number 2 answer

i, Sample: this is defined as a part of population observed.it is also defined as the largest collection of entities for which we have an interest at a particular time.types of sampling are; Random, systematic, convenience, cluster and stratified sampling.

ii, Population: This is the entire group of individuals that we are interested in making a statement about.

iii, Continuous variable: This the type of variable for which writing the limits the variable ranges, any value is possible. This means that it can take any value between s certain set of real numbers.

iv, Descrete variable: These are the variables or data that exist only as whole number and are not divisible. It is also known as categorical variables.

v, Statistics: This can be defined as the study of ways of collecting, analysing and interpreting numerical facts or data.it also shows the deriving, summarizing, presenting and analysing of data .

vi, Data: This can be defined as a collection of facts.It can be seen as information in raw or unorganized state.It can be qualitative or quantitative.

Class interval Midpoint Freq Cum Freq Rel freq Rel cum freq.

17-18 17.5 5 5. 15.5 15.15

19-20 19.5 6. 11. 18.18 3.3

21-22. 21.5 8. 19. 24.24. 57.5

23-24. 23.5 7. 26. 21.21. 78.78

25-26. 25.5 4. 30. 12.12 90.90

27-28 27.5 3. 33. 9.09. 100

Name: Okafor Francisca Ijeoma

Reg No: 2021/247560

Department: Economics

Email Address: ciscafrancisca68@gmail.com

An Assignment Given on Eco 131: Sampling and others

Question1

Class interval Midpoint F CF RF RCF

17_18 17.5 5 5 15.5 15.15

19_20 19.5 6 11 18.18 3.3

21_22 21.5 8 19 24.24 57.57

23_24 23.5 7 26 21.21 78.78

25_26 25.5 4 30 12.12 90.90

27_28 27.5 3. 33 9.09 100

Total 33

Question 2:

1. Sampling

Sampling is a procedure by which one or more members of a population are selected from the population. The objective is to make certain observations about the members of the sample and then, on the basis of these results, to draw valid conclusions about the characteristics of the entire population.

2. Population

Population is defined as the entire group about which information is desired. It is also described as a largest collection of entities for which we have an interest at a particulat time; an entire set of objects, observations, or scores that have something in common. To analyse a population a census is taken.

3. Continuous variable

Continuous variable is one for which, within the limits the variable ranges, any value is possible. Continuous variable can take any value between a certain set of real numbers. The value given to an observation for a continuous variable can include values as small as the instrument of measurement allows.

Continuous variable can be classified into three categories: Interval-scale variables, Continuous ordinal variables, Ratio-scale variables.

4. Discrete variable

Discrete variable or data also known as categorical variables. They are variables or data that exist only as a whole numbers and are not divisible. A discrete variables can take a finite number of numerical values, categories of codes.

5. Statistics

Statictics is concerned with the scientific method of collecting, organising, summarising, presenting and analysing data. Functions of statistics include: Condensation, Comparison, Forecasting, Estimation and Tests of Hypothesis.

6. Data

Data can be seen as a collection of fasts, such as numbers, words, measurements, observation or even just descriptions of things. Data could be qualitative or quantitative. Data can be classified into primary data and secondary data.

C.I. MP. F CF. RF. CRF

17-18. 17.5. 5. 5. 15.2. 4.03

19-20 19.5. 6. 11. 18.2. 8.87

21-22. 21.5. 8. 19. 24.2. 15.32

23-24. 23.5. 7. 26. 21.2. 20.96

25-26. 25.5. 4. 30. 12.1. 24.91

27-28. 27.5. 3. 33. 9.09. 26.61

33. 124

2i. Sampling is the process of selecting a subset of individuals or observations from a larger population in order to estimate the characteristics or parameters of the population. Here are some key points to note about sampling:

Sampling can be done in many ways, including simple random sampling, stratified sampling, cluster sampling, and systematic sampling.

Simple random sampling involves selecting individuals or observations from a population at random, such that each member of the population has an equal chance of being selected.

Stratified sampling involves dividing the population into subgroups (or strata) based on certain characteristics, and then selecting individuals or observations from each stratum at random.

Cluster sampling involves selecting groups (or clusters) of individuals or observations from the population, and then randomly selecting individuals or observations from within each cluster.

Systematic sampling involves selecting individuals or observations from a population at regular intervals, such as every 10th or 20th member of the population.

Sampling is often used in research to collect data and make inferences about a population. However, it is important to ensure that the sample is representative of the population and that appropriate sampling methods are used to minimize bias and increase the accuracy of the estimates.

New chat

nwigwegiftonyinye@gmail.com

Write short notes on sampling

Sampling is the process of selecting a subset of individuals or observations from a larger population in order to estimate the characteristics or parameters of the population. Here are some key points to note about sampling:

Sampling can be done in many ways, including simple random sampling, stratified sampling, cluster sampling, and systematic sampling.

Simple random sampling involves selecting individuals or observations from a population at random, such that each member of the population has an equal chance of being selected.

Stratified sampling involves dividing the population into subgroups (or strata) based on certain characteristics, and then selecting individuals or observations from each stratum at random.

Cluster sampling involves selecting groups (or clusters) of individuals or observations from the population, and then randomly selecting individuals or observations from within each cluster.

Systematic sampling involves selecting individuals or observations from a population at regular intervals, such as every 10th or 20th member of the population.

Sampling is often used in research to collect data and make inferences about a population. However, it is important to ensure that the sample is representative of the population and that appropriate sampling methods are used to minimize bias and increase the accuracy of the estimates.

ii.Population refers to a group of individuals or objects that share one or more common characteristics. Here are some key points to note about population:

Population can refer to a variety of things, including people, animals, plants, or even inanimate objects.

In statistics, population often refers to a large group of people or objects from which a sample is selected for study.

A population can be finite or infinite. A finite population has a fixed number of members, while an infinite population has an unlimited number of members.

The characteristics or parameters of a population can be described using various statistical measures, such as the mean, standard deviation, or proportion.

It is important to ensure that the sample selected for study is representative of the population in order to make accurate inferences about the population. This can be done through appropriate sampling methods.

In some cases, it may be impossible or impractical to study the entire population, and a sample must be used instead. However, care must be taken to ensure that the sample accurately represents the population and that any limitations or biases in the sample are properly accounted for.

iii.A continuous variable is a type of quantitative variable that can take on any value within a specific range. It is a variable that can be measured along a continuous scale and can have an infinite number of possible values.

For example, height, weight, time, temperature, and distance are all examples of continuous variables. In contrast, a categorical variable, such as gender or eye color, is a variable that can only take on a limited number of distinct values.

Continuous variables are often measured using instruments with a high degree of precision, such as a ruler or a thermometer, and are typically represented by decimal numbers. Statistical analyses, such as correlation and regression analysis, are commonly used to analyze the relationships between continuous variables.

It is important to note that continuous variables are not necessarily normally distributed, although they often are. They can also have different distributions, such as skewed or bimodal distributions.

iv.A discrete variable is a type of variable in statistics that can only take on a finite or countably infinite set of possible values. This means that the variable can only assume specific values, and cannot take on any value between those values.

Examples of discrete variables include the number of children in a family, the number of cars in a parking lot, or the number of items sold by a store in a day. In contrast, continuous variables, such as height or weight, can take on any value within a range.

Discrete variables are typically analyzed using descriptive statistics, such as frequency distributions, mean, and standard deviation, as well as inferential statistics, such as hypothesis testing and regression analysis. The probability distributions used to model discrete variables include the binomial distribution, the Poisson distribution, and the hypergeometric distribution.

v.Discrete variable explained.

nwigwegiftonyinye@gmail.com

Write short notes on discrete variable

A discrete variable is a type of variable in statistics that can only take on a finite or countably infinite set of possible values. This means that the variable can only assume specific values, and cannot take on any value between those values.

Examples of discrete variables include the number of children in a family, the number of cars in a parking lot, or the number of items sold by a store in a day. In contrast, continuous variables, such as height or weight, can take on any value within a range.

Discrete variables are typically analyzed using descriptive statistics, such as frequency distributions, mean, and standard deviation, as well as inferential statistics, such as hypothesis testing and regression analysis. The probability distributions used to model discrete variables include the binomial distribution, the Poisson distribution, and the hypergeometric distribution.

V. Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves applying mathematical techniques and models to data in order to draw conclusions and make decisions based on that data.

Statistics is used in a wide range of fields, including business, economics, medicine, psychology, and sociology. It can be used to investigate relationships between variables, make predictions, test hypotheses, and identify patterns and trends in data.

There are two main branches of statistics: descriptive statistics and inferential statistics. Descriptive statistics involves summarizing and describing the features of a dataset, such as the mean, median, mode, and standard deviation. Inferential statistics involves making inferences and predictions about a population based on a sample of data.

Some common statistical methods include hypothesis testing, regression analysis, analysis of variance (ANOVA), and time series analysis. Statistics also involves the use of software and programming languages, such as R, Python, and SPSS, to analyze data and generate reports and visualizations.

Vi.Data refers to a collection of facts, figures, statistics, or any other information that can be analyzed or processed to gain insights and knowledge. In today’s digital world, data is generated at an unprecedented rate from various sources such as sensors, social media, and transactions.

Data can be categorized into two types: structured and unstructured. Structured data refers to information that is organized in a specific format, such as in tables, while unstructured data refers to information that does not have a specific format and is often text-based.

Data can be analyzed using various techniques such as data mining, machine learning, and statistical analysis to extract meaningful insights and patterns. The insights gained from data analysis can be used to make informed decisions, identify opportunities, and solve problems.

Data is also a valuable asset for businesses and organizations. Data-driven decision making is becoming increasingly popular as businesses use data to identify trends, target audiences, and optimize operations. However, the use of data also raises concerns about privacy, security, and ethics.

Overall, data is an important tool for gaining knowledge and making informed decisions, but it is crucial to use it responsibly and ethically.

n=33

Using Sturge rule for the class interval

K=1+3.322 log N

K=1 +3.322 log 33

=6.04

K= 6 class intervals

Class interval Midpoint f CF RF RCF

17-22 19.5. 18. 18. 0.6. 40

23-28 25.5 12. 30. 0.4. 60

30. 48

2. Sample: A sample in statistics is a small data set that you obtain from a larger set of data to represent a whole, for example, the entire population.

i.Population:A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic.

ii.Continuous variable:A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values.

iii.Discrete variable:Discrete variables are countable in a finite amount of time. For example, you can count the change in your pocket. You can count the money in your bank account.

iv.Statistics:Statistics is a branch of applied mathematics that involves the collection, description, analysis, and inference of conclusions from quantitative data.

v.Data:data are individual pieces of factual information recorded and used for the purpose of analysis. It is the raw information from which statistics are created.

Scores. Frequency Class interval Mid point

17. 3

18. 2

19. 3

20. 3

22. 8 17-19. 17.5

23. 4. 20-22. 20.5

24. 3. 23-25. 23.5

25. 4. 26-28. 26.5

27. 1

28. 2

Frequency. Cf. Rf. Rcf

8. 8. 24.2. 8.8

11 19. 33.3. 21.1

11. 30. 33.3. 33.3

3. 33. 19.1. 36.6

Using sturge rule to get the class interval

N = number of observations

K = 1+3.3log(33)

K=60=6

Sturge rule = 1+3.3 logN

Rf =8/33×100/1=24.2

11/33×100/1 =33.3

Rcf=8/90×100/1=8.8

19/90×100/1=21.1

2. A sample is defined as a subset comtaiing only a finite number of units from the population. It involves the selection of a number of study units from a defined population. It’s therefore a smaller representative of a population. There are 2 types of sampling techniques; Non- probability sampling: here, the unit of the population is not known and can’t be determined this is the vice versa of the probability sampling.

Population; This is the totality of all units with identified characteristics of interest.it refers to any well defined class of people, animal, plants objects etc. It’s the complete enumeration of the entire units in population during a survey called census.

Continous variables: Here the range of a continous variable consists of a set of real numbers. A continuous variable is used in measurements of weights, height , blood pressure, etc.

Descrete variable : it’s used to model count data such as the number of accidents in a year etc.

Statistics: this is concerned with the scientific method of collecting, organizing, summarizing, analyzing and presenting data as well as drawing vital conclusions and making reasonable decisions on the basis of such analysis. It’s the body of decisions in the face of uncertainty or incomplete information.

Data: these are informations gathered from facts a given research variable.

Types of data include;

Time dimension

Degree of aggregation

Level of measurability

Methods of data collection include

Interview

Observation

Mail questionnaire

Projective techniques

Documentary techniques

Name: Omeogo mmesoma Esther

Dept:. Social science education (economics Education)

Faculty: Education

Reg number:2021/245468

1: kg(C.l). X F. C.F R.F R.C.F

17-18. 17.5. 5. 05. 15.2. 4.0%

19-20. 19.5. 6. 11. 18.2. 33%

21-22. 21.5. 8. 19. 24.2. 58%

23-24. 23.5. 7. 26. 21.2. 79%

25-26. 25.5. 4. 30. 12.1. 91%

27-28. 27.5. 3. 33. 09.2. 100%

No. 2 brief note on

1. Sample can be defined as part or portion of a population (an observation)and is taken for representation of it( the population) eg are the heights of students in a faculty for representation of the height of students.

2. Population is the entire collection of groups, items,or individual from which information is gathered and which you choose to examine at a particular time,it is the largest collection of entities that we have interest on at a given time.

3. Continuous variable is the opposite of discreet variable it can assume any value from a range of variables.eg are income of a staff paid in naira and Kobo they are measured in continuous scale (metres, centimeters,e.t.c)

4. Discreet variable is a variable that can only be counted when represented In a whole number,they don’t contain decimal point or places eg age of a student e.t.c.

5. Statistics refers to numerical facts such as number of events occurring in a time , is a field of study that concerns the layout of experiment, collection, tabulation, measurements, organizing, interpretation, presentation and analyzing of data.

6. Data is a numerical statement or collection of facts ( eg numbers, words, observation and measurements)in a specific field of inquiry,they refer to numbers that results from taking measurements eg recording light, weight or temperature measurements.

Thanks…

Name: Omeogo mmesoma Esther

Dept:. Social science education (economics Education)

Faculty: Education

Reg number:2021/245468

1: kg(C.l). X F. C.F R.F R.C.F

17-18. 17.5. 5. 05. 15.2. 4.0%

19-20. 19.5. 6. 11. 18.2. 33%

21-22. 21.5. 8. 19. 24.2. 58%

23-24. 23.5. 7. 26. 21.2. 79%

25-26. 25.5. 4. 30. 12.1. 91%

27-28. 27.5. 3. 33. 09.2. 100%

No. 2 brief note on

1. Sample can be defined as part or portion of a population (an observation)and is taken for representation of it( the population) eg are the heights of students in a faculty for representation of the height of students.

2. Population is the entire collection of groups, items,or individual from which information is gathered and which you choose to examine at a particular time,it is the largest collection of entities that we have interest on at a given time.

3. Continuous variable is the opposite of discreet variable it can assume any value from a range of variables.eg are income of a staff paid in naira and Kobo they are measured in continuous scale (metres, centimeters,e.t.c)

4. Discreet variable is a variable that can only be counted when represented In a whole number,they don’t contain decimal point or places eg age of a student e.t.c.

5. Statistics refers to numerical facts such as number of events occurring in a time , is a field of study that concerns the layout of experiment, collection, tabulation, measurements, organizing, interpretation, presentation and analyzing of data.

6. Data is a numerical statement or collection of facts ( eg numbers, words, observation and measurements)in a specific field of inquiry,they refer to numbers that results from taking measurements eg recording light, weight or temperature measurements.

Thanks…

1. Computing the following as follows Using the sturge rule

Solution.

{Sturge rule} k=1+3.3 log N

K=1+3.3 log 33

K=1+3.3(1.5185)

K=1+5.0

K=6

:no of class= 6

Range =28-17

=11

Class interval=11/6

=1.8. (approximately) =2.

Class intervals Mid point Frequency Cumulative frequency Relative frequency Relative cumulative frequency

17-18 17.5 5 5 5/33 *100 =15.15% 5/33*100= 15.15%

19-20 19.5 6 11 6/33*100= 18.18% 11/33*100= 33.3%

21-22 21.5 8 19 8/33*100= 24.24% 19/33*100= 57.57%

23-24 23.5 7 26 7/33*100 =21.21% 26/33*100= 78.78%

25-26 25.5 3 30 3/33*100 =9.09% 30/33*100= 90.90%

27-28 27.5 4 33 4/33*100 =12.12% 33/33*100= 100%

Total:33

class. frequency cum.frequency rel.frequency

17_18. 5. 5. 0.15

19_20. 6. 11. 0.18

21_22. 8. 19. 0.24

23_24. 7. 26. 0.21

25_26. 4. 30. 0.12

27_28. 3. 33. 0.09

mid point. relative cum. frequency

17.5. 15.5%

19.5. 33.33%

21.5. 51.5%

23.5. 78.7%

25.5. 90.9%

27.5. 100%

2. Discuss the following::::::

1. A sample:

A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations.

2. A Population:

A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic. In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study.

3. A continuous variable:

A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. Continuous variables are generally measured on scales such as height, weight, temperature, etc. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range.

With the help of continuous variables, one can measure mean, median, variance, or standard deviation.

4. A discrete variable:

A discrete variable is a variable which exists only as a whole number and is not divisible. It can take a while or finite number of numerical value,categories or codes.

Discrete variables can also called a categorical variable. For example, you can count the change in your pocket.

5. A Data:

Data are measurements or observations that are collected as a source of information.

Data can come in the form of text, observations, figures, images, numbers, graphs, or symbols. For example, data might include individual prices, weights, addresses, ages, names, temperatures, dates, or distances.

6. A Statistics:

Statistics is a branch that deals with every aspect of the data. Statistical knowledge helps to choose the proper method of collecting the data and employ those samples in the correct analysis process in order to effectively produce the results.

Name:Emerhe Lucky Ejirooghene

Email: Ejirochosen@gmail.com

Matric No: 2021/246367

QUESTION TWO

SAMPLE

Sample means a procedure by which one or more members of a population are selected from the population. The objective is to make certain observations about members of the sample, and then, based on these results draw valid conclusions about the characteristics of the entire population. Since it is usually impractical to test every member of a population, a sample from the population is typically the best approach available.

There are five types of sampling namely Random, Systematic, Convenience, Cluster and Stratified.

POPULATION

The population can be defined as the entire group of individuals that we are interested in making a statement about. It is also defined as the entire group about which information is desired. It is also described as the largest collection of entities in which we have an interest at a particular time; an entire set of objects, observations, or scores that have something in common.

CONTINUOUS VARIABLES

A continuous variable is one for which, within the limits of the variable ranges, any value is possible. Continuous variables can take any value between a certain set of real numbers. The value given to an observation for a continuous variable can include values as small as the instrument of measurement allows. For example, the variable “time to solve an algebra problem” is continuous since it could take 1min, 2mins, 4mins etc to finish a problem.

DISCRETE VARIABLES

A discrete variable can be defined as a variable that exists only as whole numbers and is not divisible. It’s the variable that can take in a finite number of numerical values, categories or codes. Discrete variables can be classified into Nominal variables, Ordinal variables, Dummy variables from quantitative variables, preference variables and multiple response variables.

STATISTIC

The statistic can be defined as numerical facts such as the number of events occurring in time or the number of people living in a particular area. Croxton and Cowden define statistics as the science of collection, presentation, analysis and interpretation of numerical data. Bowley (n.d) defined statistics as the scheme of average or numerical statements of fact in any department of enquiry about each other. The functions of statistics are condensation, comparison, forecasting, estimation and test of hypothesis.

DATA

Data can be defined as a collection of facts, such as numbers, words, measurements, observations, or even just descriptions of things. It could also be seen as information in a raw or unorganized form( such as alphabets, numbers, or symbols) that refers to or represent, conditions, ideas, or objects. Data could be qualitative or quantitative. We also have primary and secondary data.

Name: Onu faithfulness chinyere

Reg no: 2021/244051

Department: economics

Email: onfaithfulness@gmail.com

Question one. 1)class interval of: 6. (17-22, 23-28). 2) midpoint;19.5 & 25.5 = 45. 3)frequency; 33. 4) cumulative frequency; 52. 5) relative frequency; 57.57 & 42.42 = 99.99. 6) relative cumulative frequency; 36.53 & 63.46 = 99.99

Question two:

1)Sample: a sample is a part of the population that we observe. it is also a procedure by which one or more members of a population are selected from the population. The objective is to make certain observations about the members of the sample, and then , on the basis of these results, draw valid conclusion about the characteristics of the entire population. Since it is usually impractical to test every member if a population , a sample from the population is typically the best approach. A sample must be representative of a population in all ramifications.

2) Population; a population is defined as the entire group of individuals that we are interested in making a statement about. It is also the entire group about which information is desired.

3)continuous variable; continuous variable is one for which, within the limits the variable ranges, any value is possible. Continuous variable can take any value between a certain set of real numbers. The value given to an observation for a continuous variable can include values as small as the instrument of measurement allows.

4)Discrete variable; it is also known as categorical variables. They are variables or data that exist only as whole numbers and are not divisible. S discrete variable can take on a finite number of numerical values, categories or codes.

5)Statistics; it refers to numerical facts such as the number of events occurring in time or the number of people living in a particular area. It also involves the study of ways of collecting , analyzing and interpreting numerical facts or numerical data. Statistics is concerned with the scientific method of collecting, organising , summarising, presenting and analyzing data. It aksp entails deriving valid conclusions and making reasonable decisions on the basis of analysis.

6) Data: data could be seen as a collection of facts, such as numbers, words , measurements, observations or even just descriptions of things. It could be seen as information in raw or unorganized form (such as, numbers , alphabets or symbols) that refers to or represent, conditions , ideas, or objects. Data could be qualitative or quantitative.

1. Computing the following as follows Using the sturge rule

Solution.

{Sturge rule} k=1+3.3 log N

K=1+3.3 log 33

K=1+3.3(1.5185)

K=1+5.0

K=6

:no of class= 6

Range =28-17

=11

Class interval=11/6

=1.8. (approximately) =2.

Class intervals Mid point Frequency Cumulative frequency Relative frequency Relative cumulative frequency

17-18 17.5 5 5 5/33 *100 =15.15% 5/33*100= 15.15%

19-20 19.5 6 11 6/33*100= 18.18% 11/33*100= 33.3%

21-22 21.5 8 19 8/33*100= 24.24% 19/33*100= 57.57%

23-24 23.5 7 26 7/33*100 =21.21% 26/33*100= 78.78%

25-26 25.5 3 30 3/33*100 =9.09% 30/33*100= 90.90%

27-28 27.5 4 33 4/33*100 =12.12% 33/33*100= 100%

Total:33

class. frequency cl. frequency rel.frequency

17_18. 5. 5. 0.15

19_20. 6. 11. 0.18

21_22. 8. 19. 0.24

23_24. 7. 26. 0.21

25_26. 4. 30. 0.12

27_28. 3. 33. 0.09

mid. point. rel.cumulative frequency

17.5. 15.15%

19.5. 33.33%

21.5. 57.5%

23.5. 78.7%

25.5. 90.9%

27.5. 100%

2. Discuss the following::::::

1. A sample:

A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations.

2. A Population:

A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic. In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study.

3. A continuous variable:

A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. Continuous variables are generally measured on scales such as height, weight, temperature, etc. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range.

With the help of continuous variables, one can measure mean, median, variance, or standard deviation.

4. A discrete variable:

A discrete variable is a variable which exists only as a whole number and is not divisible. It can take a while or finite number of numerical value,categories or codes.

Discrete variables can also called a categorical variable. For example, you can count the change in your pocket.

5. A Data:

Data are measurements or observations that are collected as a source of information.

Data can come in the form of text, observations, figures, images, numbers, graphs, or symbols. For example, data might include individual prices, weights, addresses, ages, names, temperatures, dates, or distances.

6. A Statistics:

Statistics is a branch that deals with every aspect of the data. Statistical knowledge helps to choose the proper method of collecting the data and employ those samples in the correct analysis process in order to effectively produce the results.

Mbamalu kosisochukwu

2021/241345

Question One.

1. The class interval using sturge rule:

Sturge rule formula= k= 1 + 3.322 logN

Where N= Total number of observations.

K= 1 + 3.322 log33

K= 1 + 3.322(1.5185)

K= 1 + 5.0445

K= 6.0445

K= 6~

Class interval= Range/1 + 3.322 logN

Range=Highest value – Lowest value

Range= 28 – 17 = 11

Class interval= 11/ 1+3.322log33

= 11/6

=1.83

= 2~

Class Interval Mid-point F. C.F. R.F. R.C.F

17 – 18 17.5 5 5 15.15 15.15

19 – 20 19.5 6 11 18.18 33.33

21 – 22 21.5 8 19 24.24 57.57

23 – 24 23.5 7 26 21.21 78.78

25 – 26 25.5 4 30 12.12 90.90

27 – 28 27.5 3 33 9.09 100

Total=

33

Question Two.

1. Sample: A sample is a subset of fraction of the population selected as a representative of the population for study. It is also defined as a part of fraction of the population selected from the population in order to study it and use the result obtained from it to make generalization about the population from where it is drawn.

4. Discrete Variable: Discrete variables or data are also known as categorical variables.They are variables or data that exist only as whole numbers and are not divisible. A discrete variable can take an finite number of numerical values, categories or codes.

5. Statistics: The word ‘Statistic’ refers to numerical facts such as the number of events occurring in time or the number of people living in a particular area. It also involves the study of ways of collecting analysing and interpreting numerical facts or numerical data. Statistic is broadly divided into two main branches which are; descriptive and inferential statistic. Descriptive statistics studies a body of numerical information (data) without using the results obtained to make inference or generalization about the population from where they are drawn. It involves the use of charts; diagrams etc to study a set of data. While inferential statistics study a body statistical data with the intent of using the result obtained to make generalization or inference about the population where they are gotten. It is the science of using sample results to make generalization about the population data.

6. Data: Data are raw facts, sets of numbers, figures or symbols obtained from enumerations or measurements. Data are unprocessed information often in the form of facts of figure obtained from surveys or experiments, used as a basis to making calculation or drawing conclusions. They could be in form of numbers, texts, images, symbols, and sounds, in form that is suitable for processing and storage.

Name: Prince Emmanuel Obia

Department: Economics

Level: 100

Reg No.: 11024701IE

Course: Eco 101

Sample: A sample is a subset of a larger group or population that is selected and studied to gain insights into the characteristics of the larger group. In research, a sample is often used when it is not feasible or practical to study the entire population.

Population: A population is a group of individuals, objects, or events that share one or more common characteristics. In research, the population is the entire group that the researcher is interested in studying.

Continuous Variable: A continuous variable is a type of variable that can take on any value within a certain range. Examples of continuous variables include height, weight, temperature, and time.

Discrete Variable: A discrete variable is a type of variable that can only take on specific values. Examples of discrete variables include the number of children in a family, the number of pets someone has, and the number of cars a person owns.

Statistics: Statistics is the branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It provides methods for summarizing and describing data, making inferences about populations based on samples, and test tones.

Data: Data refers to information or facts that are collected, stored, and analyzed in order to gain insights or knowledge about a particular topic. Data can be quantitative or qualitative and can be collected through various methods such as surveys, experiments, and observations.

Name : Emmanuel izuchukwu Godslove

Course code : Eco 131

Department: economics

Matric number: 2021/241331

1. Computing the following as follows Using the sturge rule

Solution.

{Sturge rule} k=1+3.3 log N

K=1+3.3 log 33

K=1+3.3(1.5185)

K=1+5.0

K=6

:no of class= 6

Range =28-17

=11

Class interval=11/6

=1.8. (approximately) =2.

Class intervals Mid point Frequency Cumulative frequency Relative frequency Relative cumulative frequency

17-18 17.5 5 5 5/33 *100 =15.15% 5/33*100= 15.15%

19-20 19.5 6 11 6/33*100= 18.18% 11/33*100= 33.3%

21-22 21.5 8 19 8/33*100= 24.24% 19/33*100= 57.57%

23-24 23.5 7 26 7/33*100 =21.21% 26/33*100= 78.78%

25-26 25.5 3 30 3/33*100 =9.09% 30/33*100= 90.90%

27-28 27.5 4 33 4/33*100 =12.12% 33/33*100= 100%

Total:33

Class interval:

17-18 ,19-20,21-22,23-24,25-26,27-28

Mid point:

17.5, 19.5, 21.5, 23.5, 25.5, 27.5.

Frequency:

5, 6 ,8, 7, 4, 3

5+6+8+7+4+3=30

Cumulative frequency:

5, 11, 19, 26, 30, 33

Relative frequency

5/33 *100 =15.15%

6/33*100= 18.18%

8/33*100= 24.24%

7/33*100 =21.21%

4/33*100 =12.12%

3/33*100 =9.09%

Relative cumulative frequency

5/33*100= 15.15%

11/33*100= 33.3%

19/33*100= 57.57%

26/33*100= 78.78%

30/33*100= 90.90%

33/33*100= 100%

2. Discuss the following::::::A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations.

1. A sample:

2. A Population:

A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic. In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study.

3. A continuous variable:

A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. Continuous variables are generally measured on scales such as height, weight, temperature, etc. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range.

With the help of continuous variables, one can measure mean, median, variance, or standard deviation.

4. A discrete variable:

A discrete variable is a variable which exists only as a whole number and is not divisible. It can take a while or finite number of numerical value,categories or codes.

Discrete variables can also called a categorical variable. For example, you can count the change in your pocket.

5. A Data:

Data are measurements or observations that are collected as a source of information.

Data can come in the form of text, observations, figures, images, numbers, graphs, or symbols. For example, data might include individual prices, weights, addresses, ages, names, temperatures, dates, or distances.

6. A Statistics:

Statistics is a branch that deals with every aspect of the data. Statistical knowledge helps to choose the proper method of collecting the data and employ those samples in the correct analysis process in order to effectively produce the results.

seconds ago

Name: ukpai Victoria chinenye

reg number:2021/241964

department: Economics

a)class interval using sturge rule

17-18.

19-20.

21-22.

23-24

25-26

27-28

b)midpoint

17.5

19.5

21.5

23.5

25.5

27.5

c) frequency

5

6

8

7

4

3

_____

33

_____

d) cumulative frequency

5

11

19

26

30

33

______

124

——–

e)relative frequency

15.15

18.18

24.24

21.2

12.12

9.09

f) relative cumulative frequency

4.03

8.87

15.32

20.96

24.19

26.6

2 Sample:A sample is a part of the population that we actually observed.sample is a proportion or part of the population, usually the proportion from which information is gathered.it is also described as a largest collection of entities for which we have an interest at a particular time;an entire set of objects, observations,or scores that have something in common

Types of sampling

there are five types of sampling:

*Random

*systematic

*convinience

*cluster and

*stratified

b) Population:is the entire group of individuals that we are interested in making a statement about.population is defined as the entire group about which information is desired

C) continuous Variable:a continuous variable is one for which,within the limits the variable ranges,any value is possible.continous variable can take any value between a certain set of real numbers

Continuous variable can be classified into

*interval-scale variably

*continuous ordinal variably

*ratio-scale variable

D) Discrete variable:discrete variable or data are also known as categorical variables.theu are variables or data that exist only as whole numbers and are not divisible.a discrete variable can take on a finite number of numerical, categories or codes

it can be categorized into

*nominal variables

*ordinal variables

*dummy variables from quantitative variable

*preference variable

*multiple response variable

E) statistics: the word statistics refers to numerical facts such at the number of events occurring in time or the number of people living in a particular area..it also involves the study of ways of collecting, analyzing and interpreting numerical facts or numerical data

F)Data:data could be seen as a collection of facts,such as numbers,words, measurements, observation or even just description of things.it could also be seen as information in rae or unorganized form such as alphabet, numbers or symbols that refer to or represent,conditions,ideas or subject

Data can be quantitative i.e data that deal with numbers or qualitative i.e data that deals with description

Name: ukpai Victoria chinenye

reg number:2021/241964

department: Economics

Group. md(x). frequency CF RF. RCF

17-18. 17.5. 5. 5. 15.15. 4.03

19-20. 19.5. 6. 11. 18.18. 8.87

21-22. 21.5. 8. 19 24.24. 15.32

23-24. 23.5. 7. 26. 21.2. 20.96

25-26. 25.5. 4. 30. 12.12. 24.19

27-28. 27.5. 3. 33. 9.09. 26.6

_____. _____

33. 124

———- ——-

2 Sample:A sample is a part of the population that we actually observed.sample is a proportion or part of the population, usually the proportion from which information is gathered.it is also described as a largest collection of entities for which we have an interest at a particular time;an entire set of objects, observations,or scores that have something in common

Types of sampling

there are five types of sampling:

*Random

*systematic

*convinience

*cluster and

*stratified

b) Population:is the entire group of individuals that we are interested in making a statement about.population is defined as the entire group about which information is desired

C) continuous Variable:a continuous variable is one for which,within the limits the variable ranges,any value is possible.continous variable can take any value between a certain set of real numbers

Continuous variable can be classified into

*interval-scale variably

*continuous ordinal variably

*ratio-scale variable

D) Discrete variable:discrete variable or data are also known as categorical variables.theu are variables or data that exist only as whole numbers and are not divisible.a discrete variable can take on a finite number of numerical, categories or codes

it can be categorized into

*nominal variables

*ordinal variables

*dummy variables from quantitative variable

*preference variable

*multiple response variable

E) statistics: the word statistics refers to numerical facts such at the number of events occurring in time or the number of people living in a particular area..it also involves the study of ways of collecting, analyzing and interpreting numerical facts or numerical data

F)Data:data could be seen as a collection of facts,such as numbers,words, measurements, observation or even just description of things.it could also be seen as information in rae or unorganized form such as alphabet, numbers or symbols that refer to or represent,conditions,ideas or subject

Data can be quantitative i.e data that deal with numbers or qualitative i.e data that deals with description

Question One.

1. The class interval using sturge rule:

Sturge rule formula= k= 1 + 3.322 logN

Where N= Total number of observations.

K= 1 + 3.322 log33

K= 1 + 3.322(1.5185)

K= 1 + 5.0445

K= 6.0445

K= 6~

Class interval= Range/1 + 3.322 logN

Range=Highest value – Lowest value

Range= 28 – 17 = 11

Class interval= 11/ 1+3.322log33

= 11/6

=1.83

= 2~

Class Interval Mid-point F. C.F. R.F. R.C.F

17 – 18 17.5 5 5 15.15 15.15

19 – 20 19.5 6 11 18.18 33.33

21 – 22 21.5 8 19 24.24 57.57

23 – 24 23.5 7 26 21.21 78.78

25 – 26 25.5 4 30 12.12 90.90

27 – 28 27.5 3 33 9.09 100

Total=

33

Question Two.

1. Sample: A sample is a subset of fraction of the population selected as a representative of the population for study. It is also defined as a part of fraction of the population selected from the population in order to study it and use the result obtained from it to make generalization about the population from where it is drawn.

4. Discrete Variable: Discrete variables or data are also known as categorical variables.They are variables or data that exist only as whole numbers and are not divisible. A discrete variable can take an finite number of numerical values, categories or codes.

5. Statistics: The word ‘Statistic’ refers to numerical facts such as the number of events occurring in time or the number of people living in a particular area. It also involves the study of ways of collecting analysing and interpreting numerical facts or numerical data. Statistic is broadly divided into two main branches which are; descriptive and inferential statistic. Descriptive statistics studies a body of numerical information (data) without using the results obtained to make inference or generalization about the population from where they are drawn. It involves the use of charts; diagrams etc to study a set of data. While inferential statistics study a body statistical data with the intent of using the result obtained to make generalization or inference about the population where they are gotten. It is the science of using sample results to make generalization about the population data.

6. Data: Data are raw facts, sets of numbers, figures or symbols obtained from enumerations or measurements. Data are unprocessed information often in the form of facts of figure obtained from surveys or experiments, used as a basis to making calculation or drawing conclusions. They could be in form of numbers, texts, images, symbols, and sounds, in form that is suitable for processing and storage.

Name: Mbamalu kosisochukwu

Reg No: 2021/241345

Email: Kosisochukwu.mbamalu.241345@unn.edu.ng

Question One.

1. The class interval using sturge rule:

Sturge rule formula= k= 1 + 3.322 logN

Where N= Total number of observations.

K= 1 + 3.322 log33

K= 1 + 3.322(1.5185)

K= 1 + 5.0445

K= 6.0445

K= 6~

Class interval= Range/1 + 3.322 logN

Range=Highest value – Lowest value

Range= 28 – 17 = 11

Class interval= 11/ 1+3.322log33

= 11/6

=1.83

= 2~

Class Interval Mid-point F. C.F. R.F. R.C.F

17 – 18 17.5 5 5 15.15 15.15

19 – 20 19.5 6 11 18.18 33.33

21 – 22 21.5 8 19 24.24 57.57

23 – 24 23.5 7 26 21.21 78.78

25 – 26 25.5 4 30 12.12 90.90

27 – 28 27.5 3 33 9.09 100

Total=

33

Question Two.

1. Sample: A sample is a subset of fraction of the population selected as a representative of the population for study. It is also defined as a part of fraction of the population selected from the population in order to study it and use the result obtained from it to make generalization about the population from where it is drawn.

The sturges rule is used to determine the number of classes when the total number of observation is given. It is written as:

K=1+3.322×Log N

Where N is the total number of observation.

: K=1+3.322×Log33

K=1+3.322×1.5185

k=6

Then our class interval becomes

=Max value – min value/6

=28 – 17/6

=11/6 = 1.8333 ~ 2

Class Frequency Midpoint. C.F R.F. R.C.F

Interval x

17-18 5 17.5. 5. 15% 12%

19-20 6. 19.5. 11. 18% 14.5%

21-22 8 21.5. 19. 24% 19.4%

23-24 7 23.5. 26. 21% 16.9%

25-26 4. 25.5. 30. 12% 9.6%

27-28 3. 27.5. 33. 9% 7.3%

2i. Sample can be defined as a portion of a population. It is a procedure by which one or more members of a population are selected from the population. There are five types of sample which are: Random, Systematic, Convenience, Cluster and Statified.

ii. Population can be defined as the entire group about which information is desired. It is also described as an entire sets of objects, observation or scores that have something in common.

iii. A continuous variable is one for which, within the limits the ranges, and value is possible. It can take any value between a set of real numbers.

iv. Discrete variables or data are also known as categorical variables. They are variables or data that exist only as whole numbers and are not divisible.

v. Statistics refer to numerical facts such as the number of events occurring in time or the number of people living in a particular area.

vi. Data can be seen as a collection of facts, such as numbers, words, measurements, observation or even just descriptions of things.

1.Sample is examining of a portion of the population to draw conclusion about the whole population using sample estimates.

2.Population is defined as the entire group about which information is desired.

3.Continuous variables is one for which,within the limits the variable ranges,any value is possible.

4.Discrete variables are data that exists only as whole numbers and are not divisible.

5.Statistics is a number that describes a sample.

6.Data is a collection of facts and figures with description of things.

Chukwudile Chinomso Wendy

2021/245480

Chukwudilewendy@gmail.com

Class interval Midpoint(x). Frequency(f). Cumulative frequency

Relative frequency Relative cumulative frequency

17-18

17.5

5

5

5/33 × 100/1 = 15.2%

5/33 × 100/1 = 15.2%

19-20

19.5

6

11

6/33 × 100/1 = 18.2%

11/33 × 100/1 = 33.4%

21-22

21.5

8

19

8/33 × 100/1 = 24.2%

19/33 × 100/1 = 57.6%

23-24

23.5

7

26

7/33 × 100/1 = 21.2%

26/33 × 100/1 = 78.8%

25-26

25.5

4

30

4/33 × 100/1 = 12.1%

30/33 × 100/1 = 90.9%

27-28

27.5

3

33

3/33 × 100/1 = 9.1%

33/33 × 100/1 = 100%

33

100%

1.) A sample is a smaller set of data that a researcher chooses or selects from a larger population using a pre-defined selection method. These elements are known as sample points, sampling units, or observations.

Creating a sample is an efficient method of conducting research. Researching the whole population is often impossible, costly, and time-consuming. Hence, examining the sample provides insights the researcher can apply to the entire population.

2.) A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic.

In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped by a common feature can be said to be a population. A sample may also refer to a statistically significant portion of a population, not an entire population. For this reason, a statistical analysis of a sample must report the approximate standard deviation, or standard error, of its results from the entire population. Only an analysis of an entire population would have no standard error.

3.) A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range. Thus, the range of real numbers between x and y with x, y ∈ R and x ≠ y; is said to be uncountable and infinite.

In continuous optimization problems, different techniques of calculus are often used in which the variables are continuous. Also, the probability distributions of continuous variables can be stated in expressions of probability density functions in statistical theory.

4.) A discrete random variable is a type of variable whose value is determined by the numerical results of particular random phenomena. Also referred to as a stochastic variable. Discrete random variables are always entire, easily countable numbers. The probability distribution of a discrete random variable is characterised by a probability mass function.

5.) Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In other words, it is a mathematical discipline to collect, summarize data. Also, we can say that statistics is a branch of applied mathematics. However, there are two important and basic ideas involved in statistics; they are uncertainty and variation. The uncertainty and variation in different fields can be determined only through statistical analysis. These uncertainties are basically determined by the probability that plays an important role in statistics.

6.) In computing, data is information that has been translated into a form that is efficient for movement or processing. Relative to today’s computers and transmission media, data is information converted into binary digital form. It is acceptable for data to be used as a singular subject or a plural subject. Raw data is a term used to describe data in its most basic digital format.

NAME: OKOLIE OGOCHUKWU MITCHELL

REG NO: 19734272GH

FACULTY: SOCIAL SCIENCE

DEPT: ECONOMICS

DATE: 8th March, 2023.

*QUESTION 1*

Firstly, get the number of classes

Using Sturge Rule;

k = 1 + 3.322( log n)

Where:

k = the number of classes

n = the number of observations in the data set. Which is 33.

Therefore, number of classes is:

k= 1+ 3.322(log 33)

k= 6

Knowing this we can form a table:

*Class interval*

17-18.

19+20.

21+22.

23+24.

25+26.

27+28.

*Mid point*

17+18÷2=17.5

19+20÷2=19.5

21+22÷2=21.5

23+24÷2=23.5

25+26÷2=25.5

27+28÷2=27.5

*Frequency*

5

6

8

7

4

3

*Cumulative Frequency*

5

5+6=11

11+8=19

19+7=26

26+4=30

30+3=33

*Relative Frequency*

5÷33*100=15.15

6÷33*100=18.18

8÷33*100=24.24

7÷33*100=21.21

4÷33*100=12.12

3÷33*100=9.09

*Relative Cumulative Frequency*

5÷124*100=4.03

11÷124*100=8.87

19÷124*100=15.32

26÷124*100=20.96

30÷124*100=24.19

33÷124*100=26.61

*QUESTION TWO*

1.) SAMPLE: A sample is quite simply, a subset of a given population in a statistical study. This is used to make inference about the population. It is commonly used in place of the population to its comparative ease as regards data collection, its comparative cost-effectiveness, etc.

2.) POPULATION: This is the total number of target observations or elements in a statistical study. Data collection from the population is normally eschewed in favour of a sample from it due to the previously mentioned reasons. However, it is sometimes used, especially when the results to be gotten from the statistical study would be incomplete or inconclusive without the inclusion of every element.

3.) CONTINUOUS VARIABLE: This is a type of variable which can assume any numerical value in a given range of an infinite number of values. Continuous variables have valid fractional and decimal values. Also, they can be meaningfully split into smaller parts. A continuous variable is measured, rather than counted. Examples of continuous variables are:

age

height

weight

temperature

time, etc.

4.) DISCRETE VARIABLE: This is a distinct variable. Meaning that this type of variable can only assume a specific value. Also this value cannot be subdivided into smaller parts like the continuous variable. Discrete variables are counted, rather than measured, and cannot have fractional or decimal values. Examples of discrete variables are:

Number of companies listed on the NGX

The total working population of a country

Number of universities, etc

5.) STATISTICS: Statistics is a term that has different but related meanings. On one hand, statistics can refer to numerical facts such as averages, percentages, index numbers, etc which are used to understand a variety of situations in a variety of areas, such as business, economics, etc. On the other hand, statistics can be defined as the art or science of collecting, analyzing, presenting and interpreting data so as to enable decision makers understand certain situations and make the best decisions possible.

6.) DATA: Data are the facts and figures which are collected, analyzed, and summarized for presentation and interpretation. All the data collected in a particular study are referred to as the data set for the study. It is important to remember that data are the raw, unprocessed information

Name:Asogwa Arinze Godwin

Reg No: 2016/235173

Email: Godwintej@gmail.com

Question One.

1. The class interval using sturge rule:

Sturge rule formula= k= 1 + 3.322 logN

Where N= Total number of observations.

K= 1 + 3.322 log33

K= 1 + 3.322(1.5185)

K= 1 + 5.0445

K= 6.0445

K= 6~

Class interval= Range/1 + 3.322 logN

Range=Highest value – Lowest value

Range= 28 – 17 = 11

Class interval= 11/ 1+3.322log33

= 11/6

=1.83

= 2~

Class Interval Mid-point F. C.F. R.F. R.C.F

17 – 18 17.5 5 5 15.15 15.15

19 – 20 19.5 6 11 18.18 33.33

21 – 22 21.5 8 19 24.24 57.57

23 – 24 23.5 7 26 21.21 78.78

25 – 26 25.5 4 30 12.12 90.90

27 – 28 27.5 3 33 9.09 100

Total=

33

5. Statistics: The word ‘Statistic’ refers to numerical facts such as the number of events occurring in time or the number of people living in a particular area. It also involves the study of ways of collecting analysing and interpreting numerical facts or numerical data. Statistic is broadly divided into two main branches which are; descriptive and inferential statistic. Descriptive statistics studies a body of numerical information (data) without using the results obtained to make inference or generalization about the population from where they are drawn.

6. Data: Data are raw facts, sets of numbers, figures or symbols obtained from enumerations or measurements.

NAME:ORJIUDE NNAORJI IZUCHUKWU

DEPARTMENT:ECONOMICS

REG NO:2021/241360

CLASS INTERVAL MP FREQ CUMM FREQ RELAT FREQ RELAT CUMM FREQ

17-18 17.5 5 5 15.2 3.9

19-20 19.5 6 11 18.2 8.7

21-22 21.5 9 20 27.3 15.7

23-24 23.5 7 27 21.2 21.3

25-26 25.5 4 31 12.1 24.4

27-28 27.5 2 33 6.1 26

Sample and Population:

In economics, a population refers to the entire group of individuals, objects, or events that are of interest to the researcher and on which inferences and conclusions are to be drawn. For example, the population of interest in economics could be all households in a particular country, all firms in a particular industry, or all stocks listed on a particular exchange. However, studying the entire population can be time-consuming, expensive, and sometimes impossible. Therefore, economists often draw a sample from the population to make inferences about the population as a whole.

A sample is a subset of the population that is used to draw conclusions about the population. Sampling can be done in several ways, such as simple random sampling, stratified sampling, or cluster sampling. Economists use sampling to estimate population parameters such as the mean, variance, or correlation coefficient. Sampling helps economists make accurate inferences about the population based on a smaller, more manageable dataset.

Continuous and Discrete Variables:

In economics, variables are used to represent different aspects of a phenomenon or system that is being studied. A continuous variable is one that can take on any value within a certain range. For example, income is a continuous variable, as it can take on any value within a certain range (e.g., $0 to infinity). Other examples of continuous variables in economics include age, time, and weight. Continuous variables are typically measured using decimal numbers, and they can be either positive or negative.

A discrete variable is one that can only take on certain specific values. For example, the number of employees in a firm, the number of products sold, or the number of customers served in a restaurant are all examples of discrete variables. Discrete variables are typically measured using integer numbers, and they can only take on specific values. Discrete variables are often used in economics to represent count data, such as the number of transactions or the number of employees.

Statistics and Data:

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. In economics, statistics is used to study and analyze economic phenomena and make predictions or forecasts. Statistics is used to help economists understand the relationships between different economic variables, test hypotheses, and evaluate the effectiveness of policies or programs.

Data refers to the information that is collected and used to draw conclusions and make decisions. In economics, data can be collected through surveys, experiments, observations, or other methods. Data is used to analyze economic trends, make predictions, and evaluate policies and programs. For example, economists might use data on GDP growth, inflation rates, unemployment rates, or stock prices to make predictions about the future state of the economy or to evaluate the effectiveness of different economic policies.

In summary, in economics, sampling and population are used to draw conclusions about a larger group of interest. Continuous and discrete variables are used to represent different aspects of the phenomenon being studied, while statistics and data are used to analyze, interpret and present information about the economic system being studied. Together, these tools provide economists with the means to understand, explain and predict economic phenomena.

Question1

Class interval Midpoint F CF RF RCF

17_18 17.5 5 5 15.5 15.15

19_20 19.5 6 11 18.18 3.3

21_22 21.5 8 19 24.24 57.57

23_24 23.5 7 26 21.21 78.78

25_26 25.5 4 30 12.12 90.90

27_28 27.5 3. 33 9.09 100

Total 33

Question 2:

1: Samples represents part or a single item from a larger whole or group especially when presented for inspection or shown as evidence of quality. Samples are easier to collect data from because they are practical, cost-effective.

2: Populations are used when a research question requires data from every member of the population. This is usually only feasible when the population is small and easily accessible.

3: A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range.

4: A discrete variable is a variable whose value is obtained by counting. Examples: number of students present. number of red marbles in a jar. number of heads …

5:statistics is dealing with the collection, analysis, interpretation, and presentation of masses of numerical data. : a collection of quantitative data.

6:In computing, data is information that has been translated into a form that is efficient for movement or processing. Relative to today’s computers and transmission media, data is information converted into binary digital form. It is acceptable for data to be used as a singular subject or a plural subject.

Question1

Class interval Midpoint F CF RF RCF

17_18 17.5 5 5 15.5 15.15

19_20 19.5 6 11 18.18 3.3

21_22 21.5 8 19 24.24 57.57

23_24 23.5 7 26 21.21 78.78

25_26 25.5 4 30 12.12 90.90

27_28 27.5 3. 33 9.09 100

Total 33

Question 2:

1: Samples are used to make inferences about populations. Samples are easier to collect data from because they are practical, cost-effective, convenient, and manageable.

5:statistics, the science of collecting, analyzing, presenting, and interpreting data.

Igwe Ebubechukwu victor

rgduniverse370@gmail.com

10375074EB

Answer 1

1. k= 1+3.33logN

k=1+3.33log33

k=1+3.33×1.5185

k=6.056605

therefore k=6

2. mid-point=lower class limit + upper class limit/2

therefore 17+28/2 = 45/2 = 22.5

3. Frequency:

kg frequency

17 3

18 2

19 3

20 3

22 8

23 4

24 3

25 4

27 1

28 2

___________

Total= 33

4. cumulative frequency:

kg frequency cumulative frequency

17 3 3

18 2 5

19 3 8

20 3 11

22 8 19

23 4 23

24 3 26

25 4 30

27 1 31

28 2 33

Answer 2

1. Sample: A sample is a proprotion or part of the population from which information is gathered.

2. Population: Population is defined as the entire group about which information is desired.

3. Continuous variable: A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. A continuous variable is one for which, within the limits the variable ranges, any value is possible.

4. Discrete variable: A discrete variable is a variable whose value is obtained by counting. They are variables or data that exist only as whole numbers and are not divisible.

5. Statistics: Statistics is the scientific method of collecting, organising, summarising, presenting and analysing of data

6. Data: Data could be defined as a collection of facts such as numbers, words, measurements, observations, or even just description of things.

it could also be defined as the raw information from which statistics are created.

Ani Peace Ngozi

2021/245427

anipeacengozi@gmail.com

2i, Sample:sample can be defined as a selection of examples of a class of objects, whose characteristics are used to infer those of the whole class or population. Sampling is used where it would be impossible, too slow, or too costly to examine the entire population. Inference from sample to population constitutes the subject matter of statistics.

Ii, Population:this can be seen as the total amount or headcount of people or objects in a given data.

Iii, Continuous variable:A variable is said to be continuous or have a continuous distribution if it can assume any value from a continuous range. The range can be infinite. The cumulative distribution function (cdf) of a continuous random variable is continuous in its domain.

Iv, Discrete valuable:this is a variable which can only take certain particular values, for example integers. This is contrasted with a continuous variable, which can take any value over some interval.

V, statistics: this may be seen as statistics a branch of mathematics dealing with the methods of collection and analysis of samples of data, used to infer the properties, or the unobserved characteristics, of the population.

Vi, Data:this is a raw an unprocessed information.

K= 1+3.3logN

= 1+3.3log(33)

= 6.01

student Age midpoint F CF RF RCF

17-18 17.5 5 5 15.15 4.03

19-20 19.5 6 11 18.18. 8.87

21- 22 21.5 8 19 24.24 15.3

23- 24. 23.5 7 26 21.21 20.9

25 – 26. 25.5 4 30 12.12 24.1

27 – 28 27.5 3 33 9.09 26.6

TOTAL; 33 124

SAMPLE; a smaller and more larger manageable representation of a larger group.

POPULATION ; is a set of similar items or events that is of interest for some question or experiment.

CONTINUOUS VARIABLE ; is a variable that can take an uncountable set of values or infinite set of values.

DISCRETE VARIABLE; It is a variable whose value is obtained by counting.

STATISTICS; It is a study of collection, analysis, interpretation, presentation, and organisation of data.

DATA; data are measurements or observations that are collected as a source of information.

QUESTION ONE

1. Class interval using sturge’s rule. K = 1 + 3.3logN.

K = 1 + 3.3log33.

K = 1 + 3.3(1.5185).

K = 1 + 5.0111.

K = 6.

Class interval are: 17-18 19-20 21-22 23-24 25-26 27-28.

2. MID-POINT; (Upper class boundary + Lower class boundary) / 2. a) (17+18)/2 = 17.5

b) (19+20)/2 = 19.5

c) (21+22)/2 = 21.5

d) (23+24)/2 = 23.5

e) (25+26)/2 = 25.5

f) (27+28)/2 = 27.5.

3. FREQUENCY;

a) 17-18: 5

b) 19-20: 6

c) 21-22: 8

d) 23-24: 7

e) 25-26: 4

f) 27-28: 34.

4. CUMULATIVE FREQUENCY:

a) 17-18: 5

b) 19-20; 11

c) 21-22: 19

d) 23-24: 26

e) 25-26: 30

f) 27-28: 33

5. RELATIVE FREQUENCY: (Frequency /total observations) * 100.

a) 5/33 * 100 = 15.15

b) 6/33 * 100 = 18.18

c) 8/33 * 100 = 24.24

d) 7/33 * 100 = 21.21

e) 4/33 * 100 = 12.12

f) 3/33 * 100 = 9.09.

6. RELATIVE CUMULATIVE FREQUENCY: (Cumulative Frequency /total cumulative frequency) * 100.

a) 5/124 * 100 = 4.03

b) 11/124 * 100 = 8.87

c) 19/124 * 100 = 15.32

d) 26/124 * 100 = 20.97

e) 30/124 * 100 = 24.19

f) 33/124 * 100 = 26.61

QUESTION TWO

1. SAMPLE-

A sample is defined as a smaller and more manageable representation of a larger group usually a population. It is a subset or portion of a population which has the characteristics of that population and is examined in order to try and draw conclusions about the whole using sample estimates. It is divided into random, cluster, stratified sampling etc. 2. POPULATION –

In statistics, population refers to a pool of individuals or objects used for study in order to draw conclusions or make statements. It is a set of items, events , individuals etc which is of interest to be studied or used for experiments. It is from the the population that a portion is carved out for study (sample).

3. DISCRETE VARIABLES-

A discrete variable is a type of variable that takes on distinct, countable values. This variable can only take on specific values and data which can only exist as whole numbers and are not divisible. The values here can be obtained by counting and it assumes s distinct or separate value. Examples of discrete variables are number of planets, number of pupils in a class, number of objects in a collection etc. Discrete variable is also known as categorical variable.

4. CONTINUOUS VARIABLES-

This type of variable can take on any value within a range. Continuous variable represent measurable amounts such as volume, weight etc. It can take on uncountable of infinite sets of values which can be represented in whole numbers, fractions or decimals. The range of numbers here is incomplete and it can assume any value between two values. Examples of these variables are weight of baby elephants, height of students in a class etc.

5. STATISTICS-

Statistics is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data. It can also be defined as the collation and analysis of numerical data to arrive at a specific inference. The two categories of statistics are descriptive and inferential statistics.

6. DATA-

Data is the information used for calculation, analysis, or planning. It is the collection of fact or raw and unorganized information such as words, numbers, symbols etc. The two categories of data include qualitative data (i.e data that deal with description) and quantitative data (i.e data that deals with numbers).,

NAME:

UGWUANYI DUMEBI DOMINIC

REG NO:

2021/241948

DEPARTMENT:

ECONOMICS

DATE:

10/03/2023

1the class interval using the

CLASS INTERVAL USING STURGES RULE= K=1-+3.3LOG (N) =N=EF WHICH IS = 33 ; CLASS

INTER VAL=1+3.3LOG(33) =1+5.01=6.01=6

RELATIVE FREQUENCY=F/N MUITIPLED BY 100/1

RELATIVE CUMULATIVE FREQUENCY=CF/ECF MUITIPLED BY100/1

kg

M.P

FREQ

CF

RF

RCF

17-18

17.5=17+18/2 5

1

ST FREQ=5 15.15=

4.03

19-20

19.5=19+20/2 6

6+5=11

18.18

8.87

21-22

21.5=21+22/2 8

11+8=19

24.24

15.32

23-24

23.5=23+24/2 7

19+7=26

21.21

20.97

25-26

25.5=25+26/2 4

26+4=30

90.91

24.19

27-28

27.5=27+28/2 3

33

100

26.61

EF=33

ECF=124

2 this is basically on some terms

SAMPLES IT IS USUALLY DIFFCULT TO EXAMINE AII MEMBERS OF A POPULATION DUE TO TIME

,COSTAND OTHER CONSTRAINTS .SO WE EXAMINE ONLY A PORTION OF THE POPULATION AND

TRY TO DRAW CONCLUSIONS ABOUT THE WHOLE USING SAMPLE ESTIMATES .THE PROCESS OF

GENERALISING THE RESULTS IN OUR SAMPLE TO THAT OF THE ENTIRE POPULATION IS KNOWN

AS STATISTICAL INFERENCE.

POPULATION: THIS IS THE ENTIRE GROUP OF INDIVIDUALS WE ARE INTERESTED IN MAKING A

STATEMENT ABOUT;IT CAN BE DEFINED AS THE ENTIRE GROUP ABOUT WHICH INFORMATION IS

DESIRED.

A CONTINUOUS VARIABLE: IS ONE FOR WHICH ,WITHIN THE LIMTS THE VARIABLE RANGES,ANY

VALUE IS POSSIBLE,IT CAN TAKE ANY VALUE BETWEEN A CERTAIN SET OF REAL NUMBERS,THE

VALUE GIVEN TO AN OBSERATION FOR CONTINUOUS VARIABLE CAN VALUES AS SMALL AS THE

INTRUMENT OF MEASUREMENT ALLOWS.

DISCRETE VARIABLES: DISCRETE VARIABLES OR DATA ARE KNOWN AS CATEGORICAL

VARIABLES.THEY ARE VARIABLES OR DATA THAT EXIST ONLY AS WHOLE NUMBERS AND NOT

DIVISIBLE. A DISCRETE VARIABLE CAN ON A FINITE NUMBER OF NUMERICAL

VALUES,CATEGORIES OR CODES.

STATISTICS: IT CAN BE DEFINED AS A FIELD OF STUDY CONCERNING THE LAYOUT OF

EXPERIMENT,COLLECTION,CALCULATIONS,SUMMARIZATION AND ANALYSIS OF DATA.IT AISO

INVOLUES INTERPRETATION OF RESULTS OR DRAWING OF INFERENCE.

DATA: IS A NUMERICALSTATEMENT OF FACTS IN A SPECIFIC SPEED OF ENQUIRY OR SIMPLY

NUMBERS WHICH MAY RESULT FROM TAKING

MEASUREMENTS;EG=RECORDING,HEIGHTS,WEIGHT OR TEMPERATURE MEASUREMENTS.SSS

NAME:

UGWUANYI DUMEBI DOMINIC

REG NO:

2021/241948

DEPARTMENT:

ECONOMICS

DATE:

10/03/2023

1

CLASS INTERVAL USING STURGES RULE= K=1-+3.3LOG (N) =N=EF WHICH IS = 33 ; CLASS

INTER VAL=1+3.3LOG(33) =1+5.01=6.01=6

RELATIVE FREQUENCY=F/N MUITIPLED BY 100/1

RELATIVE CUMULATIVE FREQUENCY=CF/ECF MUITIPLED BY100/1

kg

M.P

FREQ

CF

RF

RCF

17-18

17.5=17+18/2 5

1

ST FREQ=5 15.15=

4.03

19-20

19.5=19+20/2 6

6+5=11

18.18

8.87

21-22

21.5=21+22/2 8

11+8=19

24.24

15.32

23-24

23.5=23+24/2 7

19+7=26

21.21

20.97

25-26

25.5=25+26/2 4

26+4=30

90.91

24.19

27-28

27.5=27+28/2 3

33

100

26.61

EF=33

ECF=124

SAMPLES IT IS USUALLY DIFFCULT TO EXAMINE AII MEMBERS OF A POPULATION DUE TO TIME

,COSTAND OTHER CONSTRAINTS .SO WE EXAMINE ONLY A PORTION OF THE POPULATION AND

TRY TO DRAW CONCLUSIONS ABOUT THE WHOLE USING SAMPLE ESTIMATES .THE PROCESS OF

GENERALISING THE RESULTS IN OUR SAMPLE TO THAT OF THE ENTIRE POPULATION IS KNOWN

AS STATISTICAL INFERENCE.

POPULATION: THIS IS THE ENTIRE GROUP OF INDIVIDUALS WE ARE INTERESTED IN MAKING A

STATEMENT ABOUT;IT CAN BE DEFINED AS THE ENTIRE GROUP ABOUT WHICH INFORMATION IS

DESIRED.

A CONTINUOUS VARIABLE: IS ONE FOR WHICH ,WITHIN THE LIMTS THE VARIABLE RANGES,ANY

VALUE IS POSSIBLE,IT CAN TAKE ANY VALUE BETWEEN A CERTAIN SET OF REAL NUMBERS,THE

VALUE GIVEN TO AN OBSERATION FOR CONTINUOUS VARIABLE CAN VALUES AS SMALL AS THE

INTRUMENT OF MEASUREMENT ALLOWS.

DISCRETE VARIABLES: DISCRETE VARIABLES OR DATA ARE KNOWN AS CATEGORICAL

VARIABLES.THEY ARE VARIABLES OR DATA THAT EXIST ONLY AS WHOLE NUMBERS AND NOT

DIVISIBLE. A DISCRETE VARIABLE CAN ON A FINITE NUMBER OF NUMERICAL

VALUES,CATEGORIES OR CODES.

STATISTICS: IT CAN BE DEFINED AS A FIELD OF STUDY CONCERNING THE LAYOUT OF

EXPERIMENT,COLLECTION,CALCULATIONS,SUMMARIZATION AND ANALYSIS OF DATA.IT AISO

INVOLUES INTERPRETATION OF RESULTS OR DRAWING OF INFERENCE.

DATA: IS A NUMERICALSTATEMENT OF FACTS IN A SPECIFIC SPEED OF ENQUIRY OR SIMPLY

NUMBERS WHICH MAY RESULT FROM TAKING

MEASUREMENTS;EG=RECORDING,HEIGHTS,WEIGHT OR TEMPERATURE MEASUREMENTS.SSS

NAME:

UGWUANYI DUMEBI DOMINIC

REG NO:

2021/241948

DEPARTMENT:

ECONOMICS

DATE:

10/03/2023

1

CLASS INTERVAL USING STURGES RULE= K=1-+3.3LOG (N) =N=EF WHICH IS = 33 ; CLASS

INTER VAL=1+3.3LOG(33) =1+5.01=6.01=6

RELATIVE FREQUENCY=F/N MUITIPLED BY 100/1

RELATIVE CUMULATIVE FREQUENCY=CF/ECF MUITIPLED BY100/1

AGE

M.P

FREQ

CF

RF

RCF

17-18

17.5=17+18/2 5

1

ST FREQ=5 15.15=

4.03

19-20

19.5=19+20/2 6

6+5=11

18.18

8.87

21-22

21.5=21+22/2 8

11+8=19

24.24

15.32

23-24

23.5=23+24/2 7

19+7=26

21.21

20.97

25-26

25.5=25+26/2 4

26+4=30

90.91

24.19

27-28

27.5=27+28/2 3

33

100

26.61

EF=33

ECF=124

2

SAMPLES IT IS USUALLY DIFFCULT TO EXAMINE AII MEMBERS OF A POPULATION DUE TO TIME

,COSTAND OTHER CONSTRAINTS .SO WE EXAMINE ONLY A PORTION OF THE POPULATION AND

TRY TO DRAW CONCLUSIONS ABOUT THE WHOLE USING SAMPLE ESTIMATES .THE PROCESS OF

GENERALISING THE RESULTS IN OUR SAMPLE TO THAT OF THE ENTIRE POPULATION IS KNOWN

AS STATISTICAL INFERENCE.

POPULATION: THIS IS THE ENTIRE GROUP OF INDIVIDUALS WE ARE INTERESTED IN MAKING A

STATEMENT ABOUT;IT CAN BE DEFINED AS THE ENTIRE GROUP ABOUT WHICH INFORMATION IS

DESIRED.

A CONTINUOUS VARIABLE: IS ONE FOR WHICH ,WITHIN THE LIMTS THE VARIABLE RANGES,ANY

VALUE IS POSSIBLE,IT CAN TAKE ANY VALUE BETWEEN A CERTAIN SET OF REAL NUMBERS,THE

VALUE GIVEN TO AN OBSERATION FOR CONTINUOUS VARIABLE CAN VALUES AS SMALL AS THE

INTRUMENT OF MEASUREMENT ALLOWS.

DISCRETE VARIABLES: DISCRETE VARIABLES OR DATA ARE KNOWN AS CATEGORICAL

VARIABLES.THEY ARE VARIABLES OR DATA THAT EXIST ONLY AS WHOLE NUMBERS AND NOT

DIVISIBLE. A DISCRETE VARIABLE CAN ON A FINITE NUMBER OF NUMERICAL

VALUES,CATEGORIES OR CODES.

STATISTICS: IT CAN BE DEFINED AS A FIELD OF STUDY CONCERNING THE LAYOUT OF

EXPERIMENT,COLLECTION,CALCULATIONS,SUMMARIZATION AND ANALYSIS OF DATA.IT AISO

INVOLUES INTERPRETATION OF RESULTS OR DRAWING OF INFERENCE.

DATA: IS A NUMERICALSTATEMENT OF FACTS IN A SPECIFIC SPEED OF ENQUIRY OR SIMPLY

NUMBERS WHICH MAY RESULT FROM TAKING

MEASUREMENTS;EG=RECORDING,HEIGHTS,WEIGHT OR TEMPERATURE MEASUREMENTS.SSS

NAME:

UGWUANYI DUMEBI DOMINIC

REG NO:

2021/241948

DEPARTMENT:

ECONOMICS

DATE:

10/03/2023

1

CLASS INTERVAL USING STURGES RULE= K=1-+3.3LOG (N) =N=EF WHICH IS = 33 ; CLASS

INTER VAL=1+3.3LOG(33) =1+5.01=6.01=6

RELATIVE FREQUENCY=F/N MUITIPLED BY 100/1

RELATIVE CUMULATIVE FREQUENCY=CF/ECF MUITIPLED BY100/1

AGE

M.P

FREQ

CF

RF

RCF

17-18

17.5=17+18/2 5

1

ST FREQ=5 15.15=

4.03

19-20

19.5=19+20/2 6

6+5=11

18.18

8.87

21-22

21.5=21+22/2 8

11+8=19

24.24

15.32

23-24

23.5=23+24/2 7

19+7=26

21.21

20.97

25-26

25.5=25+26/2 4

26+4=30

90.91

24.19

27-28

27.5=27+28/2 3

33

100

26.61

EF=33

ECF=124

2

SAMPLE: IT IS USUALLY DIFFCULT TO EXAMINE AII MEMBERS OF A POPULATION DUE TO TIME

,COSTAND OTHER CONSTRAINTS .SO WE EXAMINE ONLY A PORTION OF THE POPULATION AND

TRY TO DRAW CONCLUSIONS ABOUT THE WHOLE USING SAMPLE ESTIMATES .THE PROCESS OF

GENERALISING THE RESULTS IN OUR SAMPLE TO THAT OF THE ENTIRE POPULATION IS KNOWN

AS STATISTICAL INFERENCE.

POPULATION: THIS IS THE ENTIRE GROUP OF INDIVIDUALS WE ARE INTERESTED IN MAKING A

STATEMENT ABOUT;IT CAN BE DEFINED AS THE ENTIRE GROUP ABOUT WHICH INFORMATION IS

DESIRED.

A CONTINUOUS VARIABLE: IS ONE FOR WHICH ,WITHIN THE LIMTS THE VARIABLE RANGES,ANY

VALUE IS POSSIBLE,IT CAN TAKE ANY VALUE BETWEEN A CERTAIN SET OF REAL NUMBERS,THE

VALUE GIVEN TO AN OBSERATION FOR CONTINUOUS VARIABLE CAN VALUES AS SMALL AS THE

INTRUMENT OF MEASUREMENT ALLOWS.

DISCRETE VARIABLES: DISCRETE VARIABLES OR DATA ARE KNOWN AS CATEGORICAL

VARIABLES.THEY ARE VARIABLES OR DATA THAT EXIST ONLY AS WHOLE NUMBERS AND NOT

DIVISIBLE. A DISCRETE VARIABLE CAN ON A FINITE NUMBER OF NUMERICAL

VALUES,CATEGORIES OR CODES.

STATISTICS: IT CAN BE DEFINED AS A FIELD OF STUDY CONCERNING THE LAYOUT OF

EXPERIMENT,COLLECTION,CALCULATIONS,SUMMARIZATION AND ANALYSIS OF DATA.IT AISO

INVOLUES INTERPRETATION OF RESULTS OR DRAWING OF INFERENCE.

DATA: IS A NUMERICALSTATEMENT OF FACTS IN A SPECIFIC SPEED OF ENQUIRY OR SIMPLY

NUMBERS WHICH MAY RESULT FROM TAKING

MEASUREMENTS;EG=RECORDING,HEIGHTS,WEIGHT OR TEMPERATURE MEASUREMENTS.SSS

Name:Okoronkwo Chimuanya Sharon

Matric number:2021/241960

Department:Economics

Course code:ECO131

Answers to the questions

Question1

Class interval Midpoint F CF RF RCF

17_18 17.5 5 5 15.5 15.15

19_20 19.5 6 11 18.18 3.3

21_22 21.5 8 19 24.24 57.57

23_24 23.5 7 26 21.21 78.78

25_26 25.5 4 30 12.12 90.90

27_28 27.5 3. 33 9.09 100

Total 33

Question 2:

5:statistics, the science of collecting, analyzing, presenting, and interpreting data.

Name:Okoronkwo Chimuanya Sharon

Department:Economics Department

Course code :ECO131

Year: Eco 025 first year

Question

22, 20, 19, 25, 22, 17, 28, 20, 22, 23, 17

18, 24, 25, 22, 20, 23, 25, 22, 28, 19, 22

25, 27, 23, 24, 17, 18, 22, 19, 22, 23, 24

Compute the table as follows:

The class interval using sturge rule

Mid-point

Frequency

Cumulative Frequency

Relative Frequency

Relative Cumulative Frequency

QUESTION TWO

Write a brief note on the following:

Sample

Population

Continuous Variable

Discrete variable

Statistics

Data

Answers to the questions:

Question1

Class interval Midpoint F CF RF RCF

17_18 17.5 5 5 15.5 15.15

19_20 19.5 6 11 18.18 3.3

21_22 21.5 8 19 24.24 57.57

23_24 23.5 7 26 21.21 78.78

25_26 25.5 4 30 12.12 90.90

27_28 27.5 3. 33 9.09 100

Total 33

Question 2:

5:statistics, the science of collecting, analyzing, presenting, and interpreting data.

1.class interval |m.point |freq |c.f |r.f | |r.c.f|

17-18. 17.5 5 5. 15.2%. 15.2%

19-20 19.5 6 11 18.2 %. 33.4%

21-22. 21.5 8. 19. 24.2%. 57.6%

23-24. 23.5. 7. 26. 21.2%. 78.8%

25-26. 25.5. 4. 30. 12.1%. 90.9%

27-28. 27 5. 3. 33. 9.1%. 100%

2.i.sample:it is a smaller and more manageable representation of a larger group

ii..Population:it is a set of similar items of which id of for some experiment

iii:continious variable:this is a variable thdt can take an uncountable set of or infinite set of value

iv:Discrete variable:it is a variable tgat takes on distinct,countable values

v:statistics:it is the collation and analysis of numerical data to arrive at a specific inference

vi:Data:data is measurement or observation tgat are collected as a source of information.

NAME :AMOGU SUNNY NDUKWE

REG NUMBER: 2021/245590

DEPARTMENT: ECONOMICS

(QUESTION ONE)

Firstly, get the number of classes

Using Sturge Rule;

k = 1 + 3.322( log n)

Where:

k = the number of classes

n = the number of observations in the data set. Which is 33.

Therefore, number of classes is:

k= 1+ 3.322(log 33)

k= 6

Knowing this, we can form a table

Class Interval

Midpoint

Frequency

Cumulative Frequency

Relative Frequency

Relative Cumulative Frequency

17-18

17.5

5

5

15.15

4.03

19-20

19.5

6

11

18.18

8.87

21-22

21.5

8

19

24.24

15.32

23-24

23.5

7

26

21.21

20.96

25-26

25.5

4

30

12.12

24.19

27-28

27.5

3

33

9.09

26.61

(QUESTION TWO)

1.) SAMPLE: A sample is quite simply, a subset of a given population in a statistical study. This is used to make inference about the population. It is commonly used in place of the population to its comparative ease as regards data collection, its comparative cost-effectiveness, etc.

2.) POPULATION: This is the total number of target observations or elements in a statistical study. Data collection from the population is normally eschewed in favour of a sample from it due to the previously mentioned reasons. However, it is sometimes used, especially when the results to be gotten from the statistical study would be incomplete or inconclusive without the inclusion of every element.

3.) CONTINUOUS VARIABLE: This is a type of variable which can assume any numerical value in a given range of an infinite number of values. Continuous variables have valid fractional and decimal values. Also, they can be meaningfully split into smaller parts. A continuous variable is measured, rather than counted. Examples of continuous variables are:

age

height

weight

temperature

time, etc.

4.) DISCRETE VARIABLE: This is a distinct variable. Meaning that this type of variable can only assume a specific value. Also this value cannot be subdivided into smaller parts like the continuous variable. Discrete variables are counted, rather than measured, and cannot have fractional or decimal values. Examples of discrete variables are:

Number of companies listed on the NGX

The total working population of a country

Number of universities, etc

5.) STATISTICS: Statistics is a term that has different but related meanings. On one hand, statistics can refer to numerical facts such as averages, percentages, index numbers, etc which are used to understand a variety of situations in a variety of areas, such as business, economics, etc. On the other hand, statistics can be defined as the art or science of collecting, analyzing, presenting and interpreting data so as to enable decision makers understand certain situations and make the best decisions possible.

6.) DATA: Data are the facts and figures which are collected, analyzed, and summarized for presentation and interpretation. All the data collected in a particular study are referred to as the data set for the study. It is important to remember that data are the raw, unprocessed information.

NAME : AMOGU SUNNY

REG NUMBER: 2021/245590

EMAIL : amogusunny77@gmail.com

DEPARTMENT: ECONOMICS.

THANK YOU

midpoint: 1. 15+17÷2=16.

2:. 18+20 ÷2=19

3: 21+23÷2=22

4: 24+26÷2=25

5:. 27+29÷2=28

frequency

16×3 =48

19×8=152

22×12 =264

25×7=175

28×3=84

cumulative frequency

3

8+3=11

12+11=23

7+23=30

3+30=33

relative frequency

3×100÷33=9.09

8×100÷33=24.24

12×100÷33= 36.36

7×100÷33=21.21

3×100÷33=9.09

question no 2

sample: sample Is a smaller manageable version of a larger group , it’s a subset containing the characteristics of a larger population , samples are used in statistical testing , the use of samples allow researchers to conduct their research with a more manageable data and in a timely manner , a sample can also be defined as an unbiased number of observations taken from a population

population:

it’s all the elements from the data set and measurable characteristics , a population is any complete group with at least one characteristic in common , populations are not just people , populations may consist of but are not limited to people , animals , businesses , buildings , objects or events

continuous variable:

a variable is said to be continuous if it can assume an infinite number of real values within a given interval . the body mass is an example of continuous variable , even though one can define a value for body mass

discreet variable:

it’s a variable that takes on distinct , countable values , it’s a variable that takes on any value within a range , and the number of possible values within that range is infinite , discreet values have values that are counted

statistics:

statistics is the practice or science of collecting and analysing numerical data in large quantities, especially for the purpose of inferring proportions in a whole from those in a representative sample , statistics can be used to predict the future , determine the probability that a specific event will happen , or help answer questions about a survey

data:

data are measurements or observations collected as a source of information, the data are individual pieces of factual information recorded and is used for the purpose of analysis process, the 2 processes of data analysis are interpretation and presentation , types of data nominal Data, discreet data, continuous data, ordinal

Name: Ibiam Nkemdilim Clara

Reg no: 2021/241336

Question1

Class interval Midpoint F CF RF RCF

17_18 17.5 5 5 15.5 15.15

19_20 19.5 6 11 18.18 3.3

21_22 21.5 8 19 24.24 57.57

23_24 23.5 7 26 21.21 78.78

25_26 25.5 4 30 12.12 90.90

27_28 27.5 3. 33 9.09 100

Total 33

Question 2:

5:statistics, the science of collecting, analyzing, presenting, and interpreting data.

Name:Ibiam Nkemdilim Clara

Reg no: 2021/241336

Question1

Class interval Midpoint F CF RF RCF

17_18 17.5 5 5 15.5 15.15

19_20 19.5 6 11 18.18 3.3

21_22 21.5 8 19 24.24 57.57

23_24 23.5 7 26 21.21 78.78

25_26 25.5 4 30 12.12 90.90

27_28 27.5 3. 33 9.09 100

Total 33

Question 2:

5:statistics, the science of collecting, analyzing, presenting, and interpreting data.

Name: UDEZE Mmesoma Marycynthia

Reg.Number: 2020/247504

Department: Economics

Course: Introduction to Economic Statistics

Course Code: Eco 131

Answers to question 1

CLASS INTERVAL ; 17-18, 19-20,21-22,23-24,25-26,27-28

MID POINT; 17.5,19.5,21.5,23.5,25.5,27.5

FREQUENCY ; 5,6,8,7,4,3=33

CUMULATIVE FREQUENCY ; 5,11,19,26,30,33=124

RELATIVE FREQUENCY;15.15,18.18,24.24,21 21,12.12,9.09

RELATIVE CUMULATIVE FREQUENCY;4.03,8.87,15.32,20.96,24.19,26.61,=99.98

Answers to question 2

1. Sample: A sample can be defined as a smaller and more manageable representation of a large group.it can be further defined as the methods of collecting, summarizing, presenting, analyzing and interpreting numerical variables or sample data.

2. Population: A population can be defined as the entire group of individual which we are interested in making a statement about. it can be further said to be the entire group about which information is desired.

3.Continous variable: A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values.

4. Discrete variable: A discrete variable is a variable whose value is obtained by counting. that is it’s variables are countable in a finite amount of time.

5.Statistics: Statistics can be referred to as numerical facts such as numbers of events occurring at a particular time etc and it can be further defined as the study which involves the collecting, analyzing of numerical data or facts.

4. Data: Data can be defined as the collect8of facts such as numbers, words, measurements, observations or even just description of things.

Name: FELIX FAVOUR CHIDUMEBI

Reg No: 2021/241943

Email: felixfavour419@gmail.com

1. The class interval using sturge rule:

Sturge rule formula= k= 1 + 3.322 logN

Where N= Total number of observations.

K= 1 + 3.322 log33

K= 1 + 3.322(1.5185)

K= 1 + 5.0445

K= 6.0445

K= 6~

Class interval= Range/1 + 3.322 logN

Range=Highest value – Lowest value

Range= 28 – 17 = 11

Class interval= 11/ 1+3.322log33

= 11/6

=1.83

= 2~

Class Interval Mid-point F. C.F. R.F. R.C.F

17 – 18 17.5 5 5 15.15 15.15

19 – 20 19.5 6 11 18.18 33.33

21 – 22 21.5 8 19 24.24 57.57

23 – 24 23.5 7 26 21.21 78.78

25 – 26 25.5 4 30 12.12 90.90

27 – 28 27.5 3 33 9.09 100

Total=

33

Name: onyeocha blessing chinyere. Department: economic. Matric no 2021/246563. Email: Onyeocha blessing2@gmail.com Course: Economic statistics. Section 1. According to sturge rule the class interval is K =1+3.3logN,K=1+log33×32k=6.01 Section 2. A sample refers to a smaller, manageble version of a large group. It is a subset containing the characteristics of a large population. Sample are used in statistical testing when population size are too large for the test to include all possible member or observation. A sample should be represent the population as a whole and not reflect any bias toward a specific attribute. Types of sample. Simple random: sampling is deal if every entity in the population is identical. (2) Population is the total number of observation (i.e individuals, animals,items,data) it includes all the element from the data set and measurable characteristics of population such as mean and standard deviation as known as a parameter, example all living in Nigeria indicate the population of Nigeria. There are different types of population. (I). Finite population ( ii). Infinite population ( III). Existent population ( iv). Hypothetical population. 3 Continuous variable is a variable which can take an uncountable set of value or infinite set of value. Types of continuous variables. (I). Instant variable. (ii). Ratio variable. (I). Instant variable is a distance or level between each category that is equal and statics. (ii). Ratio variable this variable has only one variable from an interval variable. 4. Discrete variable is a variable that take on distinct, countable value. Example of discrete variable are (I). Number for a particular politicians (ii) . Years of schooling. (III). Number of goals made in a soccer match. (iv). Votes for a particular politicians. 5. Statistics is a method of interpreting analysing and summarising the data or statistics is a branch of applied mathematics analysis, and inference of conclusion from quantitive data. Three types of statistics are (i) mean. (ii))medians (iii) mode. 6. Data can be systematic record of a particular quantity. The data is classified into majority 4 categories. (I) norminal data (ii). Ordinal data (iii) discrete data (iv). Continuous data.

Using sturge rule

K= 1+3.3Log(n)

Question 1

Class interval: 17-18, 19-20, 21-22, 23-24, 25-26,

27-28

Mid point: 17.5, 19.5, 21.5, 23.5, 25.5, 27.5

Frequently: 5, 6, 8, 7, 4, 3=33

Cumulative frequency: 5, 11, 19, 26, 30, 33=124

R frequently: 15.15, 18.18, 24.24, 21.21, 12.12, 9.09

Relative Cumulative frequency: 4.03, 8.87, 15.32, 20.96, 24.19, 26.61=99.98

QUESTION 2

A sample is a smaller set of data that a researcher chooses or selects from a larger population using a pre-defined selection method. These elements are known as sample points, sampling units, or observations.

Methods of sample

Probability sampling is a method of deriving a sample where the objects are selected from a population-based on probability theory. This method includes everyone in the population, and everyone has an equal chance of being selected. Hence, there is no bias whatsoever in this type of sample.

Each person in the population can subsequently be a part of the research. The selection criteria are decided at the outset of the market research study and form an important component of research.

Non probability sample

The non probability sample method uses the researcher’s discretion to select a sample. This type of sample is derived mostly from the researcher’s or statistician’s ability to get to this sample.

This type of sampling is used for preliminary research where the primary objective is to derive a hypothesis about the topic in research. Here each member does not have an equal chance of being a part of the sample population, and those parameters are known only post-selection to the sample.

POPULATION

A population is the group of people from which a statistical sample is taken in statistics. Therefore, a population is any collection of people who have something in common. A statistically substantial subset of a population, rather than the complete population, may be referred to as an example or sample. In addition to this, a statistical analysis of a sample needs to provide an estimate of the standard deviation, or the standard error, of its findings from the total population. Only a whole or complete population analysis would have zero standard error

COnTINOUS VARIABLE

A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range. Thus, the range of real numbers between x and y with x, y ∈ R and x ≠ y; is said to be uncountable and infinite.

In continuous optimization problems, different techniques of calculus are often used in which the variables are continuous. Also, the probability distributions of continuous variables can be stated in expressions of probability density functions in statistical theory.

Types of Continuous Variables

There are two types of continuous variables namely interval and ratio variables.

Instant variable

Ratio variable

Instant variable

A variable can be defined as the distance or level between each category that is equal and static. For example, what is the average day time temperature in Bangalore during the summer?

Ratio variable

Ratio variable is another type of continuous variable. This type of variable has only one variation from an interval variable. The only difference is that the ratio between the scores gives information regarding the relationship between the responses.

Difference between Discrete and Continuous Variable

Below are the main differences between discrete and continuous variables.

Discrete Variable

Continuous Variable

It is a variable whose value is obtained by counting.

It is a variable whose value is obtained by measuring.

Examples:

Number of planets around the Sun

Number of students in a class

Examples:

Number of stars in the space

Height or weight of the students in a particular class

Range of specified numbers is complete.

Range of specified numbers is incomplete, i.e. infinite.

It assumes a distinct or a separate value.

It assumes any value between two values.

Continuous Variable Example

Continuous variables would take forever to count. In fact, we would get to forever and never finish counting them. For example, take an age. We can’t count “age”. Because it would literally take forever. For example, it could be 37 years, 9 months, 6 days, 5 hours, 4 seconds, 5 milliseconds, 6 nanoseconds, 77 picoseconds…and so on.

DISCRETE VARIABLE

A discrete variable is a variable that takes on distinct, countable values. In theory, you should always be able to count the values of a discrete variable.

Examples

Examples of discrete variables include:

Years of schooling

Number of goals made in a soccer match

Number of red M&M’s in a candy jar

Votes for a particular politician

Number of times a coin lands on heads after ten coin tosses

All of these variables take a finite number of values that you can count. They are examples of discrete variables.

STATISTICS

Statistics is simply defined as the study and manipulation of data. As we have already discussed in the introduction that statistics deals with the analysis and computation of numerical data. Let us see more definitions of statistics given by different authors here.

According to Merriam-Webster dictionary, statistics is defined as “classified facts representing the conditions of a people in a state – especially the facts that can be stated in numbers or any other tabular or classified arrangement”.

According to statistician Sir Arthur Lyon Bowley, statistics is defined as “Numerical statements of facts in any department of inquiry placed in relation to each other”

.

Basics of Statistics

The basics of statistics include the measure of central tendency and the measure of dispersion. The central tendencies are mean, median and mode and dispersions comprise variance and standard deviation.

Mean is the average of the observations. Median is the central value when observations are arranged in order. The mode determines the most frequent observations in a data set.

Variation is the measure of spread out of the collection of data. Standard deviation is the measure of the dispersion of data from the mean. The square of standard deviation is equal to the variance.

DATA

Data types are important concepts in statistics, they enable us to apply statistical measurements correctly on data and assist in correctly concluding certain assumptions about it

Having an adequate comprehension of the various data types is significantly essential for doing Exploratory Data Analysis or EDA since you can use certain factual measurements just for particular data types.

SImilarly, you need to know which data analysis and its type you are working to select the correct perception technique. You can consider data types as an approach to arrange various types of variables.

If you go into detail then there are only two classes of data in statistics, that is Qualitative and Quantitative data. But, after that, there is a subdivision and it breaks into 4 types of data. Data types are like a guide for doing the whole study of statistics correctly!

1. Using sturge rule,

K = 1+3.3Log(N)

K= 1+ 3.3Log33

Therefore K =6.0

2. The midpoint of the yield = 17.5,19.5,21.5,23.5,25.5,27.5

Calculations:- for the interval of 17-18, 17+18/2 = 17.5. The same method is followed to solve the rest.

3. Frequency:- 5,6,8,7,4,3 =33

4. Cumulative frequency:-5,11,19,26,30,33 =124

Calculations:- 5 is constant, then addition of frequency and cumulative frequency ( 5+6= 11). The same method is followed for the rest.

5. Relative frequency:- 0.15, 0.18, 0.24, 0.21, 0.12, 0.09.

Calculations:- dividing a unit of a frequency by the total of a frequency ( 5/33= 0.15)

6. R.C.F:- 0.15, 0.33, 0.57, 0.78, 0.9, 0.99

Calculations:- this is the addition of relative frequencies. (0.15 being constant, 0.15 +0.18= 0.33).the rest solved in that manner

2.

a. Sample:- it is a part or portion of the population on which further analysis is sought

b. Population:- This is a group or collection of items of the same nature which are under study. E.g, groups of consumer in a market, number of retired workers in a country.

c. Continuous variable:- it is a variable which can take an uncountable set of value or infinite set of values. E.g the height of a student. The height of a student can be considered any value.

d. Discrete variable:- it is a quantitative variable that are typically obtained by measuring or counting respectively. e.g the score given by a judge to a gymnast in a competition. The range is 0 to 10 and the score is always given to one decimal ( e.g a score of 8.5)

e. Statistics:- it is a science or study of collecting, analyzing, presenting, and interpreting data.

f. Data:- is an information in it’s original form. They can also be stated as fact and statistics collected together for reference or analysis.

Name:Ugochi Marylillian Ogonnaya

Faculty: Faculty of the Social Sciences

Department: Economics

Reg No.:2021/247082

Brief notes on the following:

1.Sample

2 Population

3.Continuous Variable

4.Discrete Variable

5.Statistics

6.Data

Solutions

1.Sample

A sample is a part of the population we can actually observe.A sample is a portion or part of the population from which information is gathered. Sampling is a procedure by which one or more members of a population are selected from the population the objective is to make certain observations about the members of the sample and then on the basis of these results to draw valid conclusions about the characteristics of the entire population. We have five types of sample which are Random, Systematic, Convenience,Cluster and Stratified

2.Population.

Population is the total number of people inhabiting a particular place at a time. Population is the entire group of which information is desired. To analyse a population, a census is taken. A census is a total count of every entity in the population,

For example;

1. All girls of age 15 and 18 in Nigeria

2. All employees of the University of Nigeria nsukka campus

3.All markets_bound goat

3.Continuous Variable

A continuous variable is one for which within the limits the variable range any value is possible. Continuous variable can take any value between a certain set of real numbers. The value given to an observation for a continuous variable can include values as small as the instrument of measurement allows. For example the variable “time to solve an algebra problem” is continuous since it could take 2 minutes , 2.13 minutes, 5 minutes e t c to finish the problem however the variable “number of correct answers on a 100-point multiple choice test” is not a continuous variable since it is not possible to get 54.12 problems correct. Continuous variables is also known as quantitative variables and can exist both as whole numbers and or fractions they can be decimalised and have the attributes of such division into smaller units. Examples include the height of a group of students, length of a pair of trouser.Other examples of continuous variable include Heights, time, age and temperature. Continuous variable can be classified into interval scale variables ,continuous ordinal variables and ratio scale variables.

4.Discrete Variable

Discrete variables or data are also known as categorical variables. They are variables or data that exist only as whole numbers and are not divisible. A discrete variable can take on a finite number of numerical values categories or code. Discrete variables can be classified into the categories

1.Nominal variables

2.Ordinal variables

3.Dummy variables from quantitative variables

4.Preference variables

5.Multiple response variables

5.Statistics

Statistics is the numerical fact such as number of events occurring in time or the number of people living in a particular area. It also involves the study of ways of collecting analysing and interpreting numerical facts or numerical data. Statistics entails the fury and methods of collecting organising presenting analysing and interpreting data sets so as to determine the Essential characteristics. It is the development and application of methods to the collection analysis and interpretation of observed information from planned investigations. Statistics is used for condensation, comparison, forecasting, estimation and testing of hypothesis.

6.Data

Data is a collection of facts such as numbers words measurement observations or even just descriptions of things. It is also information in raw or unorganised form(such as alphabet numbers or symbols) that refer to or represent conditions ideas or objects that could be qualitative that is, data that deals with description or quantitative that is, data that deals with numbers. Data collection is a fundamental aspect of research. Data are required for empirical analysis and other forms of analysis. We have primary data and secondary data .

(2)a) sample: sample is the act of selecting one or more members of a population to make observations about the members selected and on the basis of the results,to draw valid conclusion about the characteristics of the entire population.

(2b) population:it can be defined as the total number of people living within a country or a geographical area at a particular time. it refers to the total number of children, adult men and women, youths (boys and girls), living in a given geographical area, which may be a town, village or a country.

(2c) continuous variable: it is defined as a variable that ranges within a limit.it can also take any value between a certain set of real numbers.

(2d) Discrete variables:it is also known as categorical variables.they are variables or data that exists only as whole numbers and are not divisible.it can take on a finite number of numerical values , categories or code.

(2e) statistics: statistics refers to numerical facts such as the number of events occurring in time or the number of people living in a particular area. it also involves the collecting, analyzing and interpreting numerical facts or numerical data.

(2f) Data: data are facts or raw facts or a collection of facts such as numbers, words, measurements, observations or description of things.

Question1

Class interval Midpoint F CF RF RCF

17_18 17.5 5 5 15.5 15.15

19_20 19.5 6 11 18.18 3.3

21_22 21.5 8 19 24.24 57.57

23_24 23.5 7 26 21.21 78.78

25_26 25.5 4 30 12.12 90.90

27_28 27.5 3. 33 9.09 100

Total 33

Question 2:

5:statistics, the science of collecting, analyzing, presenting, and interpreting data.

Name: Okoro Emmanuel Chukwubuikem

Reg no: 10777812fj

Department: Economics

Email Address: okoroe682@gmail.com

Stuge rule K= 1+3.3 log n

N=Total number of observations

Log= logarithm of the number

K= Number of class interval

Then k=1+3.3 log(33)=6

Sizes of class interval= range÷number ofclass interval = 28-17÷6= 2

Class Mid-point Frequency

17-18 17.5 5

19-20 19.5 6

21-22 21.5 8

23-24 23.5 7

25-26 25.5 4

27-28 27.5 3

Cumulative. Relative. Relative

Frequency. Frequency. CF

5 15.2 15.2

11 18.2 33.3

19 24.2 57.6

26 21.2 78.8

30 12.1 90.9

33 9.1 100

1. SAMPLE

This is defined as part or portion of a population and it is taken from the population as a representation of it. In other words sampling is a procedure by which one or more members of a population are selected from the population.

Example, a height of students in the faculty of health sciences taken to represent the height of students in the department. The objective is to make certain observations about the members of the sample, and then, on the basis of these results, to draw valid conclusions about the characteristics of the entire population.

Selecting a Sample

I. Haphazard sample: A Sample selection constructed by arbitrarily selecting individual members of the sample.

2. Random sample: In a random sample there are several methods for constructing random samples. Here only simple random sample is considered. This process operates so that each member of the population has an equal chance of being selected into the sample.

Types of Sampling

There are five types of Sampling namely: Random sampling

Systematic sampling

Convenience sampling

Cluster sampling

Stratified sampling

2. POPULATION

This is the entire collection of items or individuals which one/somebody wishes to examine at a particular time. It is the entire group of individuals that we are interested in making a statement about. It is also described as a largest collection of entities for which we have an interest at a particular time; an entire set of objects, observations,or scores that have something in common. To analyze a population a census is taken.

Examples

All Females between the ages of 16 and 19 in Germany.

All eligible votes in Nigeria

All University of Pennsylvania students

3. CONTINUOUS VARIABLE

If a variable can take on two or more distinct real values so that it can also take all real values between them ( even values that are randomly close together) In this case, the variable is continuous in the given interval.

A continuous variable is a type of variable which can take an uncountable set of values or infinite set of values. Continuous variables can assume any value from a range of values.

Examples: Measurement of height of a plant, bank interest rate, weight of an animal etc

Continuous variables can be classified into the following categories.

1. Interval-scale variables

2. Continuous ordinal variables

3. Ratio-scale variables

4. DISCRETE VARIABLE

This is also known as categorical variables. This is in the case of a variable that can only be counted and represents in a whole number. They exist only as whole numbers and are not divisible. A discrete variable can take on a finite number of numerical values or codes.

Example, number of seeds per cartoon, number of students in economics department, number of seats in a plane etc.

Discrete variables can be classified into the following categories.

1. Nominal variables

2. Ordinal variables

3. Dummy variables from quantitative variables

4. Preference variables

5. Multiple response variables

5. STATISTICS

Derived from the Latin word statisticum collegium (council of states) and the Italian word statista (statesman or politician) It acquired the meaning of the collection and classification of data generally in the 19th century. Introduced into the English in 1791 by Sir John Sinclair.

This can be defined as a field of study consign with layout of experiment, collection, calculation, summarization and analysis of data. It also involves interpretation of result or drawing of inference. The word ‘statistics’ refers to numerical facts such as the number of events occurring in time or the number of people living in a particular area. Statistics has been defined differently by different authors. According to Upton and Cook (2008) , statistics is a scientific method for collecting, organising, summarizing, analysing and presenting data as well as drawing valid inferences or conclusions and making reasonable decisions on the basis of such analysis.

Horace Secrist (n.d) defined it as the aggregate of facts affected to a marked extent by multiplicity of causes, numerically expressed, enumerated or estimated according to a reasonable standard of accuracy, collected in a systematic manner, for a predetermined purpose and placed in relation to each other.

Bowley ( n.d) said that statistics may be rightly called the scheme of averages or numerical statement of facts in any department of enquiry in relation to each other.

Croxton and Cowden ( n.d) defined statistics as the science of collection, presentation, analysis and interpretation of numerical data. According to the definition, there are four basic steps involved in statistics:

1. Collection of data

2. Presentation of data

3. Analysis of data

4. Interpretation of data

6. DATA

This is a numerical statement of fact in a specific field of enquiry or simply numbers which may result from taking measurement. It could be seen as a collection of facts, such as numbers, words, measurements, observations or even just descriptions of things. It could also be seen as information in a raw or unorganized form(such as alphabets, numbers or symbols)that refer to, or represent, conditions, ideas or objects etc.

Examples, recording height, weight or temperature measurement etc

Types of data

Primary data

Secondary data

Primary data: data collected for the first time by an organization and is being used by the organization. It is also described as a raw data or first hand data

Secondary data: A data that has previously been gathered and can be accessed by researchers.

Examples, tax records and social security data, census data, health records data etc.

Name: Okoro Emmanuel Chukwubuikem

Reg no: 10777812fj

Department: Economics

Email Address: okoroe682@gmail.com

Stuge rule K= 1+3.3 log n

N=Total number of observations

Log= logarithm of the number

K= Number of class interval

Then k=1+3.3 log(33)=6

Sizes of class interval= range÷number ofclass interval = 28-17÷6= 2

Class Mid-point Frequency

17-18 17.5 5

19-20 19.5 6

21-22 21.5 8

23-24 23.5 7

25-26 25.5 4

27-28 27.5 3

Cumulative. Relative. Relative

Frequency. Frequency. CF

5 15.2 15.2

11 18.2 33.3

19 24.2 57.6

26 21.2 78.8

30 12.1 90.9

33 9.1 100

1. SAMPLE

This is defined as part or portion of a population and it is taken from the population as a representation of it. In other words sampling is a procedure by which one or more members of a population are selected from the population.

Example, a height of students in the faculty of health sciences taken to represent the height of students in the department. The objective is to make certain observations about the members of the sample, and then, on the basis of these results, to draw valid conclusions about the characteristics of the entire population.

Selecting a Sample

I. Haphazard sample: A Sample selection constructed by arbitrarily selecting individual members of the sample.

2. Random sample: In a random sample there are several methods for constructing random samples. Here only simple random sample is considered. This process operates so that each member of the population has an equal chance of being selected into the sample.

Types of Sampling

There are five types of Sampling namely: Random sampling

Systematic sampling

Convenience sampling

Cluster sampling

Stratified sampling

2. POPULATION

This is the entire collection of items or individuals which one/somebody wishes to examine at a particular time. It is the entire group of individuals that we are interested in making a statement about. It is also described as a largest collection of entities for which we have an interest at a particular time; an entire set of objects, observations,or scores that have something in common. To analyze a population a census is taken.

Examples

All Females between the ages of 16 and 19 in Germany.

All eligible votes in Nigeria

All University of Pennsylvania students

3. CONTINUOUS VARIABLE

If a variable can take on two or more distinct real values so that it can also take all real values between them ( even values that are randomly close together) In this case, the variable is continuous in the given interval.

A continuous variable is a type of variable which can take an uncountable set of values or infinite set of values. Continuous variables can assume any value from a range of values.

Examples: Measurement of height of a plant, bank interest rate, weight of an animal etc

Continuous variables can be classified into the following categories.

1. Interval-scale variables

2. Continuous ordinal variables

3. Ratio-scale variables

4. DISCRETE VARIABLE

This is also known as categorical variables. This is in the case of a variable that can only be counted and represents in a whole number. They exist only as whole numbers and are not divisible. A discrete variable can take on a finite number of numerical values or codes.

Example, number of seeds per cartoon, number of students in economics department, number of seats in a plane etc.

Discrete variables can be classified into the following categories.

1. Nominal variables

2. Ordinal variables

3. Dummy variables from quantitative variables

4. Preference variables

5. Multiple response variables

5. STATISTICS

Derived from the Latin word statisticum collegium (council of states) and the Italian word statista (statesman or politician) It acquired the meaning of the collection and classification of data generally in the 19th century. Introduced into the English in 1791 by Sir John Sinclair.

This can be defined as a field of study consign with layout of experiment, collection, calculation, summarization and analysis of data. It also involves interpretation of result or drawing of inference. The word ‘statistics’ refers to numerical facts such as the number of events occurring in time or the number of people living in a particular area. Statistics has been defined differently by different authors. According to Upton and Cook (2008) , statistics is a scientific method for collecting, organising, summarizing, analysing and presenting data as well as drawing valid inferences or conclusions and making reasonable decisions on the basis of such analysis.

Horace Secrist (n.d) defined it as the aggregate of facts affected to a marked extent by multiplicity of causes, numerically expressed, enumerated or estimated according to a reasonable standard of accuracy, collected in a systematic manner, for a predetermined purpose and placed in relation to each other.

Bowley ( n.d) said that statistics may be rightly called the scheme of averages or numerical statement of facts in any department of enquiry in relation to each other.

Croxton and Cowden ( n.d) defined statistics as the science of collection, presentation, analysis and interpretation of numerical data. According to the definition, there are four basic steps involved in statistics:

1. Collection of data

2. Presentation of data

3. Analysis of data

4. Interpretation of data

6. DATA

This is a numerical statement of fact in a specific field of enquiry or simply numbers which may result from taking measurement. It could be seen as a collection of facts, such as numbers, words, measurements, observations or even just descriptions of things. It could also be seen as information in a raw or unorganized form(such as alphabets, numbers or symbols)that refer to, or represent, conditions, ideas or objects etc.

Examples, recording height, weight or temperature measurement etc

Types of data

Primary data

Secondary data

Primary data: data collected for the first time by an organization and is being used by the organization. It is also described as a raw data or first hand data

Secondary data: A data that has previously been gathered and can be accessed by researchers.

Examples, tax records and social security data, census data, health records data etc.

Name: Depuun Jessica Doose

Reg no: 2021/241953

Faculty: Social science

Department: Economics

Email: jessicadepuun@gmail.com

For the given set of data,

1.Class interval: 17-19, 20-22, 23-25, 26-28; where 2 is the interval.

C.I. x F. C.F. R.F. RCF

17-19 18 8. 8. 24.24%. 24.24%

20-22. 21 11. 19. 33.33%. 57.57%

23-25. 24 11. 30. 33.33%. 90.90%

26-28. 27 3. 33. 9.09%. 100%

TF=33

2.A sample: Sample is a subset of individuals from a larger population. Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in your university, you could survey a sample of 100 students.

In statistics, sampling allows you to test a hypothesis about the characteristics of a population.

3.Population: This refers to the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic.

In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped by a common feature can be said to be a population. A sample may also refer to a statistically significant portion of a population, not an entire population. For this reason, a statistical analysis of a sample must report the approximate standard deviation, or standard error, of its results from the entire population. Only an analysis of an entire population would have no standard error.

4.Continuous Variable: It is a type of variable in Mathematics and Statistics. A variable is referred to as a numerical expression whose value varies. There are only two types of variables namely the Continuous variable and the Discrete variable. A continuous variable can be defined as a numerical variable whose value is attained by measuring. These variables can take any type of numeric value and can be divided into further relevant smaller increments such as fractional and decimal values. A continuous variable is a kind of quantitative variable that is frequently used in machine learning and statistical modeling to describe data that is measurable in some way. Continuous variables are measured on scales such as height, temperature, weight, etc.

5.A Discrete variable: This is a kind of statistics variable that can only take on discrete specific values. The variable is not continuous, which means there are infinitely many values between the maximum and minimum that just cannot be attained, no matter what.

6.Statistics: This is a branch of mathematics dealing with gathering, analyzing, and making inferences from data. Originally associated with government data (e.g., census data), the subject now has applications in all the sciences. Statistical tools not only summarize past data through such indicators as the mean (see mean, median, and mode) and the standard deviation but can predict future events using frequency distribution functions. Statistics provides ways to design efficient experiments that eliminate time-consuming trial and error. Double-blind tests for polls, intelligence and aptitude tests, and medical, biological, and industrial experiments all benefit from statistical methods and theories. The results of all of them serve as predictors of future performance, though reliability varies. See also estimation; hypothesis testing; least squares method; probability theory; regression.

7.Data: It can be defined as a systematic record of a particular quantity. It is the different values of that quantity represented together in a set. It is a collection of facts and figures to be used for a specific purpose such as a survey or analysis. When arranged in an organized form, can be called information. The sources of data are primary data, secondary data. The two types are qualitative and quantitative data.

Kalu Valentina Onyinyechi

2021/246562

ECO 101 quiz

Question One

1. Class interval using sturge rule 1+3.3logN =6.01.

Class midpoint f. CF. RF RCF

Interval (X)

17 -18. 17.5 5 5 15.15 4.03

19 – 20. 19.5 6 11 18.18 8.87

21 – 22. 21.5 8 19 24.24 15.32

23 – 24. 23.5 7 26 21.21 20.96

25 – 26. 25.5 4 30 12.12 24.19

27 – 28. 27.5 3 33 9.09 26.61

= 33 124 99.99 99.98

Question 2

1:. Sample: Sample is defined as part or portion of a population which is taken from the population. A sample must be representative of the population in all ramifications.

2:. Population: Population is the entire group of individuals or collections of items one wishes to examine at a particular time.

3:. Continuous variable: Continuous variable take any value between a certain set of real number. It is measured in continuous scale.

4:. Discrete variable: This is a type of characteristic that can be counted and represented as a whole number.

5:. Statistics: This is the scientific method of collecting, organizing, summarizing, presenting and analysing data.

6:. Data: Data is a numerical statement or fact in a specific field or enquiry. It is information in raw or unorganized form that represent ideas,objects e.t.c.

NAME:. Ugwoke ukamaka confidence

Department: social science education

Unit:. Economics education

reg number: 2021/245467

Course code Eco 131

Course outline:. Statistics

1: class interval using sturge rule:

K: 1+3.3 LogN

K: 1+3.3 Log(33)

K:6.0

C: interval. Mid point freq. Cf Rf. Rcf

17_18. 42.5. 5. 5. 15.15. 4.03

19_20. 19.5 6. 11. 18.18. 8.87

21_22. 21.5. 8. 19. 24.24. 15.32

23_24. 23.5. 7. 26. 21.21. 20.96

25_26. 25.5. 4. 30 12.12. 24.19

27_28 27.5. 3.:;33 33:;124 9.09 26.61

Question 2

1. SAMPLE. A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations. A sample should represent the population as a whole and not reflect any bias toward a specific attribute.

2. POPULATION. a population is a set of similar items or events which is of interest for some question or experiment. A statistical population can be a group of existing objects or a hypothetical and potentially infinite group of objects conceived as a generalization from experience.

3. CONTINUOS VARIABLE. A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range.

4. DISCRETE VARIABLE A discrete variable is a variable whose value is obtained by counting. Examples: number of students present. number of red marbles in a jar. number of heads when

flipping three coins.

5. STATISTICS. Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied.

6. DATA. data are individual pieces of factual information recorded and used for the purpose of analysis. It is the raw information from which statistics are created. Statistics are the results of data analysis – its interpretation and presentation.

Caleb Princess Adaeze

2021/241313

Calebadaeze22@gmail.com

Answer 1

1.sturge rule

1+3.3logn

N=number of observation

Therefore class interval(k)=1+3.3log(33)

=6.011096002

Approximately =6

Range=highest value-lowest value

28-17=11

Therefore class size(c)=range(r)/class interval

=11/6

=1.8 approximately 2

2. midpoint

Lower class boundary+upper class boundary/2

3. frequency

Number of times each observation appeared

4. cumulative frequency

Addition of the observed frequency bit by bit in descending order

5. relative frequency

Frequency/total number of observations

6.relative cumulative frequency

Addition of relative frequency bit by bit in descending order

Class intervals Midpoint(x)) F C.F R.F R.C.F

17-18 17.5 5 5 0.15 0.15

19-20 19.5 6 11 0.18 0.33

21-22 21.5 8 19 0.24 0.57

23-24 23.5 7 26 0.21 0.78

25-26 25.5 4 30 0.12 0.09

27-28 27.5 3 33 0.09 1

33 124

Answer 2

1. Sample

A sample refers to a smaller manageable version of a larger group. It is a subset containing the characteristics of a larger population. They are used in statistical testing when population sizes are too large for the test to include all possible members or observations. Example, the age of students in faculty of law taken to represent the age of students in the department.

2. Population

A population is the pool of individuals from which a statistical sample is drawn for study. Therefore, any selection of individuals grouped by a common feature can be said to be a population.

3. Continuous variable

A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. Example, counting the amount of money in everyone’s bank accounts.

4. Discrete variable

A discrete variable is a variable whose value is obtained by counting. Example, number of balls in a bag, number of meats in a pot.

5. Statistics

It is the practice or science of collecting and analyzing numerical data in large quantities, especially for the purpose of inferring proportions in a whole from those in a representative sample.

6. Data

Data are measurements or observations that are collected as a source of information. It is used to create new information or knowledge.

Name: Nnoruka benedicta chinecherem

Reg no: 2021/241348

1.

Interval, ????????(????) ???? ????f. ???????? ????????????

17−18 17.5 5 5 15.15% 4.03%

19−20 19.5 6 11 18.18% 8.87%

21- 22 21.5 8 19 24.24% 15.32%

23−24 23.5 7 26 21.21% 20.96%

25−26. 25.5 4 30 12.12% 24.19

27−28 27.5 3 33 9.09% 26.61%

33 124 87.87% 99.98%

2.

Sample: A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations. A sample should represent the population as a whole and not reflect any bias toward a specific attribute.

There are several sampling techniques used by researchers and statisticians, each with its own benefits and drawbacks.

KEY TAKEAWAYS

In statistics, a sample is an analytic subset of a larger population.

The use of samples allows researchers to conduct their studies with more manageable data and in a timely manner.

Randomly drawn samples do not have much bias if they are large enough, but achieving such a sample may be expensive and time-consuming.

In simple random sampling, every entity in the population is identical, while stratified random sampling divides the overall population into smaller groups.

Types or sampling

Random sampling

Systematic sampling

Convenience sampling

Cluster sampling.

B: Population

A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic.

In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped by a common feature can be said to be a population. A sample may also refer to a statistically significant portion of a population, not an entire population. For this reason, a statistical analysis of a sample must report the approximate standard deviation, or standard error, of its results from the entire population. Only an analysis of an entire population would have no standard error.

C. Continuous variable:

A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range. Thus, the range of real numbers between x and y with x, y ∈ R and x ≠ y; is said to be uncountable and infinite.

In continuous optimization problems, different techniques of calculus are often used in which the variables are continuous. Also, the probability distributions of continuous variables can be stated in expressions of probability density functions in statistical theory.

Types of Continuous Variables

There are two types of continuous variables namely interval and ratio variables.

Instant variable

Ratio variable

D. Discrete variable:A discrete variable is a variable that takes on distinct, countable values. In theory, you should always be able to count the values of a discrete variable.

Examples

Examples of discrete variables include:

Years of schooling

Number of goals made in a soccer match

Number of red M&M’s in a candy jar

Votes for a particular politician

Number of times a coin lands on heads after ten coin tosses

E. Statistics:

Statistics, the science of collecting, analyzing, presenting, and interpreting data. Governmental needs for census data as well as information about a variety of economic activities provided much of the early impetus for the field of statistics. Currently the need to turn the large amounts of data available in many applied fields into useful information has stimulated both theoretical and practical developments in statistics.

F. Data:

Data is the base of all operations in statistics. So let us learn more about data collection, primary data, secondary data, and a few other important terms.

Data can be defined as a systematic record of a particular quantity. It is the different values of that quantity represented together in a set. It is a collection of facts and figures to be used for a specific purpose such as a survey or analysis. When arranged in an organized form, can be called information. The source of data ( primary data, secondary data) is also an important factor.

Types of Data

Data may be qualitative or quantitative. Once you know the difference between them, you can know how to use them.

Qualitative Data: They represent some characteristics or attributes. They depict descriptions that may be observed but cannot be computed or calculated. For example, data on attributes such as intelligence, honesty, wisdom, cleanliness, and creativity collected using the students of your class a sample would be classified as qualitative. They are more exploratory than conclusive in nature.

Quantitative Data: These can be measured and not simply observed. They can be numerically represented and calculations can be performed on them. For example, data on the number of students playing different sports from your class gives an estimate of how many of the total students play which sport. This information is numerical and can be classified as quantitative

1. Using Sturge’s rule, class interval

K=1+3.33logN

where;

K= number of classes

N= total frequency

Here, N=33. So, K=1+3.3log33

K=6.0

Therefore, our class interval=6

Class interval 17-23 23-29

Midpoint (x) 20 26

Frequency (f) 23 10

Cumulative Freq. 23 33

Relative Freq. (23/33)=0.697 (10/33)=0.303

Relative CF. (23/33)×100 (33/33)×100

=69.7% 100

2.a SAMPLE

It is the portion of the population (which must be a representative of the population in all ramifications) that is being drawn out for conclusions since it is usually difficult to examine all members of the population due to time, cost and other constraints.

Sampling is a procedure by which one or more members of a population are selected from the population.

b. POPULATION

It is the entire group of individuals that we’re interested in making a statement about. It is the entire group about which information is desired.

It can also be described as the largest collection of entities for which we have an interest at a particular time; an entire set of objects, observations, or scores that have something in common.

c. CONTINUOUS VARIABLE

A continuous variable is one for which, within the limits the variable changes, any value is possible.

A variable is said to be continuous if it can assume an infinite number of real values within a given interval. For instance, consider the height of a student. The height can’t take any values. It can’t be negative and it can’t be higher than three metres.

d. DISCRETE VARIABLES

Discrete variables or data are also known as categorical variables. They are variables which exist only as whole numbers and are not divisible. A discrete variable can take on a finite number of numerical values, categories or codes.

e. STATISTICS

Statistics, in itself, is the collation and analysis of numerical data to arrive at specific inference. This academic discipline finds application in various other branches of studies, such as Economics. Any study about Economics and Statistics involves the validation of theories with quantified data sets.

Statistics concerns the collection, processing, compilation, dissemination, and analysis of economic data. It is closely related to business statistics and econometrics.

f. DATA

Data are raw facts or unprocessed information that has been collected for use. The collection may include numbers, words, measurements, observations or even descriptions of things.

They are the raw material from which econometric analysis is constructed. Just as a building is no stronger than the wood or steel used in its framework, an econometric study is only as reliable as the data used in its analysis. Many econometricians over the years have written about problems with data.

Eco 131 assignment

NAME:Agbo ifeanyi Samuel

Dept: Economics

Reg no: 2021/244128

Date:. 06–03–23

Question 1

ClASS INT. : MIDP: FREQ: CF : RF: RCF

1-18. 17.5. 5. 5. 15.5. 15.15

19-20. 19.5. 6. 11. 18.18. 33.3

21-22. 21.5 . 8. 19. 24.24. 57.57

23-24. 23.5. 7. 26. 21.21. 78.78

25-26. 25.5. 4. 30. 12.12. 90.90

27-28. 27.5. 3. 33. 9.09. 100

i, to get mid point= sum the upper and lower boundary and divide by 2

ii, to get frequency= number of occurrence

iii, cumulative frequency=sum of the frequency of the class and the frequency of the previous class

iv, relative frequency= frequency divided by cumulative frequency multiply by 100 over 1

v, relative cumulative frequency= cumulative frequency divided by frequency multiply by 100 over 1

Question 2

1, SAMPLE: in statistics, sample is the selection of a subset of individuals from within a statistical population to estimate characteristics of the whole population. In it’s broadest sense, sampling is a procedure by which one or more members of a population are selected from the population.

2, POPULATION: population is defined as the entire group about which information is desired.

A population parameter is a numerical quantity measuring some aspect of a population of scores, for example, the mean is a measure of central tendency. Population parameters are rarely known and are usually estimated by statistics computed in sample.

3, CONTINUOUS VARIABLE: A continuous variable is one for which, within the limits the variable, range, any value is possible. Continuous variable can take any value between a certain set of real numbers.

4, DISCRETE VARIABLE: A discrete variable or data are also known categorical variable. They are variables or data that exist only as a whole numbers and are not divisible. A discrete variable can take on a finite number or numerical values, categories or codes.

5, STATISTICS: the word “statistics” refers to numerical facts such as the number of events occuring in time or the number of people living in a particular area. It’s also involves the study of ways of collecting, analyzing and interpreting numerical facts or data.

6, DATA: can be defined as a raw facts or information which has not been processed. In it’s simple form , data could be seen as a collection of facts, such as numbers, words, measurements, observations or even just descriptions of things.

OBIORA CHUKWUEMEKA 2021/243059 (COMBINED SOCIAL SCIENCE)

1.

Class interval Mid-point F CF RF RCF

17-18 17.5. 5. 5. 15. 15

19-20. 19.5. 6. 11. 18. 33

21-22. 21.5. 8. 19. 24. 57

23-24. 23.5. 7. 26. 21. 78

25-26. 25.5. 4. 30. 12. 90

27-28. 27.5. 3. 33. 9. 99

33

Class interval using sturges rule

K=1+3.3logN

Where k is number of classes and N is total frequency

K= 1+3.3log(33)

K=1+3.3(1.51)

K=1+5

K=6

2.SAMPLE:A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. it can also be said to be proportion or part of the population

POPULATION: A population is the entire group of individuals that we are interested in making a statement about.A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic.

CONTINUOUS VARIABLE: A continuous variable is one for which, within the limits the variables ranges, any value is possible

DISCRETE VARIABLES: These are variables or data that exist only as whole numbers and are not divisible. A discrete variable can take on a finite number of numerical values,categories or codes

STATISTICS:It could be defined as the theory and methods of collecting,organizing,presenting,analyzing, and interpreting data sets so as to determine their essential characteristics

DATA: Data could be seen as a collection of facts ,such as numbers ,words ,measurements,observations or even just descriptions of things .it could be also seen as information in raw or unorganized form

NAME: ONUOKA ANTHONIA CHIAMAKA

REG NO: 2021/243690

EMAIL: anthoniaonuoka@gmail.com

QUESTION ONE ANSWER:

Interval,????????(????) ???? ????f. ???????? ????????????

17−18 17.5 5 5 16.6 4.4

19−20 19.5 5 10 16.6 8.9

21- 22 21.5 7 17 56.6 15.1

23−24 23.5 6 23 20 20.5

25−26. 25.5 4 27 13.3 24.1

27−28 27.5 3 30 10 26.7

30 112 133.1 99.7

QUESTION TWO ANSWER

1. Sample : It is a proportion or part of the population – usually the proportion from which information is gathered.

2. Population : It is defined as the entire group about which information is desired.

3. Continuous variables : It is one for which, within the limits the variable ranges, any value is possible.

4. Discrete variables : These are variables of data that exist only as a whole number and are not divisible.

5. Statistics : It is the scientific method of collecting, organising, summarising, presenting, and analysing data.

6. Data : This is the collection of facts such as numbers, words, measurements or even just descriptions of things. It can also be defined as information in raw or unorganised form.

Name: Chike-ijei Chiwendu Victoria

Department: Economics

Registration number:2021/243693

Email: chiwenduchikeijei@gmail.com

Using sturge rule

K =1+3.3 log(N)

1+3.3 log(total frequency)

1+3.3 log(33)

1+5.01=6.01 Class interval Mid point F RF CF RCF

17_18 17.5 5 15.15 5 4.09

19_20 19.5 5 15.15 10 8.20

21_22 21.5 8 24.24 18 14.75

23_24 23.5 8 24.24 26 21.31

25_26 25.5 4 12.12 30 24.59

27_28 27.5 3 9.09 33 27.05

=33 =122

(2)

(i) Sample: Sample is a procedure by which one or more members of a population are selected from the population

(ii) Population:It is described as a largest collection of entities for which we have an interest at a particular time

(iii) Continuous variables:A continuous variable is one for which, within the limits the variable ranges,any value is possible.

(iv) Discrete variables:They are variables or data that exist only as whole numbers and are not divisible

(v) Statistics:It refers to numerical facts such as the number of events occurring in time or the number of people living in a particular area.

(vi)Data: Data could be seen as a collection of facts,such as numbers,words, measurements, observation or even just descriptions of things

Ekpo munachimso praise

2021/241315

Economics

Faculty of social sciences

2)write a brief note on the following

a Sample

A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations. A sample should represent the population as a whole and not reflect any bias toward a specific attribute.

b population

A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic.In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped by a common feature can be said to be a population. A sample may also refer to a statistically significant portion of a population, not an entire population. For this reason, a statistical analysis of a sample must report the approximate standard deviation, or standard error, of its results from the entire population. Only an analysis of an entire population would have no standard error.

c continuous variable

A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range. Thus, the range of real numbers between x and y with x, y ∈ R and x ≠ y; is said to be uncountable and infinite.In continuous optimization problems, different techniques of calculus are often used in which the variables are continuous. Also, the probability distributions of continuous variables can be stated in expressions of probability density functions in statistical theory.

d discrete variable

Variables that can only take on a finite number of values are called “discrete variables.” All qualitative variables are discrete. Some quantitative variables are discrete, such as performance rated as 1,2,3,4, or 5, or temperature rounded to the nearest degree. Sometimes, a variable that takes on enough discrete values can be considered to be continuous for practical purposes. One example is time to the nearest millisecond.Variables that can take on an infinite number of possible values are called “continuous variables.”

e statistics

Statistics is simply defined as the study and manipulation of data.According to Merriam-Webster dictionary, statistics is defined as “classified facts representing the conditions of a people in a state – especially the facts that can be stated in numbers or any other tabular or classified arrangement”.

According to statistician Sir Arthur Lyon Bowley, statistics is defined as “Numerical statements of facts in any department of inquiry placed in relation to each other”.

f data

In the most general sense, data refers to a collection of individual values that, when processed, convey information. Computer data is information that is stored and processed digitally on a computer. Data on a computer can take many forms, including text, images, audio, or video. It may be loaded into memory and processed by the computer’s CPU, then stored as files in folders on a hard drive or solid-state drive.QUESTION ONE

1

Using Sturge Rule;

k = 1 + 3.322( log n)

Where:

k = the number of classes

n = the number of observations in the data set. Which is 33.

Therefore, number of classes is:

k= 1+ 3.322(log 33)

k= 6

*Class Interval

★Midpoint

*Frequency

★Cumulative Frequency

*Relative Frequency

★Relative Cumulative Frequency

17-18.17.5,5,5,15.15,4.03

19-20.19.5,6,11,18.18,8.87

21-22.21.5,8,19,24.24,15.32

23-24.23.5,7,26,21.21,20.96

25-26.25.5,4,30,12.12,24.19

27-28.27.5,3,33,9.09, 26.61

Name::: Ezugwu peter Nnaemeka

Reg No::: 2021/244727

Faculty:: Education

Department:: Educational foundations

Unit: Special Education

ECO 131 Assignment

ANSWERS

1.) CI. X. F CF. RF. RCF

17-19 18 8 8 24.2 24.2

20-22 21 11 19 33.3 57.6

23-25 24 11 30 33.3 90.9

26.28 27 3 33 9.09 100

=90 =33.

2. SAMPLE:::

SAMPLE:::

A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations. A sample should represent the population as a whole and not reflect any bias toward a specific attribute.

Types of Sampling::

Simple Random Sampling

Simple random sampling is ideal if every entity in the population is identical.

Stratified Random

This type of sampling, also referred to as proportional random sampling or quota random sampling, divides the overall population into smaller groups.

POPULATION::

A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic.

CONTINUOUS VARIABLE

Continuous variable, as the name suggest is a random variable that assumes all the possible values in a continuum. Simply put, it can take any value within the given range. So, if a variable can take an infinite and uncountable set of values, then the variable is referred as a continuous variable.

A continuous variable is one that is defined over an interval of values, meaning that it can suppose any values in between the minimum and maximum value. It can be understood as the function for the interval and for each function, the range for the variable may vary.

DISCRETE VARIABLE

A discrete variable is a type of statistical variable that can assume only fixed number of distinct values and lacks an inherent order.

Also known as a categorical variable, because it has separate, invisible categories. However no values can exist in-between two categories, i.e. it does not attain all the values within the limits of the variable. So, the number of permitted values that it can suppose is either finite or countably infinite. Hence if you are able to count the set of items, then the variable is said to be discrete.

STATISTICS

Generally, the subject matter of statistics deals with the quantification of data. It revolves around concrete figures to represent qualitative information. Simply, it is a collection of data. But that’s not all. As economics students, we need to learn about the techniques of dealing with a collection of data, tabulation, classification, and presentation of data.

DATA::::

is a collection of discrete values that convey information, describing quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted. A datum is an individual value in a collection of data. Data is usually organized into structures such as tables that provide additional context and meaning, and which may themselves be used as data in larger structures. Data may be used as variables in a computational process. Data may represent abstract ideas or concrete measurements. Data is commonly used in scientific research, economics, and in virtually every other form of human organizational activity. Examples of data sets include price indices (such as consumer price index), unemployment rates, literacy rates, and census data. In this context, data represents the raw facts and figures which can be used in such a manner in order to capture the useful information out of it.

1.stures rule =K=1+3.3logN

where K = number of intervals

log N = logarithm of total number of observations.

i.e K= 1+3•3log33 = 6•5

Class interval X. F. Cf. Rf. Rcf

17-18. 17•5. 5. 5. 15•15. 15•15

19-20. 19•5. 6. 11. 18•18. 33•33

21-22. 21•5. 8. 19. 24•24. 57•57

23-24. 23•5. 7. 26. 21•21. 78•78

25-26. 25•5. 4. 30. 12•12. 90•90

27-28. 27•5. 3. 33. 9•09. 100

2. SAMPLE : A sample is a smaller set of data that a researcher chooses or selects from a larger population using a predefined selection method . These elements are known as sample points,sampling units or observatios .

Creating a sample is an efficient method of conducting research. Researching the whole population is often impossible, costly and time-consuming . Hence, examining the sample provides insights the researcher can apply to the entire population.

POPULATION:population is the entire group about which information is desired . It is also described as the largest collection of entities for which we have an interest at a particular time; an entire set of objects, observations , or scores that have something in common.

CONTINUOUS VARIABLE : A continuous variable is one for which , within the limits the variable ranges, any value possible. Continuous variables can take any value between a certain set of real numbers . The value given to an observation for a continuous variable can include values as small as the instrument of measurement allows

DISCRETE VARIABLE: Discrete varibles or data are also known as categorical variables. They are variables or data that exist only as whole numbers and are not divisible . A discrete variable can take on a finite number or numerical values,categories or codes.

STATISTICS: This could be seen as the numerical facts such as the number of events occurring in time or the number of people living in a particular area. It also involves the study of ways of collecting ,analyzing and interpreting numerical facts or numerical data .

DATA : Data could be seen as a collection of facts ,such as numbers ,words, measurement, observations or even just descriptions of things . It could also be seen as information in raw or unorganized form that refer to, or represent,conditions, ideas or objects. Data could be qualitative or quantitative .

Name::: Ezugwu peter Nnaemeka

Reg No::: 2021/244727

Faculty:: Education

Unit: Special Education

Department:: Educational foundations

ECO 131 Assignment

ANSWERS

1.) CI. X. F CF. RF. RCF

17-19 18 8 8 24.2 24.2

20-22 21 11 19 33.3 57.6

23-25 24 11 30 33.3 90.9

26.28 27 3 33 9.09 100

=90 =33.

2. SAMPLE:::

SAMPLE:::

A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations. A sample should represent the population as a whole and not reflect any bias toward a specific attribute.

Types of Sampling::

Simple Random Sampling

Simple random sampling is ideal if every entity in the population is identical.

Stratified Random

This type of sampling, also referred to as proportional random sampling or quota random sampling, divides the overall population into smaller groups.

POPULATION::

A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic.

CONTINUOUS VARIABLE::

Continuous variable, as the name suggest is a random variable that assumes all the possible values in a continuum. Simply put, it can take any value within the given range. So, if a variable can take an infinite and uncountable set of values, then the variable is referred as a continuous variable.

A continuous variable is one that is defined over an interval of values, meaning that it can suppose any values in between the minimum and maximum value. It can be understood as the function for the interval and for each function, the range for the variable may vary.

DISCRETE VARIABLE::

A discrete variable is a type of statistical variable that can assume only fixed number of distinct values and lacks an inherent order.

Also known as a categorical variable, because it has separate, invisible categories. However no values can exist in-between two categories, i.e. it does not attain all the values within the limits of the variable. So, the number of permitted values that it can suppose is either finite or countably infinite. Hence if you are able to count the set of items, then the variable is said to be discrete.

STATISTICS::

Generally, the subject matter of statistics deals with the quantification of data. It revolves around concrete figures to represent qualitative information. Simply, it is a collection of data. But that’s not all. As economics students, we need to learn about the techniques of dealing with a collection of data, tabulation, classification, and presentation of data.

DATA::::

is a collection of discrete values that convey information, describing quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted. A datum is an individual value in a collection of data. Data is usually organized into structures such as tables that provide additional context and meaning, and which may themselves be used as data in larger structures. Data may be used as variables in a computational process. Data may represent abstract ideas or concrete measurements. Data is commonly used in scientific research, economics, and in virtually every other form of human organizational activity. Examples of data sets include price indices (such as consumer price index), unemployment rates, literacy rates, and census data. In this context, data represents the raw facts and figures which can be used in such a manner in order to capture the useful information out of it.

Name::: Ezugwu peter Nnaemeka

Reg No::: 2021/244727

Faculty:: Education

Department:: Educational foundations

Unit:. Special Education

ECO 131 Assignment

ANSWERS

1.) CI. X. F CF. RF. RCF

17-19 18 8 8 24.2 24.2

20-22 21 11 19 33.3 57.6

23-25 24 11 30 33.3 90.9

26.28 27 3 33 9.09 100

=90 =33.

2. SAMPLE:::A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations. A sample should represent the population as a whole and not reflect any bias toward a specific attribute.

Types of Sampling::

Simple Random Sampling

Simple random sampling is ideal if every entity in the population is identical.

Stratified Random

This type of sampling, also referred to as proportional random sampling or quota random sampling, divides the overall population into smaller groups.

POPULATION::A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic.

CONTINUOUS VARIABLE:::

Continuous variable, as the name suggest is a random variable that assumes all the possible values in a continuum. Simply put, it can take any value within the given range. So, if a variable can take an infinite and uncountable set of values, then the variable is referred as a continuous variable.

A continuous variable is one that is defined over an interval of values, meaning that it can suppose any values in between the minimum and maximum value. It can be understood as the function for the interval and for each function, the range for the variable may vary.

DISCRETE VARIABLE:::

A discrete variable is a type of statistical variable that can assume only fixed number of distinct values and lacks an inherent order.

Also known as a categorical variable, because it has separate, invisible categories. However no values can exist in-between two categories, i.e. it does not attain all the values within the limits of the variable. So, the number of permitted values that it can suppose is either finite or countably infinite. Hence if you are able to count the set of items, then the variable is said to be discrete.

STATISTICS:::

Generally, the subject matter of statistics deals with the quantification of data. It revolves around concrete figures to represent qualitative information. Simply, it is a collection of data. But that’s not all. As economics students, we need to learn about the techniques of dealing with a collection of data, tabulation, classification, and presentation of data.

DATA::::

is a collection of discrete values that convey information, describing quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted. A datum is an individual value in a collection of data. Data is usually organized into structures such as tables that provide additional context and meaning, and which may themselves be used as data in larger structures. Data may be used as variables in a computational process. Data may represent abstract ideas or concrete measurements. Data is commonly used in scientific research, economics, and in virtually every other form of human organizational activity. Examples of data sets include price indices (such as consumer price index), unemployment rates, literacy rates, and census data. In this context, data represents the raw facts and figures which can be used in such a manner in order to capture the useful information out of it.

Economics department

Obiania Gloria Mkpuruchukwu

2021/244124

QUESTION ONE

Using Sturge Rule to get the number of class interval

k = 1 + 3.3log N

Where:

k = the number of classes

N = the number of observations in the data set. = 33.

Therefore, number of classes is:

k= 1+ 3.3log 33

k= 6

With this information we can make the table:

Class. Mid. F. C.F. R.F. R.C.F

Interval. Point

17-18 17.5 5 5 15.15 15.15

19-20 19.5 6 11 18.18 33.33

21-22 21.5 8 19 24.24 57.57

23-24 23.5 7 26 21.21 78.78

25-26 25.5 4 30 12.12 90.9

27-28 27.5 3 33 9.09 99.99

QUESTION TWO

1) A sample in economics is a portion of a larger population that is chosen for study or research. Without having to survey or examine every single person in the population, sampling is used to gather data that can be utilized to make generalizations about the wider population.

In order to get representative data on different economic variables, such as income, consumer spending, employment, and economic growth, sampling is frequently employed in economic research. To accurately reflect the characteristics of the larger population, the sample must be carefully chosen.

2) A population is any collection of people, homes, businesses, or other entities that share particular traits or features and is used in economics. Depending on the situation and goal of the analysis, populations can be defined in a variety of ways.

A population might consist of all the homes in a nation, all the businesses in a particular sector, or all the people with a particular degree of education, for instance. Other factors, such as income, age, education level, or geographic location, can also be used to characterize the population.

3) A continuous variable in economics is a kind of numerical variable that can have any value within a given range. Any continuous scale value, including fractions and decimals, is acceptable. In economic research, continuous variables are frequently employed to assess economic phenomena that can fluctuate along a continuum. Examples of continuous variables include income, age, and time. Any value between $0 and infinity can be considered as income. Time can range from zero to the maximum length of time that is being measured, while age can range from 0 to infinity.

Several economic investigations and models, such as regression analysis, demand and supply modeling, and economic forecasting, employ continuous variables.

4) A discrete variable in economics is a kind of numerical variable that has a limited or countable range of unique values. In economic research, discrete variables are frequently employed to assess economic phenomena that can only have certain, distinct values or categories.

Discrete variables include things like the number of employees at a corporation, the quantity of goods sold, and the total number of students in a class. Only specified, whole number values can be assigned to them. Continuous variables, which can have any value within a range, are frequently compared with discrete variables. Age and income are two examples of continuous variables with a large range of possible values.

5) Statistics in economics refers to the process of gathering, analyzing, and interpreting data in order to characterize or draw conclusions about economic processes. Economics uses statistics to quantify and comprehend economic trends, patterns, and behavior.

Many economic variables, including prices, output levels, employment rates, and income distribution, can be described using economic statistics. These data can be used to chart changes over time and between areas, to spot trends and connections between variables, and to guide decisions about economic policy.

Descriptive statistics, which summarize and describe data using metrics like averages, standard deviations, and percentiles, as well as inferential statistics are statistical techniques used in economics.

6) Data in economics refers to details that are gathered and examined to comprehend economic events. Data can come from a variety of places, including surveys, governmental organizations, businesses that conduct economic research, and financial markets.

Primary data and secondary data are the two categories into which economic data may be divided. Information gathered directly from people or organizations using surveys, interviews, or experiments is referred to as primary data. On the other hand, secondary data describes information gathered from sources other than the original researcher, such as official statistics, financial reports, or scholarly studies.

Economic data can be used to uncover patterns and trends in economic behavior, track changes over time, and guide economic policy decisions.

Onah Chisom Evelyn

Reg number: 2021/246809

onahchisomevelyn@gmail.com

QUESTION ONE.

ANSWERS

NO.1.1 Using Sturges rule the class interval=

Solution:

K = 1+3.33LOG N. (Sturges rule)

K=1+3.33LOG 33

K=1+3.33(1.5185)

K=1+5.0

K=6. i e No of classes=6

Range= 28-17

=11

Class interval= 11/6 = 1.8 approximately 2

CLASS INTERVAL

17-18

19-20

21-22

23-24

25-26

27-28

No.1.2 Answer

Mid point=

17+18= 17.5

19+20= 19.5

21+22= 21.5

23+24= 23.5

25+26= 25.5

27+28= 27.5

NO.1.3 ANSWER

CLASS INTERVAL FREQUENCY

17-18. 5

19-20. 6

21-22. 8

23-24. 7

25-26. 4

27-28. 3

TOTAL=33

NO.1.4 ANSWER

CUMULATIVE FREQUENCY

5

5+6=11

11+8=19

19+7=26

26+4=30

30+3=33

NO.1.5Answer

RELATIVE FREQUENCY

5/33 * 100/1= 15.2%

6/33 *100/1 = 18.2%

8/33 * 100/1 = 24.2%

7/33 * 100/1 = 21.2%

4/33 * 100/1= 12.1%

3)33 * 100/1 = 9.1%

NO.1.6 ANSWER

RELATIVE CUMULATIVE FREQUENCY

5/33 * 100/1 = 15.2%

11/33 * 100/1 = 33.3%

19/33 * 100/1 = 57.6%

26/33 * 100/1 = 78.8%

30/33 * 100/1 = 90.9%

33/33 * 100/1 = 100%

QUESTION TWO

NO.2.1 ANSWER

SAMPLE: A Sample is a subset of a smaller portion of a larger population that’s selected for observation, or analysis. In research Sampling is the process of selecting a representative group of individual or objects from a population to study or make inferences about the population.

NO.2.2 ANSWER

POPULATION: In statistics Population refers to the entire group of individual or objects that are of interest to a researcher. It can be a group of people, animals, plants,or any other set of objects that share common characteristics. The population is often defined by specific criteria or characteristics, such as age, gender, geographic location, or medical condition.

NO.2.3 ANSWER

CONTINUOUS VARIABLE : In statistics a continuous variable is a numerical variable that can take on any value within a given range. It is a type of Quantitative variable that can be measured and is often represented by a real number.

Continuous variables can take on an infinite number of values within a given interval, making them different from discrete variables which can only take on a finite number of values.

NO2.4 ANSWER

DISCRETE VARIABLE: A discrete variable is a type of variable in statistics and mathematics that takes on finite or countably infinite set of possible values. These values are distinct and separate, with no possible values in between. For example, the number of students in a class is a discrete variable because it can only take on integer values.

NO.2.5 ANSWER

STATISTICS: It is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organisation of data. It involves the use of Quantitative methods to understand and make sense of complex phenomena, such as social and economic trends, scientific experiment, and business operations.

NO.2.6 ANSWER

DATA : Data could be seen as a collection of facts, such as numbers, words, measurements, observations or even just descriptions of things. It could also be seen as information in raw or unorganized form such as alphabets, numbers, or symbols that refer to, or represent conditions,ideas, or objects. It can be Qualitative i e data that deals with description or quantitative i e data that deals with numbers. they are required for empirical analysis and other forms of analysis.

ONUNKWO CHISOM CYNTHIA

2021/241349

Answers

Yields. Mid point. Freq. Cf. Rf. RCF

17-19. 28. 8. 8. 24 5.8

19-21. 20. 3. 11. 9. 8.0

21-23. 22. 12. 23. 36. 16.9

23-25. 24. 7. 30. 21. 22

25-27. 26. 1. 31. 3. 22.7

27-29. 28. 2. 33. 6. 24.3

Total. 33 136

2) sample: sample is the portion of the population that we actually observe.

Population: population refers to the total group about which information is desired.

Continuous variable: is the type of variable which can assume any value from a range of values. E.g height, income of staff etc

Discrete variable: this are variables that can only be counted and represented as whole numbers e.g age of students.

Statistics: statistics is a field of study which is concerned with layout experiment, collection, tabulation, summarization and analysis of data.

Data: Data is information in it’s original form. It is a numerical statement of facts in a specific field of study.

Question1

Class interval Midpoint F CF RF RCF

17_18 17.5 5 5 15.5 15.15

19_20 19.5 6 11 18.18 3.3

21_22 21.5 8 19 24.24 57.57

23_24 23.5 7 26 21.21 78.78

25_26 25.5 4 30 12.12 90.90

27_28 27.5 3 33 9.09 100

Total 33

Question 2:

1: Samples refers to a smaller, manageable version of a larger group used to make inferences about populations. Samples are easier to collect data from because they are practical, cost-effective, convenient, and manageable.

2: Populations: polulations are used when a research question requires data from every member of the population. This is usually only feasible when the population is small and easily accessible.

3: Continuously variable: A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range.

4: Discrete variable: A discrete variable is a variable whose value is obtained by counting. Examples: number of students present. number of red marbles in a jar. number of heads …

5: Statistics: statistics is defined as the science of collecting, analyzing, presenting, and interpreting data.

6: Data: data is information that has been translated into a form that is efficient for movement or processing. Relative to today’s computers and transmission media, data is information converted into binary digital form. It is acceptable for data to be used as a singular subject or a plural subject.

Name: Onwuachumba Chinenye Jessica

Reg no: 2021/246559

Dept: Combined Social Science ( Economics/Sociology)

Name: Ndiomarake Ngozi Judith

Department: Economics

Registration number: 2021/244127

1). Using sturge rule =1+3.3logN

=1+3.3log33=6

So we have 6 class interval

A) Class interval= 17-18,19-20,21-22,23-24,25-26,27-28

B) Midpoint (x)= 17.5,19.5,21.5,23.5,25.5,27.5

C) Frequency= 5,6,8,7,4,3

D) Cumulative frequency= 5,11,19,26,30,33

E) Relative frequency= frequency÷Total number ×100. 15.2%,18.2%,24.3%,21.2%,12.1%,9.1%

F) Relative cumulative frequency= cumulative frequency ÷total number ×100. 15.2%,33.3%,57.6%,78.8%,90.9%,100%

2). Sample: refers to a smaller, manageable version of a larger group.

Population: is the entire set of item from which u draw data for a statistical study.

Continuous variable: is a variable which can take an uncountable set of value or infinite set of value.

Discrete variable: is a variable that may assume only countable and usually finite number of a numerical category.

Statistics: is the practice or science of collecting and analysing numerical data in large quantities especially for the purpose of inferring proportion in a while from those in a representative sample.

Data: is a measurement or observation that are collected as a source of information.

Name: OKEKE DANIEL AYOMIDE

Reg no: 10574211FD

Email: olasunkanmidaniels28@gmail.com

Answers to the Assignment

Class interval f x CF RF C.RF

17-18 5 17.5 5 0.15 0.15

19-20 6 19.5 11 0.18 0.33

21-22. 8 21.5 19 0.24 0.57

23-24. 7 23.5 26 0.21 0.78

25-26. 4 25.5 30 0.12 0.09

27-28. 3 27.5 33 0.09 1

SAMPLE: A subset of a population selected for measurement, observation or questioning, to provide statistical information about the population.

POPULATION:group of units (persons, objects, or other items) enumerated in a census or from which a sample is drawn.

CONTINUOUS VARIABLE: continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values.

DISCRETE VARIABLE: Discrete variables are countable in a finite amount of time

STATISTICS: discipline, principally within applied mathematics, concerned with the systematic study of the collection, presentation, analysis, and interpretation of data.

DATA: Recorded observations that are usually presented in a structured format.

Name: ilo Destiny Chinasa

Dept: Css ( Economics/psychology)

Date:9/03/2023

Course Code: Eco 131

Reg No: 2021/243714

ASSIGNMENT

1. The class interval using sturge rule

solution

highest – lowest = 28-17=11

R=11

k= 1+3.322 log N

N=30

=1+3.322 log 30

=5.91=6

range /class size OR R/k

R=11 and K=6

11÷6 =1.83

=3

(2). MID-POINT

lowest +highest

17+28= 45÷2=22.5

(3). FREQUENCY

(11,21,3) total frequency = 35.

(4). CUMULATIVE FREQUENCY

(11,32,35) total comulative frequency is = 78

(5). RELATIVE FREQUENCY

(14.10, 26.92, 3.85) total relative frequency is =44.87

(6) RELATIVE CUMULATIVE FREQUENCY

(24.5 , 46.8, 78)

QUESTION TWO

1) SAMEPLE : is a procedure by which one or more members of a population are selected from the population. the objective is to make certain observations about the members of the sample, and then,on the basis of these results, to draw valid conclusions about the characteristics of the entire population.

2) POPULATION: is the entire group about which information is desired, it is also described as a largest collection of entities for which we have interest at a particular time.

3) CONTINOUS VARIABLE: is one for which, within the limit the variable ranges, any value is possible. continuous variable can take any value between a certain set of real numbers.

4) DISCRETE VARIABLE:this is the case of a variable that can only be counted and be represent in a whole number example, Age of a student, number of seeds per carton etc.

5) STATISTICS: can be defined as a field of studying concerning with a layout of experiments, collection, calculation,interpretation of result or drawing of inferences.

6)DATA : is numerical statement of fact in a specific field of enquiry or simply numbers which makes result from taking measurement. e.g recording height, weight or temperature measurement.

Name::: Okhiure Ebenezer Irelevbohi

Reg No::: 2021/243509

Faculty::: Education

Department::: Educational Foundations

ANSWER 1

Class Interval Mid-point Frequency

17-19 18 8

20-22 21 11

23-25 24 11

26-28 27 3

Total 33

Cumulative frequency Relative frequency

8 24.2%

19 33.3%

30 33.3%

33 9.09%

Relative cumulative frequency

24.2%

57.6%

90.9%

100%

Answer 2

1) SAMPLE: A smaller set of data that a Researcher chooses or selects from a larger population using a predefined selection method. These elements are known as sample points, sampling units or observations. In most problems concerning the administration of business, government or personal affair or in making scientific generalisation, complete information cannot be obtained, therefore sample is taken. Sample is simply taking a part of the whole to understudy or research the whole.

2) Population: Population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic.

In statistics, Population is the pool of individuals from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped by a common feature can be said to be a population. A sample may also refer to a statistically significant portion of a population, not an entire population. For this reason, a statistical analysis of a sample must report the approximate standard deviation, or standard error, of its results from the entire population. Only an analysis of an entire population would have no standard error.

3) A continuous variable can be defined as a numerical variable whose value is attained by measuring. These variables can take any type of numeric value and can be divided into further relevant smaller increments such as fractional and decimal values. A continuous variable is a kind of quantitative variable that is frequently used in machine learning and statistical modeling to describe data that is measurable in some way. Continuous variables are measured on scales such as height, temperature, weight, etc. Continuous variables can be used to calculate mean, median, variance, and standard deviation. In continuous optimization applications with continuous variables, many calculus approaches are applied. In statistical theory, the probability distributions of continuous variables can be stated in the form of expressions of probability density functions.

4) Discrete Variable: A Discrete Variable has a certain number of particular values and nothing else. For example, the set of all whole numbers is a discrete variable, because it only includes whole numbers: 1, 2, 3, 4, 5, 6, etc. Numbers in between, like 1/2, are not counted. Discrete variables can be random, but only random within the allowed set of values. If we are counting a number of things, that is a discrete value. E.g A dice roll has a certain number of outcomes, and nothing else (we can roll a 4 or a 5, but not a 4.6), the number of cars in a parking lot is a discrete variable, because we just count the cars. We don’t count parts of cars, parts of cars lying around, or tire marks. There will just be a whole number of cars, etc.

5) Statistics: Statistics is a branch of applied mathematics that involves the collection, description, analysis, and inference of conclusions from quantitative data. The mathematical theories behind statistics rely heavily on differential and integral calculus, linear algebra, and probability theory. Statistics are used in virtually all scientific disciplines such as the physical and social sciences, as well as in business, the humanities, government, and manufacturing. Statistics is fundamentally a branch of applied mathematics that developed from the application of mathematical tools.

6) Data: Data can be defined as a systematic record of a particular quantity. It is the different values of that quantity represented together in a set. It is a collection of facts and figures to be used for a specific purpose such as a survey or analysis. When arranged in an organized form, can be called information. Data are the individual pieces of factual information recorded, and it is used for the purpose of the analysis process.

NAME : Okoye Chiamaka Favour

MATRIC NO : 2021/243699

DEPARTMENT : Economics

QUESTION ONE

1. Class interval = range /k

Class interval using sturgy rule

K=1+3.3logN

Where k =class interval

N= number of observation

=K= 1+3.3log(33)

K= 6.0

Class interval= range/k

Range = highest value -lowest value

Class interval= 28-17/6

Class interval= 1.8

2. Midpoint

Upper limit+lower limit /2

Midpoint= 26, 29, 33.5, 36.5

3. Frequency

5, 6, 12, 7, 3= 33

4. Cumulative Frequency

5, 11, 23, 30, 33 = 102

5. Relative frequency

15.15, 18.18, 36.36, 21.21, 0.09

6. Cumulative Relative Frequency

Rf= CF/F *100

4.91, 10.78, 22.55, 29.41, 32.35

QUESTION TWO

1. Sample

Sampling is a procedure by which one or more members of a population are selected from the population. A sample is a part of the population that we actually observe. The objective is to make certain observation about the members of the sample and then on the basis of these results to draw valid conclusion about the characteristics of the entire population.

2. Population

Population is the entire group of individuals that we are interested in making a statement about. Population is the entire group about which information is desired.

3. Continuous Variables

A continuous variable is one which , within the limits the variable ranges, any value is possible. Continuous Variables can take any value between a certain set of real numbers.

4. Discrete Variables

Discrete Variables are variable or data that exist only as whole number and are not divisible . A discrete clean can take on a finite number of numerical values, categories or codes. They are also known as categories variables

5. Statistics

Statistics refers to numerical facts such as the number of events occurring in time or the number of people living in a particular area. Statistics is concerned with the scientific method of collecting, organising, summarising, presenting, and analyzing data.

6. Data

Data can be seen as a collection of facts, such as numbers, words, measurements, observation or even just descriptions of things. Data could be qualitative or quantitative. Data collection is a fundamental aspect of research

Onwe Stella

10003697DA

According to sturge rule

The class interval is

K=1+3.3logN

K=1+log3.3×33

K=6.01

Class

interval. midpoint. F. RF. CF RCF

17-18. 17.5. 5. 15.15. 5. 15.15

19-20 19.5. 6. 18.18. 11. 33.33

21-22. 21.5. 8. 24.24. 19. 57.57

23-24. 23.5. 7. 21.21. 26. 78.78

25-26. 25.5. 4. 12.12. 30. 90.90

27-28. 27.5. 3. 9.09. 33. 100

total 33

2.

1. Sample:

Sample is a part or portion of a population and it is taken from the population as a representation of the population. It is the portion of a population where information is gathered.

For example the height of students in the faculty of social sciences taken to represent the heights of students in all the departments

2. Population:

Population is the entire collection of items or individuals of which one wishes to examine at a particular time. It is also the largest collection of entities for which we have an interest at a particular time.

For example the number of all males between the ages of 25 and 29 in Enugu state.

3. Continuous Variable:

A continuous variable is a variable which can take an uncountable or infinite set of values. Continuous Variables are gotten from measurements on a continuous scale, and as a result can assume any value from a range of values. For example measurements of heights of a family which is measured on a centimeter or a millimeter scale and could be 10.4-5mm or 10.4573 mm.

4. Discrete Variable:

A discrete variable also called a categorical variable is a variable which exists only as a whole number and is not divisible. It can take a whole or finite number of numerical values, categories or codes. For example the smage if a child or the number of people in a room.

5. Statistics:

The word ‘statistics’ refers to numerical facts such as the number of events occurring in a particular time. It is the scientific method of collecting, organizing, summarizing, presenting and analysing data. It is also the theory and methods of collecting, organizing, presenting, analysing and interpreting data sets so as to determine their essential characteristics.

6. Data:

Data is a numerical statement of facts in a specific field of enquiry or simply numbers which may result from taking measurement. It could also be qualitative i.e. data that deals with description. Data are of two types: primary data which are data collected originally for the first time by a person who secures them by survey for his own personal use, and secondary data which are data collected by someone else from a person that originally collected them and which are processed to some extent.

Question 1

Range = Highest number – Lowest number

= 28 -17

= 11

class interval = Range / no of classes

= 11/6

1.8 (approximately= 2)

C.I M F C .F R .C F

17 – 18 17.5 5 5 5/33 * 100 = 15.2% 5/33 * 100 =15.2%

19 – 20 19.5 6 11 6/33 *100 = 18.2% 11/33 * 100 = 33.4%

21 – 22 21.5 8 19 8/33 * 100 = 24.2% 19/33 * 100 = 57.6%

23 – 24 23.5 7 26 7/33 * 100 = 21.2% 26/33 * 100 =78.8%

25 – 26 25.5 4 30 4/33 * 100 = 12.1% 30/33 * 100 =90.9%

27 – 28 27.5 3 33 3/33 * 100 = 9.1% 33/33 * 100 =100%

TOTAL 33 100%

QUESTION 2

1. SAMPLE : Sample is defined as part of quotient of a population and it is taken as representation of it

2. POPULATION: Population is the entire collection of items which one wishes to examine at a particular time

3. CONTINUOUS VARIABLE can assume any value from a range of value

4. DISCRETE VARIABLE in this case the variable can only be counted and also can be represented in the place of a whole number

5. STATISTICS can be defined as a field of study, which concerns with the practice of collecting and analyzing numerical data in large quantities, especially for the purpose of inferring proportions in a whole from those in a representative data

6. DATA is a numerical statement of fact in a specific state of enquiry or simply numbers which may result to taking measurement.

NAME: OKECHUKWU CLETUS CHIBUEZE

REG NO: 2021/246805

DEPT: ECONOMICS

COURSE: ECO 131

DATE: 9/03/2023

1. The following yield the (kg) were obtained from plots in a soyabean field given two sprays of pesticides

22,20,19,25,22,17,28,20,22,23,17

18,24,25,22,20,23,25,22,28,19,22

15,27,23,24,17,18,22,19,22,23,24

Compute the table as following

a.class interval using sturges rule

b.mid -point

c.frequency

d.cumulative frequency

e.relative frequency

f.relative cumulative frequency

*Class interval using sturges rule

K=1+3.3logN

K= 1+3.3log33

K= 1+3.3(1.5185)

K=1+5.0

K= 6

Class interval (k)

17-18

19-20

21-22

23-24

25-26

27-28

Mid – point

17+18/2= 17.5

19+20/2= 19.5

21+22/2= 21.5

23+24/2= 23.5

25+26/2= 25.5

27+28/2= 27.5

Frequency

5

6

8

7

4

3

£f=33

Cumulative frequency

5

5+6 = 11

11+8= 19

19+7= 26

26+4= 30

30+3= 33

Relative frequency

5/33= 0.15

6/33= 0.18

8/33= 0.24

7/33= 0.21

4/33= 0.12

3/33= 0.09/1

Relative cumulative frequency

0.15

0.15+0.18= 0.33

0.33+0.24= 0.57

0.57+0.21= 0.78

0.78+0.12= 0.9

0.9+0.09 = 1

2. Write a brief note on the following:

* Sample

* Population

* Continuous variable

* Discrete variable

* Statistics

* Data

a. SAMPLE : A sample refers to a smaller, manageable version of a large group, it is a subject containing the characteristics of a large population. Sample are also use in statistics testing when population size are too large for the test to include all possible members of observation

b. POPULATION : A population is the complete set of group of individuals, whether that group comprises a nation or a group of people with a common characteristics, in statistics, a population is the part of individuals from which a statistical sample is drawn for a study

c. CONTINUOUS VARIABLE : A continuous variable is defined as a variable which can take an uncountable set of values,or infinite set of value.for instance if a variable over a non- empty range of the real numbers is Continuous, then it can take on any value in that range

d. DISCRETE VARIABLE : A discrete variable is a variable that takes on distinct, countable values, it is also known as categorical variable.it exist only a while numbers and are not divisible, it can take a finite number of numerical values, categories or code

e. STATISTICS : The word “statistics”refers to numerical fact such as the number of events occuring in the time or the number of people living in a particular area,

It is also the study of the collection, analyzing,interpretation, presentation and organization of data.in other words, it is a mathematical discipline to collect, summarize data, also we can say that statistics is a branch of applied mathematics

f. DATA : A data simple mean the collection of facts, such as number, words, measurements, observation,or events just description of things, it could also be seen as information in raw or unorganized form( such as alphabets, number, or symbols) that refers to or represent condition, ideas or object. Data could be qualitative (I.e data that deal with description) or quantitative ( i.e data that deal with numbers) data are require for empirical analysis and other forms of analysis

Name: Okonkwo bright chukwuebuka

Reg no: 2021/243689

Email: bokonkwo2004@gmail.com

Blog: ebukabright.blogspot.com

Name: Abonyi Agatha mmesomachukwu

Registration Number: 2021/241937

Email: mmesomaagatha@gmail.com

Answer to number 1 question

midpoint F CF RF RCF

17-18 17.5 5 5 15.15 15.15

19-20 19.5 6 11 18.18 33.33

21-22 21.5 8 19 24.24 57.57

23-24 23.5 7 26 21.21 78.78

25-26 25.5 4 30 12.12 90.90

27-28 27.5 3 33 9.09 100

Total frequency= 5+6+8-7+4+3=33

Sturgy rule= 1+3.3logn

1+3.3log33= 1+4.95= 5.95

Approximately= 6

Answer to question number 2

SAMPLE

A sample is a smaller set of data that a researcher chooses or selects from a larger population using a pre defined selection method. These elements are known as sample points, sampling units or observations. Creating a sample is an efficient method of conducting research. Researching the whole population is often impossible, costly and time consuming. Hence, examining the sample provides insights the researcher can apply to the entire population.

POPULATION

population in statistics is the pool of individuals from which a statistical sample is drawn for a study. Thus any selection of individuals grouped by a common feature can be said to be a population.

CONTINUOUS VARIABLE

Continuous variable can be defined as numbers that may assume or infinite values between any two values of reference. For example using the values 1and 2 as reference, there is an infinite number of the decimals between them. Using decimals one may try to list all values between 1 and 2, such as 1, 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2. The interval between the values above is 0.1. However, there is no limit to the numbers that can appear after the decimal point. Thus even between 1 and 1.1, there is an infinite possibility of values, in the interval between 1 and 1.1. 1, 1.0000000….1….1. The number of zereos after the decimal point of the second value may be infinite. Thus even the interval between 1 and 0.00000001 is infinite. A continuous variable falls into this infinite spectrum of possible values. The body mass is an example of a continuous variable.

DISCRETE VARIABLE

Discrete variable are variables that can only take on a finite number of values. All qualitative variable are discrete. Some quantitative variables are discrete, such as performance rated as 1,2,3,4 or 5 or temperature rounded to the nearest degree. sometimes a variable that takes on enough discrete values can be considered to be continuous for practical purposes. One example is time to the nearest millisecond.

STATISTICS

Statistics refers to a discipline of applied mathematics that deals with the gathering, describing, analyzing and drawing conclusions from numerical data. According to Croxton and Cowden “statistics may be defined as a science of collection, organization, presentation, analyzing and interpretation of data.

DATA

Data can be defined as a systematic record of a particular quantity. It is the different values of that quantity represented together in a set. It is a collection of facts and figures to be used for a specific purpose such as survey or analysis.

Question1

Class interval Midpoint F CF RF RCF

17_18 17.5 5 5 15.5 15.15

19_20 19.5 6 11 18.18 3.3

21_22 21.5 8 19 24.24 57.57

23_24 23.5 7 26 21.21 78.78

25_26 25.5 4 30 12.12 90.90

27_28 27.5 3. 33 9.09 100

Total 33

Question 2:

5:statistics, the science of collecting, analyzing, presenting, and interpreting data.

Matric number : 2021/246371

Name: Obumneme Cynthia Mmesoma

Email:ommesomacynthia@gmail.com

Reg number:2021/243696

QUESTION ONE

using sturge rule=1+3.3Log(N)

k=1+3.3Log33

k=1+5.0111

k=6.0111 ≈6

1. The class interval using sturge rule= 17-18,19-20,21-22,23-24,25-26,27-28

2.Mid point (x)=17.5,19.5,21.5,23.5,25.5,27.5

3.frequency= 5,6,8,7,4,3

4.Cummulative frequency=5,11,19,26,30,33

5. Relative frequency=5÷33×100=15.152

6÷33×100=18.182

8÷33×100=24.242

7÷33×100=21.212

4÷33×100=12.121

3÷33×100=9.091

total=100

6. Relative cumulative frequency=15.152,33.334,57.576,78.788,90.909,100

QUESTION TWO

1. SAMPLE: This is a procedure by which one or more members of a population are selected from the population. it is also a part of the population that we actually observe.

2. POPULATION: This is defined as the entire group about which information is desired. it is also the largest collection of entities for which we have an interest at a particular time.

3. CONTINUOUS VARIABLES: This is one for which, within the limits the variable ranges, any value is possible.

4. DISCRETE VARIABLES: it is also known as categorical variables. They are variables or data that exist only as whole numbers and are not divisible.

5. STATICS: This refers to the theory and method of collecting, organizing, presenting, summarizing, analyzing and interpreting data set so as to determine there essential characteristics.

6. DATA: This refers to the collection of facts such as numbers,words, measurements, observations or even just descriptions of things.

Name:Chukwuka Godswill Kosiso

Matric Num:2021/245673

Department:Economics

(No 1)

a) Class = 17-18 ,19-20 ,21-22 ,23-24 ,25-26 ,27-28

B)Frequency =5,6,8,7,4,3

C)Cum frequency =5,11,19,26,30,33

D)Relative frequency =0.15,0.18,0.24,0.21,0.12,0.09

E)Mid point =17.5,19.5,21.5,23.5,25.5,27.5

F)Relative cumulative frequency =15.15%,33.33%,57.5%,78.7%,90.9%,100%

(No 2 )A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations.

A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic. In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study.

A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. Continuous variables are generally measured on scales such as height, weight, temperature, etc. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range.

With the help of continuous variables, one can measure mean, median, variance, or standard deviation.

A discrete variable is a variable which exists only as a whole number and is not divisible. It can take a while or finite number of numerical value,categories or codes.

Discrete variables can also called a categorical variable. For example, you can count the change in your pocket.

Data can come in the form of text, observations, figures, images, numbers, graphs, or symbols. For example, data might include individual prices, weights, addresses, ages, names, temperatures, dates, or distances.

Statistics is a branch that deals with every aspect of the data. Statistical knowledge helps to choose the proper method of collecting the data and employ those samples in the correct analysis process in order to effectively produce the results.

1. A sample:

2. A Population:

3. A continuous variable:

4. A discrete variable:

5. A Data:

Data are measurements or observations that are collected as a source of information.

6. A Statistics:

NAME:murna Livinus

REG NO:2020/250325

EMAIL: murnalivinus@gmail.com

1. class interval sturge rule=1+3.322logN

K=1+3.322logN

K=class intervals

N=number of observations

K=1+3.322logN

=1+3.322(1.5185)

=1+5.0445

K=6.0445

K=6(class intervals)

Range=Highest value -lowest value

=28-17

Range=11

class mid point. freq. Relative.

intervals. freq.

17-18. 17.5. 5. 0.151.

19-20. 19.5 6 0.181.

21-22. 21.5. 8. 0.242

23-34. 23.5. 7. 0.212.

25-26. 25.5. 4. 0.121.

27-28. 27.5. 3. 0.091.

cumulative Relative freq

0.151

0.332

0.574

0.786

0.907

0.998

i.SAMPLEA sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations. A sample should represent the population as a whole and not reflect any bias toward a specific attribute.

ii. POPULATIONA population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic.

In statistic, a population is the pool of individuals from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped by a common feature can be said to be a population. A sample may also refer to a statistically significant portion of a population, not an entire population. For this reason, a statistical analysis of a sample must report the approximate standard deviation, or standard error, of its results from the entire population. Only an analysis of an entire population would have no standard error.

iii.CONTINUOUS VARIABLE

continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. For instance, if a variable over a non-empty range of the number variable is continuous, then it can take on any value in that range. Thus, the range of real numbers between x and y with x, y ∈ R and x ≠ y; is said to be uncountable and infinite.

iv.In continuous optimization problems, different techniques of calculus are often used in which the variables are continuous. Also, the probability distributions of continuous variables can be stated in expressions of probability density functions in statistical theory.

v.DISCREET VARIABLE

A discrete variable is a kind of statistics variable that can only take on discrete specific values. The variable is not continuous, which means there are infinitely many values between the maximum and minimum that just cannot be attained, no matter what.

vi.STATISTICS

statistics, is the science of collecting, analyzing, presenting, and interpreting data. Governmental needs for census data as well as information about a variety of economic activities provided much of the early impetus for the field of statistics. Currently the need to turn the large amounts of data available in many applied fields into useful information has stimulated both theoretical and practical developments in statistics.

vii.DATA

the quantities, characters, or symbols on which operations are performed by a computer, which may be stored and transmitted in the form of electrical signals and recorded on magnetic, optical, or mechanical recording media.

Agbafo Kamsicho Chidinma

2021/241951

Economics department

Question1

Class interval Midpoint F CF RF RCF

17_18 17.5 5 5 15.5 15.15

19_20 19.5 6 11 18.18 3.3

21_22 21.5 8 19 24.24 57.57

23_24 23.5 7 26 21.21 78.78

25_26 25.5 4 30 12.12 90.90

27_28 27.5 3. 33 9.09 100

Total 33

Question 2:

5:statistics, the science of collecting, analyzing, presenting, and interpreting data.

1.) (i) The class interval using sturge rule

K = 1+3.3log(33)

= 6.01

17-18, 19-20, 21-22, 23-24, 25-26, 27-28

(ii) Mid-point

17.5, 19.5, 21.5, 23.5, 25.5, 27.5

(iii) Frequency

5, 6, 8, 7, 4, 3 = 33

(iv) Cumulative Frequency

5, 11, 19, 26, 30, 33

(v) Relative Frequency

5/33*100 = 15.2%

6/33*100 = 18.2%

8/33*100 = 24.2%

7/33*100 = 21.2%

4/33*100 = 12.1%

3/33*100 = 9.1%

(vi) Relative Cumulative Frequency

5/33*100 = 15.2%

11/33*100 = 33.3%

19/33*100 = 57.6%

26/33*100 = 78.8%

30/33*100 = 90.9%

33/33*100 = 100%

2.) (i) SAMPLE: A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. It can also be seen as a procedure by which one or more members of a population are selected from the population.

(ii) POPULATION: A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristics.

(iii) CONTINUOUS VARIABLE: is defined as a variable which can take an uncountable set of values or infinite set of values. It is a variable whose value is obtained by measuring. Continuous variable can take any value between a certain set of real numbers.

(iv) DISCRETE VARIABLES: are also known as categorical variables. They are variables or data that exist only as whole numbers and are not divisible. A discrete variable can take on a finite number of numerical values, categories or codes.

(v) DATA: it could be seen as a collection of facts, such as numbers, words, measurements, observations or even just descriptions of things. It could also be seen as information in raw or unorganized form (such as alphabets, numbers, or symbols) that refers to, or represents, conditions, ideas, or objects.

NAME: CHIME ADAEZE CHIZURUOKE

REG. NUMBER: 2021/241947

Email address: adaezechime3@gmail.com

Question 1

Using Sturge rule, the number of class intervals is 6.

Class Mid-point f c.f r.f r.c.f

interval

17 – 18 17.5 5 5 15.15 15.15

19 – 20 19.5 6 11 18.18 33.33

21 – 22 21.5 8 19 24.24 57.57

23 – 24 23.5 7 26 21.21 78.78

25 – 26 25.5 4 30 12.12 90.9

27 – 28 27.5 3 33 9.09 100

Total 33

Question 2

1. A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations.

2. Population is the entire set of items from which you draw data for a statistical study. It can be a group of individuals, a set of items, etc. It makes up the data pool for a statistical study.

Population also refers to data on your study of interest. It can be a group of individuals, objects, events, organizations, etc. You use populations to draw conclusions.

3. Continuous variables can be described as numbers that may assume one of infinite values between any two values of reference. They consist of mainly decimals numbers eg the height of an individual can be 175.8cm, the weight of a box etc.

4. Discrete variables come in the form of whole numbers and, sometimes, can be counted ‘by fingers.’ Eg the number of students in a class, number of cars parked in a street, and number of children in a family are examples of discrete variables. One can never claim that a family has 1.7 children.

5. Data are individual pieces of factual information recorded and used for the purpose of analysis. It is the raw information from which statistics are created.

Q1. According to sturges rule

K= 1+3.3 log N

K= numbers of interval

N = numbers of observation

K= 1+3.3 log 48

K= 6.5

Soyabean MD(x) F CF Rf Rcf

17-18 17.5 6 6 0.125 0.67

19-20 19.5 7 13 0.145 0.146

21-22 21.5 13 20 0.270 0.224

23-24 23.5 8 21 0.166 0.235

25-26 25.5 7 15 0.145 0.168

27-28 27.5 7 14 0.145 0.157

=48 =89

Q2)I. Sample: is a smaller set of data that a researcher chooses or select from a larger population using a pre-defined selection method. These elements are known as sample points, sampling units, or observations.

ii) Population: population is a complete collection of entities or items that has at least one characteristics in common. It is also a discrete proup of people, animals, or things that can be indentified by at least one common characteristics for the purpose of data collection and analysis.

iii). Continuous Variables: is a variable which can take and uncountable set of values or infinite set of values. For instance, if a variable over a non-empty range of the real number is continuous, then it can take on any value in that range.

iv). Discrete Variables: is a variable that takes on distinct, countable values. Also known as a categorical variable, because it has separate invisible categories. However no values can exist in-between two categories, i.e. it does not attain all the values within the limits of the variable.

V). Statistics: statistics is concern with the collection of data, organizing, interpretation, analysis and data presentation. The main purpose of using statistics is to plan the collected data in terms of experimental designs and statistical survey.

Vi). Data: data can defined as a systematic record of a particular quantity. It is the different values of that quantity represented figures to be used for a specific purpose such as a survey or analysis. When arranged in an organize form can be called information.

1a. Class interval is 6.1

b. 17.5,19.5,22.5,24.5,27.5

c. 5, 6, 11, 23, 30, 33 .

d. 5,11,23,30,33

e. 15.2,18.2,36.4,21.2,9.1

f. 4.9,10.8,22.5,29.4,32.4

2a. Sample is portion of a given population and its taken from or as a representation of it

Eg heights of students in a faculty

B. Population is the total number of people in a geographical area ussually determined by headcount.

C. Continious variable is a variable that takes or gives an infinite set of data or value eg salary if a unn staff

D. Discrete variable is a variable that can be counted or represented in whole numbers eg age of students

E. Statistics can be defined as a field of study concerning the layout ofcollection,experiment and analysis of data.it is measured i two methods

i. Parametric influential method

ii. Non parametric influencial method

F. Data is a statement of fact in a specific field of enquiry types are primary and secondary data.

1. Sturges rule = (k = 1 + 3.3log N)

K= Number of intergers

N= Number of observation

K= 1 + 3.3 log 33

= 1 + 3.3 × 1.518

= 1 + 5.0094

K= 6.0094

≈6.01

Class interval M.D Frequency CF RF RCF

17 — 18 17.5 5 5 15.15 15.15

19 — 20 19.5 6 11 18.18 33.33

21 — 22 21.5 8 19 24.24 57.57

23 — 24 23.5 7 26 21.21 78.78

25 — 26 25.5 4 30 12.12 90.90

27 — 28 27.5 3 33 9.09 100

33

2. A sample is defined as parts or portion of a population and it is taken from the population as a representation of it. It is the part of the population that is observed. It can also be described as using a proportion or part of the population to try to draw conclusion about the whole using sample estimate. In sampling, one or more members of of a population are selected from the population. The main aim is to observe members and draw valid conclusion based on the results about several characteristics of the entire population. E.g the test score of Eco 131 taken from each department to determine the total scores in the faculty of social science, the departments here represent the sample and the course reps to present this test score are the representative sample.

ii. Population is defined as the entire collection of items or individuals in a particular area at a particular time. Population in economics is defined as the entire individuals or items of which one wishes to examine at a particular time inorder to get a desired information usually from the portion or sample from which information is gathered.

iii. Continuous variable assumes any value from a range of values. Continuous variable can take any value between a certain set of real numbers.

iv. Discrete variables or data are also known as categorical variables that exist only as whole numbers and are not divisible. A discrete variable can take on a finite number of numerical values, categories or codes.

v. Statistics is defined as the theory and methods of collecting, organizing, presenting, analysing and interpreting data sets so as to determine their essential characteristics. It entails deriving valid conclusions and making reasonable decisions on the basis of analysis. Statistics also involves the study of ways of collecting,. analysing and interpreting numerical facts or numerical data

vi. Data is a raw information or an unprocessed information. It is a numerical statement of fact in a specific field of requirements i.e numbers which may result from taking measurements. In its simplest form, data is a collection of facts, such as numbers,.words, measurements, observations or even just descriptions of things. It is the fundamental aspect of research. Data could be qualitative ( data that deals with description) or quantitative ( data that deals with numbers).

Amaechina chidindu Roseline

2021/244129

Economics

NAME: UCHECHUKWU IFECHUKWU EZRA

REG NO: 2021/244047

EMAIL ADDRESS: ifechukwuuchechukwu392@gmail.com

ANSWERS

Using Sturge Rule K=1+3.3logN

N=33

K=1+3.3log (33)

K=6

(THE FOLLOWING INFORMATION IS IN TABLE FORMAT)

CLASS INTERVAL

MID POINT

(X)

FREQUENCY

CUMMULATIVE FREQUENCY

RELATIVE FRQUENCY

RELATIVE CUMMULATIVE FRQUENCY

17-18

17.5

5

5

15.15

4.0

19-20

19.5

6

11

18.18

4.8

21-22

21.5

8

19

24.24

6.4

23-24

23.5

7

26

21.21

5.6

25-26

25.5

4

30

12.12

3.2

27-28

27.5

3

33

9.09

2.4

TOTAL

33

124

SAMPLE: Sample is defined as parts or portion of a population and it taken from the population as a representation of it.

-POPULATION: Population is the entire collection of item or individuals which one wishes to examine at a particular time.

-CONTINUOUS VARIABLE: Is one for which, within the limits the variables ranges, any value is possible.

-DISCRETE VARIABLE: These are variables or data that only exist as whole numbers and are not divisible.

-STATISTICS: Statistics according to Horace Secrist can be defined as the aggregate of facts affected to a marked extent by multiplicity of causes, numerically expressed, enumerated or estimated according to a reasonable standard of accuracy, collected in a systematic manner, for a predetermined purpose and placed in relation to each other.

-DATA: Data can be defined as information in raw or unorganized form (such as alphabets, number, or symbols) that refer to, or represent, conditions, ideas, or objects.

Name: Ifechukwu Christian thankGod

Course: eco 131

Department: economics

Reg number: 2021/245589

Question1

Class interval Midpoint F CF RF RCF

17_18 17.5 5 5 15.5 15.15

19_20 19.5 6 11 18.18 3.3

21_22 21.5 8 19 24.24 57.57

23_24 23.5 7 26 21.21 78.78

25_26 25.5 4 30 12.12 90.90

27_28 27.5 3. 33 9.09 100

Total 33

Question 2:

5:statistics, the science of collecting, analyzing, presenting, and interpreting data.

Name: UGWU CHIDIEBERE LOVETH

REG NO: 2018/242902

DEPARTMENT: Education/Economics

NO1)

FIELDS(kg) MID POINT FREQUENCY CUMULATIVE FREQUENCY RELATIVE FREQUENCY RELATIVE CUMULATIVE FREQUENCY

17-18 17.5 5 5 15.5 4.03

19-20 19.5 6 11 18.18 8.87

21-22 21.5 8 19 24.24 15.32

23-24 23.5 7 26 21.21 20.96

25-26 25.5 4 30 12.12 24.19

27-28 27.5 3 33 9.09 26.61

=33 =124 =99.99 =99.98

No2A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations. A sample should represent the population as a whole and not reflect any bias toward a specific attribute.

I)What Is a Sample?

There are several sampling techniques used by researchers and statisticians, each with its own benefits and drawbacks.

II)What Is Population?A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic.

In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped by a common feature can be said to be a population. A sample may also refer to a statistically significant portion of a population, not an entire population. For this reason, a statistical analysis of a sample must report the approximate standard deviation, or standard error, of its results from the entire population. Only an analysis of an entire population would have no standard error.

III)Continuous variableIn continuous optimization problems, different techniques of calculus are often used in which the variables are continuous. Also, the probability distributions of continuous variables can be stated in expressions of probability density functions in statistical theory.

A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range. Thus, the range of real numbers between x and y with x, y ∈ R and x ≠ y; is said to be uncountable and infinite.

IV)DISCRETE VARIABLE

A discrete variable is a kind of statistics variable that can only take on discrete specific values. The variable is not continuous, which means there are infinitely many values between the maximum and minimum that just cannot be attained, no matter what.

V)What Is Statistics?

Statistics is a branch of applied mathematics that involves the collection, description, analysis, and inference of conclusions from quantitative data. The mathematical theories behind statistics rely heavily on differential and integral calculus, linear algebra, and probability theory.

Statisticians, people who do statistics, are particularly concerned with determining how to draw reliable conclusions about large groups and general events from the behavior and other observable characteristics of small samples. These small samples represent a portion of the large group or a limited number of instances of a general phenomenon.

Vi)What is Data?

is data” is that data is different types of information usually formatted in a particular manner. All software is divided into two major categories: programs and data. We already know what data is now, and programs are collections of instructions used to manipulate data.

We use data science to make it easier to work with data. Data science is defined as a field that combines knowledge of mathematics, programming skills, domain expertise, scientific methods, algorithms, processes, and systems to extract actionable knowledge and insights from both structured and unstructured data, then apply the knowledge gleaned from that data to a wide range of uses and domains.

Name: Christian Ifechukwu thankGodA sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations. A sample should represent the population as a whole and not reflect any bias toward a specific attribute.

A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic.

In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped by a common feature can be said to be a population. A sample may also refer to a statistically significant portion of a population, not an entire population. For this reason, a statistical analysis of a sample must report the approximate standard deviation, or standard error, of its results from the entire population. Only an analysis of an entire population would have no standard error.

A discrete variable is a variable that takes on distinct, countable values. In theory, you should always be able to count the values of a discrete variable.

Course: Eco 131

Reg number: 2021/245589

Department: Economics

2i) Sample

There are several sampling techniques used by researchers and statisticians, each with its own benefits and drawbacks.

ii) Population

iii) Continuous Variable

In Mathematics, a variable can be classified into two types, namely: discrete or continuous. If a variable can take on two or more distinct real values so that it can also take all real values between them (even values that are randomly close together). In this case, the variable is continuous in the given interval. If a variable will take a non-infinitesimal break on each side of it, and it does not contain any values, then it is discrete around that value. In some instances, a variable will hold discrete values in some areas of the number line and continuous in others areas. A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range. Thus, the range of real numbers between x and y with x, y ∈ R and x ≠ y; is said to be uncountable and infinite.

In continuous optimization problems, different techniques of calculus are often used in which the variables are continuous. Also, the probability distributions of continuous variables can be stated in expressions of probability density functions in statistical theory. Instant variable and Ratio variable are the types of continuous variable

iv) discrete variable

Examples

Examples of discrete variables include:

Years of schooling

Number of goals made in a soccer match

Number of red M&M’s in a candy jar

Votes for a particular politician

Number of times a coin lands on heads after ten coin tosses. All of these variables take a finite number of values that you can count. They are examples of discrete variables.

V) Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In other words, it is a mathematical discipline to collect, summarize data. Also, we can say that statistics is a branch of applied mathematics. However, there are two important and basic ideas involved in statistics; they are uncertainty and variation. The uncertainty and variation in different fields can be determined only through statistical analysis. These uncertainties are basically determined by the probability that plays an important role in statistics. Statistics is simply defined as the study and manipulation of data. As we have already discussed in the introduction that statistics deals with the analysis and computation of numerical data. Let us see more definitions of statistics given by different authors here. According to Merriam-Webster dictionary, statistics is defined as “classified facts representing the conditions of a people in a state – especially the facts that can be stated in numbers or any other tabular or classified arrangement”. According to statistician Sir Arthur Lyon Bowley, statistics is defined as “Numerical statements of facts in any department of inquiry placed in relation to each other”.

Vi) Data are measurements or observations that are collected as a source of information. There are a variety of different types of data, and different ways to represent data. The number of people in Australia, the countries where people were born, number of calls received by the emergency services each day, the value of sales of a particular product, or the number of times Australia has won a cricket match, are all examples of data.

Name : Dinneya Chidinma Favour

Department : Social Science Education

Unit: Economics Education

Reg : 2021/241490

1. Sample: A sample is a part or proportion of the population that we actually observe. It is usually difficult to examine all members of the population due to time, cost and other constraints, so sample is needed. From the sample we try to draw conclusion about the whole.

2. Population: Population is defined as the entire group about which information is desired. It is the largest collection of entities for which we have an interest at a particular time. It could be an entire set of objects, observations, or scores that have something in common.

3. Continuous Variable: The continuous variable is one for which within the limits the variable ranges, any value is possible, it can take any value within a certain set of real numbers. For example; ” The heights of students” is a continuous variable, Heights could be 5.4, 6.5 etc

4. Discrete variable: Discrete variable is also known as Categorical variable. They are variables that exist only as whole numbers and are not divisible. A discrete variable can take on a finite number of numerical values, categories or codes.

5. Statistics: Satistics refer to a numerical fact such as the number of events occuring in time or the number of people living in a particular Area. It also involves the study of ways of collecting , analyzing and interpreting numerical facts or numerical data.

6. Data: Data refers go to an information in raw or unorganized form ( such as alphabets or numbers) that represents conditions, ideas or Objects). It is simply the collection of facts such as numbers, words, measurements, observations or even just description of things. Data could be qualitative ( data that deal with description) or quantitative ( data that deal with numbers). Data is a fundamental aspect of research and is required for empirical analysis and other forms of analysis

Using sturge rule to determine the class interval

Sturge rule= 1+3.3 x Log(N), where N is the total number of obervation.

1+3.3 x Log(33) = 1+ 3.3 x 1.52= 1+5=6

Class interv. M.D FREQ. C.F. R.F R.C.F

17-18 17.5 5 5 15.15 4.03

19-20 19.5 6 11 18.18 8.87

21-22 21.5 8 19 24.24 15.32

23-24 23.5 7 26 21.2 20.96

25-26 25.5 4 30 12.12 24.19

27-28 27.5 3 33 9.09 26.61

Total 33 124

Name: Dike Grace Afuekwe

Reg Number:2021/246042

QUESTON 1

Class interval Frequency Mid-point Cumulative frequency Relative.F Cumulative.R.F

17-18 5 17.5 5 15.6 5.1

19-20 5 19.5 10 15.6 10.2

22-23 12 22.5 22 37.7 22.4

24-25 7 24.5 29 21.8 29.5

27-28 3 27.5 32 9.3 32.6

TOTAL: 32 98

QUESTION 2

Sample is defined as a numerical quantity (such as the sample mean) calculated such statistics are used to estimate parameter

Population is defined as the entire group about which information is desired

Continous Variable is one for which ,within the limits the variable ranges,any value possible

Discrete Variable are variables or data that exists only as whole numbers and are not divisible

Statistics is the practice of collecting numerical data in large quantities for the purpose of infering proportions

Data is the collection of facts such as numbers,words,measurements,observations or even descriptions of things

1.Using sturges rule

k=1+3.3 log(33)

k=1+3.3×1.52

k=1+5.01

k=6.01

k=6 intervals

class intervals midpoint(x) frequency c.f R.F. R.C.F

17-18. 17.5. 5. 5. 15.2. 4.03

19-20. 19.5. 6. 11. 18.2. 8.87

21-22. 21.5. 8. 19. 24.2. 15.32

23-24. 23.5. 7. 26. 21.2. 20.96

25-26. 25.5. 4. 30. 12.1. 24.19

27-28. 27.5. 3. 33. 9.0. 26.61

33. 124

SAMPLE: Defined as a smaller and more manageable representation of a larger group.

POPULATION: A complete set group of individuals with a common characteristic

CONTINUOUS VARIABLE: Defined as a variable which can take an uncountable set of values or infinite set of values

DISCRETE VARIABLE: Variables are countable in a finite amount of time.

STATISTICS: A branch of mathematics for collecting, analysing and interpreting data.

DATA: Factual information used as a basis for reasoning, discussion, or calculation.

UMOREN PRAISE IBORO

2021/241371.

ECONOMICS DEPT.

C.l M.P F C.F R.F R.CF 17-18 17.5 5 5 15.15 4.03

19-20 19.5 6 11 18.18 8.87

21-22 21.5 8 19 24.24 15.32

23-24 23.5 7 26 21.21 20.97

25-26 25.5 4 30 12.12 24.19

27-28 27.5 3 33 9.09 26.61

SAMPLE

sample refers to a smaller, manageable version of a larger group. It is also defined as a numerical quality (such as the sample mean). It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations. A sample should represent the population as a whole and not reflect any bias toward a specific attribute.a sample is an analytic subset of a larger population. The use of samples allows researchers to conduct their studies with more manageable data and in a timely manner. Randomly drawn samples do not have much bias if they are large enough, but achieving such a sample may be expensive and time-consuming.

POPULATION

population refers to data on your study of interest. It can also be defined as the entire group about which information is desired. It can be a group of individuals, objects, events, organizations, etc. You use populations to draw conclusions.

CONTINUOUS VARIABLE

continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range.

variable is said to be continuous if it can assume an infinite number of real values within a given interval. For instance, consider the height of a student. The height can’t take any values. It can’t be negative and it can’t be higher than three metres. But between 0 and 3, the number of possible values is theoretically infinite. A student may be 1.6321748755 … metres tall. In practice, the methods used and the accuracy of the measurement instrument will restrict the precision of the variable.

DISCRETE VARIABLES

– A discrete variable is a variable that takes on distinct, countable values,Discrete variables have values that are counted.As opposed to a continuous variable, a discrete variable can assume only a finite number of real values within a given interval. An example of a discrete variable would be the score given by a judge to a gymnast in competition: the range is 0 to 10 and the score is always given to one decimal (e.g. a score of 8.5). You can enumerate all possible values (0, 0.1, 0.2…) and see that the number of possible values is finite: it is 101! Another example of a discrete variable is the number of people in a household for a household of size 20 or less. The number of possible values is 20, because it’s not possible for a household to include a number of people that would be a fraction of an integer like 2.27 for instance.

STATISTICS

Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In other words, it is a mathematical discipline to collect, summarize data. Also, we can say that statistics is a branch of applied mathematics.Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data. Statistics is a highly interdisciplinary field; research in statistics finds applicability in virtually all scientific fields and research questions in the various scientific fields motivate the development of new statistical methods and theory. In developing methods and studying the theory that underlies the methods statisticians draw on a variety of mathematical and computational tools

DATA

data are individual pieces of factual information recorded and used for the purpose of analysis. It is the raw information from which statistics are created. Statistics are the results of data analysis – its interpretation and presentation. Data are measurements or observations that are collected as a source of information

class:: 17-18, 19-20, 21-22, 23-24, 25-26, 27-28

frequency: 5,6,8,7,4,3

midpoint: 17.5, 19.5, 21.5, 23.5, 25.5, 27.5

cumulative frequency: 5,11,19,26,30,33

Relative frequency: 0.15, 0.18, 0.24, 0.21, 0.12, 0.09

Relative cumulative frequency: 15.2%, 33.3%, 57.6%, 78.8%, 90.9%, 100%.

Name: Omeje Chisom Peace

Department: Economics

Reg number: 2021/241965

1.Computing the following as follows

Using the sturge rule

Solution.

{Sturge rule} k=1+3.3 log N

K=1+3.3 log 33

K=1+3.3(1.5185)

K=1+5.0

K=6

:no of class= 6

Range =28-17

=11

Class interval=11/6

=1.8. (approximately) =2.

Class interval:

17-18 ,19-20,21-22,23-24,25-26,27-28

Mid point:

17.5, 19.5, 21.5, 23.5, 25.5, 27.5.

Frequency:

5, 6 ,8, 7, 4, 3

5+6+8+7+4+3=30

Cumulative frequency:

5, 11, 19, 26, 30, 33

Relative frequency

5/33 *100 =15.15%

6/33*100= 18.18%

8/33*100= 24.24%

7/33*100 =21.21%

4/33*100 =12.12%

3/33*100 =9.09%

Relative cumulative frequency

5/33*100= 15.15%

11/33*100= 33.3%

19/33*100= 57.57%

26/33*100= 78.78%

30/33*100= 90.90%

33/33*100= 100%

2. Discuss the following:,,,,A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations.

1. A sample:

3. A continuous variable:

A continuous variable is a specific kind a quantitative variable used in statistics to describe data that is measurable in some way.The continuous variable refers to the numerical variable whose value is attained by measuring. Continuous variables are generally measured on scales such as height, weight, temperature, etc.

4. A discrete variable:

A discrete variable is a variable which exists only as a whole number and is not divisible. It can take a while or finite number of numerical value,categories or codes.For example,the number of people in a room or counting the money you have in ur account.

Discrete variables can also called a categorical variable.

5. A Statistics:Statistics is a branch that deals with every aspect of the data. Statistical knowledge helps to choose the proper method of collecting the data and employ those samples in the correct analysis process in order to effectively produce the results.

6. A data:

Data is information that has been translated into a form that is efficient for movement or processing. Relative to today’s computers and transmission media, data is information converted into binary digital form. It is acceptable for data to be used as a singular subject or a plural subject. Raw data is a term used to describe data in its most basic digital format.

NAME: MADUABUCHI PRECIOUS CHIDINMA

REG NO: 2021/247447

DEPARTMENT: ECONOMICS

1) CLASS INTERVAL USING STURGE RULE = 1+3.3LOG32 =5.9669

= 6

RANGE = 28 -17 = 11

INTERVAL. MD(X).| F . CF. RF. RCF.

17-18 17.5.| 5. 5. 15.6. 4.2

19-20. 19 .5. 5. 10. 15.6. 8.4

21-22. 21.5. 8. 18. 25. 15.1

23-24. 23.5. 7. 25. 21.9. 21

25-26. 25.5. 4. 29 12.5 24.4

27-28. 27.5. 3 32. 9.4 26.9

____. ____

32. 119

____. ____

2) a)SAMPLE: A sample refers to part or smaller version of a larger group .

b)POPULATION: It is the complete set of a group

C) CONTINUOUS VARIABLE: Represent measurable amounts (e.g. Water,volume,weight)

d)DISCRETE VARIABLE: Represent counts (e.g number of objects in a collection)

e)STATISTICS: It is a branch of applied mathematics that involves collection,description, analysis and inference of conclusions from quantitative data

f)DATA: Refers to raw information. It is a record of a specific quantity.

Using Struge Rule To Get Class Interval::

k=1+3.3 log N

k=1+3.3 log 33

k=1+3.3(1.5185)

k=1+5.0

k=6

range=28-17= 11

class interval =11/6 =1.8 ~ 2

cum. Relative

class. F. midpoint. frequency frequency

17 – 18. 5. 17.5. 5. 15.2%

19 – 20. 6. 19.5. 11. 18.2%

21 – 22. 8. 21.5. 19. 24.2%

23 – 24. 7. 23.5. 26. 21.2%

25 – 26. 4. 25.5. 30. 12.2%

27 – 28. 3. 27.5. 33. 9.1%

Relative cumulative frequency

15.2%

33.4%

57.6%

78.8%

90.9%

100%

2.a) Sample: A sample is a part of the population that we actually observed. It can equally be seen as a proportion or part of the population usually the part from which information is gotten

b.) Population: Population is the entire group of individual at a particular area that we are interested in making a statement about OE which information is required. It is your zone of interest.

c.) Continuous Variables: A continuous variable is one for which with the limit the variable ranges, any value is possible. Continuous Variables can take any value between a certain set of real numbers. The value given to an observation for a continuous variable can include values as small as the instrument of measurement allows.

d.) Discrete Variable: They are variables that exist only as whole numbers and are not divisible. A discrete variable can take a finite number of numerical categories or codes.

e.) Statistics: This refers to numerical facts such as the events occurring in time or the number of people living in a particular area. It also involves the study of ways of collecting analyzing and interpreting numerical facts or numerical data.

f.) Data: In its simplest form, data could be seen as a collection of fact, such as numbers, words, measurements, observation or even just descriptions of things.

Name: Chikezie Maureen Chidera

Course: ECO 131

Department: Economics

Reg. No.: 2021/244773

1. K= 1+3.3logN( sturge rule)

K= 1+3.3log33

K=1+3.3(1.5185)

K=1+5.0

K=6 or no of classes=6

Range = 28-17 =11

Class interval = 11/6 = 1.8 = 2

2. Class-interval. Midpoint. Freq. Cumulative freq. Relative freq. Relative cum.(freq)

17-18. 17.5. 5. 5. 5/33 *100/1=15.2%. 5/33*100/1=15.2%

19-20. 19.5. 6. 11. 6/33*100/1=18.2%. 11/33*100/1=33.4%

21-22. 21.5. 8. 19. 8/33*100/1=24.2%. 19/33*100/1=57.6%

23-24. 23.5. 7. 26. 7/33*100/1=21.2%. 26/33*100/1=78.8%

25-26. 25.5. 4. 30. 4/33*100/1=12.1%. 30/33*100/1=90.9%

27-28. 27.5. 3. 33. 3/33*100/1=9.1%. 33/33*100/1=100%

33. 100%.

3. Sample: A Sample is a part of the population that we actually observe.it is also a part or proportion of the population I e the proportion from the information gathered. It is also defined as a smaller and more manageable representation of a large group.

Population: The population is the entire group of individuals that we are interested in making a statement about. It is the entire group about which information is desired. it refers to the people who live in a particular area at a specific time. But in statistics, population refers to data on your study of interest. It is also described as the largest collection of entities, for which we have an interest at a particular time.

Continuous variable: It is one of which, within the limits, the variable ranges, abt value is possible. It can take any value between a certain set of real numbers. it’s also defined as a variable which can take an uncountable set of values or infinite set of values.

Discrete variable: It is also known as categorical variables or data. They are variables or data that exist only as whole numbers and are not divisible. A discrete variable can take on a finite number of numerical values, categories or codes. it’s a variable that takes on distinct, countable values.

Statistics: It refers to the numerical facts such as the number of events occuring in time or the number of people living in a particular area. It also involves the study of ways of collecting, analyzing and interpreting numerical data. It also entails deriving valid conclusion and making reasonable decisions on the basis of analysis. It is the development and application of methods to the collection, analysis and interpretation of observed information(data) from planned investigations. It’s also the study of the collection analysis, interpretation, presentation, and organization of data. In other words, it’s a mathematical discipline to collect, summarize data.

Data: Data is the collection of facts, such as numbers, measurements, observations or even just descriptions of things. It could also be seen as information in raw or unorganized form such as alphabets, numbers or symbols, that represent conditions, ideas or objects. They’re individual pieces of factual information recorded and used for the purpose of analysis.

Sturge rule} k=1+3.3 log N

K=1+3.3 log 33

K=1+3.3(1.5185)

K=1+5.0

K=6

:no of class= 6

Range =28-17

=11

Class interval=11/6

=1.8. (approximately) =2.

Class interval:

17-18 ,19-20,21-22,23-24,25-26,27-28

Mid point:

17.5, 19.5, 21.5, 23.5, 25.5, 27.5.

Frequency:

5, 6 ,8, 7, 4, 3

5+6+8+7+4+3=30

Cumulative frequency:

5, 11, 19, 26, 30, 33

Relative frequency

5/33 *100 =15.15%

6/33*100= 18.18%

8/33*100= 24.24%

7/33*100 =21.21%

4/33*100 =12.12%

3/33*100 =9.09%

Relative cumulative frequency

5/33*100= 15.15%

11/33*100= 33.3%

19/33*100= 57.57%

26/33*100= 78.78%

30/33*100= 90.90%

33/33*100= 100%

2. i. Sample: A sample refers to a smaller, manageable version of a larger group. it is a subject containing the characteristics of a larger population. samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations. A sample should represent the population as a whole and not reflect any bias towards a specific attribute.

ii. Population: Population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristics. In statistics,a population is the pool of individuals from which a statistical sample is drawn for a study. This, any selection of individuals grouped by a common feature can be said to be a population.

iii. Continuous Variable: A continuous Variable is defined as a variable which can take an uncountable set of value or infinite set of value. It is a specific kind of quantitative variable used in statistics to describe data that is measurable in some way.e.g height, weight or time.

iv. Discrete Variable: A discrete Variable is a variable that takes on distinct, countable values.e.g year of schooling,number of goals made in a soccer match,votes for a particular politician. All these variables takes a finite number of values that you can count.

v. Statistics: Statistics is the collation and analysis of numerical data to arrive at a specific inference. It refers to numerical facts such as the number of events occurring in time or the number of people living in a particular area.

vi. Data: Data could be seen as collection of facts,such as numbers, words, measurements, observations or even just description of things. It can be seen as information in raw or organized form that refer to or represent, conditions, ideas or objects.

(1).class

interval|. midpoint/F/ CF/RF/Rcf

17-18. 17.5. 5. 5. 15. 15

19-20. 19.5. 6. 11. 18. 33

21-22. 21.5. 8. 19. 24. 57

23-24. 23.5. 7. 26. 21. 78

25-26. 25.5. 4. 30. 12. 90

27-28. 27.5. 3

33. 9. 100

class interval using sturge rule

k=1+3.3 log N

where h =number of classes ,N=total frequency

k=1+3.3log 33

k =1+33 (1.518)

k=6.

(2).sample: a small part or quantity intended to show what whole looks like.

population: is the total number of people or inhabitants in a geographical area or zone.

continuous variable: is a variable which can take an uncountable set of values or infinite set of values.

Discrete variable: may assume only and usually finite , number of values.

statistics: the practice of science of collecting and analysing numerical data in large quantities.

Data: is the facts on statistics collected together for reference or analysis.

Name: CHIBUZOR GODSON CHIKWESIRI

Reg No: 2021/244133

Email Address: godson13heir@gmail.com

Course Code: ECO 131

ANSWER

Question One.

The Class Interval using “Sturge rule”;

Formula: K = 1+3.3LogN. Where N equals to total number of observations

K= 1+3.3LogN

K= 1+3.3Log33

K= 1+3.3(1.5185)

K= 1+5.01105

K= 6.01105

K~ 6.

Range = Highest Number – Lowest Number

= 28 – 17 = 11

Range/K

=11/6

=1.8333 ~ 2.

Hence, class interval is six (6), with two(2) interval of numbers each.

1. Class Interval(KG)

17-18, 19 – 20, 21- 22, 23 -24, 25 -26, 27 -28.

2. Mid Point (X)

17.5, 19.5, 21.5, 23.5, 25.5, 27.5

3. Frequency (F)

5, 6, 8, 7, 4, 3.

4. Cumulative Frequency (CF)

5, 11, 19, 26, 30, 33.

5. Relative Frequency (RF)

15.2, 18.2, 24.2, 21.2, 12.1, 9.1

N:B; To get this, the RF = F/N × 100. where F equals to Frequency and N equals to sum of observation.

6. Relative Cumulative Frequency (RCF)

15.2, 33.3, 57.6, 78.8, 90.9, 100.

N:B; To get this, the RCF= CF/N × 100

Question Two.

Writing on the following:

1. SAMPLE: A sample refers to a proportion of the population that we actually observe. It is the part or proportion from which information is gathered. The process of generalising results in our sample to that of the entire population is called ‘statistical inference’.

2. POPULATION: Population refers to the entire group of individuals that we are interested in making a statement about or the entire group about which information is desired. In other words,it is described as a largest collection of entities for which we have interest at a given period of time; an entire set of objects, observations or scores that have something in common.

3. Continuous Variable: A continuous variable refers to one for which, within the limits the variable ranges,any value is possible. It can take any value between a certain set of real numbers. The value given to an observation for a continuous variable can include values as small as the instrument of measurement allows.

4. Discrete Variable: Discrete variables refers to variables or data which exists only as whole numbers and are not divisible. A discrete variable can take on a finite number of numerical values categories , categories or codes. Discrete variables are also known as ‘Categorical variables’.

5. Statistics: Statistics refered to numerical facts such as the number of events occurring in time or the number of people living in a particular area. It involves the study of ways of collecting, analysing and interpreting numerical facts or data.

Statistics is basically concerned with the scientific method of collecting,organising,summarising, presenting and analysing data. It theoretically and methodologically entails deriving valid conclusions and making reasonable decisions on the basis of analysis.

6. Data: Data refers to an unprocessed information or information in it’s raw or unorganised form (such as alphabets, numbers or symbols) which refers to, or represent conditions,ideas or objects. In other words, data in it’s simplest form,can be seen as a collection of facts such as numbers, words, measurements, observations or even just descriptions of things. Data can be either qualitative(i.e, data that deals with description) or quantitative (i.e, data that deal with numbers). Data collection is a fundamental aspect of research and it is required for empirical analysis and other forms of analysis.

Name: Asiegbunam destiny ebubechukwu

Reg no: 10284348DA

Question1

Class interval Midpoint F CF RF RCF

17_18 17.5 5 5 15.5 15.15

19_20 19.5 6 11 18.18 3.3

21_22 21.5 8 19 24.24 57.57

23_24 23.5 7 26 21.21 78.78

25_26 25.5 4 30 12.12 90.90

27_28 27.5 3. 33 9.09 100

Total 33

Question 2:1: Samples are used to make inferences about populations. Samples are easier to collect data from because they are practical, cost-effective, convenient, and manageable.

5:statistics, the science of collecting, analyzing, presenting, and interpreting data.

Question1

Class interval Midpoint F CF RF RCF

17_18 17.5 5 5 15.5 15.15

19_20 19.5 6 11 18.18 3.3

21_22 21.5 8 19 24.24 57.57

23_24 23.5 7 26 21.21 78.78

25_26 25.5 4 30 12.12 90.90

27_28 27.5 3. 33 9.09 100

Total 33

Question 2:1: Samples are used to make inferences about populations. Samples are easier to collect data from because they are practical, cost-effective, convenient, and manageable.

5:statistics, the science of collecting, analyzing, presenting, and interpreting data.

Name: Asiegbunam destiny ebubechukwu matric no : 10284348DA

Question1

Class interval Midpoint F CF RF RCF

17_18 17.5 5 5 15.5 15.15

19_20 19.5 6 11 18.18 3.3

21_22 21.5 8 19 24.24 57.57

23_24 23.5 7 26 21.21 78.78

25_26 25.5 4 30 12.12 90.90

27_28 27.5 3. 33 9.09 100

Total 33

Question 2:1: Samples are used to make inferences about populations. Samples are easier to collect data from because they are practical, cost-effective, convenient, and manageable.

5:statistics, the science of collecting, analyzing, presenting, and interpreting data.

1)The class interval using sturge rule

a)17-18

b)19-20

c)21-22

d)23-24

e)25-26

f)27-28

2) Mid-point

a)17.5

b)19.5

c)21.5

d)23.5

e)25.5

f)27.5

3)Frequency

a)5

b)6

c)8

d)7

e)4

f)3

total 33

4)Cumulative Frequency

a)5

b)11

c)19

d)26

e)30

f)33

total 124

5)Relative Frequency

a)15

b)18

c)24

d)21

e)12

f)9

6)Relative Cumulative Frequency

a)4

b)9

c)19

d)17

e)10

f)7

2)Write a brief note on the following:

Sample;

A sample is a smaller set of data that a researcher chooses or selects from a larger population using a pre-defined selection method. These elements are known as sample points, sampling units, or observations.

Creating a sample is an efficient method of conducting research. Researching the whole population is often impossible, costly, and time-consuming. Hence, examining the sample provides insights the researcher can apply to the entire population

PopulationA population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic.

In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped by a common feature can be said to be a population

Continuous Variable

A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range.

Discrete variable

Discrete variables are countable in a finite amount of time. For example, you can count the change in your pocket. You can count the money in your bank account. You could also count the amount of money in everyone’s bank accounts. It might take you a long time to count that last item, but the point is—it’s still countable.

Statistics

statisticsis simply seen as the science of collecting, analyzing, presenting, and interpreting data.

Currently the need to turn the large amounts of data available in many applied fields into useful information has stimulated both theoretical and practical developments in statistics.

Data

Data are the facts and figures that are collected, analyzed, and summarized for presentation and interpretation.

Name: Nwigbo Blessing chiamaka

Reg Number: 2018/245390

Dept: Social science Education (Education Economics)

Email: blessingmartha232@gmail.com.

QUESTION No 1.

The class interval using sturge rule, The formular for sturge rule is k=1+3.3logal

Where: k= Number of interval

N= Number of observation.

K= 1+3.3log33.

K=6.01

Yields (kg)

Mid- point

Frequency

Cumulative frequency

Relative frequency

Relative cumulative frequency

17-18

17•5

6

5

15•15

4•03

19-20

19•5

6

11

18•18

8•87

21-22

21•5

8

19

24•24

15•37

23-24

23•5

7

26

21•21

20•96

25-26

25•5

4

30

12•12

24•19

27-28

27•5

3

33

9•09

26•61

Total

33

124

99•99

99•98

QUESTION No 2.A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range. Thus, the range of real numbers between x and y with x, y ∈ R and x ≠ y; is said to be uncountable and infinite.

In continuous optimization problems, different techniques of calculus are often used in which the variables are continuous. Also, the probability distributions of continuous variables can be stated in expressions of probability density functions in statistical theory.

1. SAMPLE: .A sample is an unbiased number of observations taken from a population. In simple terms, a population is the total number of observations (i.e., individuals, animals, items, data, etc.) contained in a given group or context. A sample, in other words, is a portion, part, or fraction of the whole group, and acts as a subset of the population.

Samples are used in a variety of settings where research is conducted. Scientists, marketers, government agencies, economists, and research groups are among those who use samples for their studies and measurements.

Using whole populations for research comes with challenges. Researchers may have problems gaining ready access to entire populations. And, because of the nature of some studies, researchers may have difficulties getting the results they need in a timely fashion. This is why people samples are used. Using a smaller number of people who represent the entire population can still produce valid results while reducing time and resources.

2. POPULATION

In most everyday uses, the word population implies a group of people or at least a group of living beings. However, statisticians refer to whatever group they are studying as a population. The population of a study might be babies born in North America in 2021, the total number of tech startups in Asia since the year 2000, the average height of all accounting examination candidates, or the mean weight of U.S. taxpayers.

Statisticians and researchers prefer to know the characteristics of every entity in a population to draw the most precise conclusions possible. This is impossible or impractical most of the time, however, since population sets tend to be quite large.

3. CONTINUOUS VARIABLE.

TYPES OF CONTINUOUS VARIABLE

There are two types of continuous variables namely interval and ratio variables.

1.Instant variable

2.Ratio variable

Instant variable

A variable can be defined as the distance or level between each category that is equal and static. For example, what is the average day time temperature in Bangalore during the summer?

Ratio variable

Ratio variable is another type of continuous variable. This type of variable has only one variation from an interval variable. The only difference is that the ratio between the scores gives information regarding the relationship between the responses.

EXAMPLE OF CONTINUOUS VARIABLE

Continuous variables would take forever to count. In fact, we would get to forever and never finish counting them. For example, take an age. We can’t count “age”. Because it would literally take forever. For example, it could be 37 years, 9 months, 6 days, 5 hours, 4 seconds, 5 milliseconds, 6 nanoseconds, 77 picoseconds…and so on

4. DISCRETE VARIABLE.

Discrete variables are countable in a finite amount of time. For example, you can count the change in your pocket. You can count the money in your bank account. You could also count the amount of money in everyone’s bank accounts. It might take you a long time to count that last item, but the point is—it’s still countable.

5. STATISTICS.

Statistics are used in virtually all scientific disciplines such as the physical and social sciences, as well as in business, the humanities, government, and manufacturing. Statistics is fundamentally a branch of applied mathematics that developed from the application of mathematical tools including calculus and linear algebra to probability theory.

In practice, statistics is the idea we can learn about the properties of large sets of objects or events (a population) by studying the characteristics of a smaller number of similar objects or events (a sample). Because in many cases gathering comprehensive data about an entire population is too costly, difficult, or flat out impossible, statistics start with a sample that can conveniently or affordably be observed.

Two types of statistical methods are used in analyzing data: descriptive statistics and inferential statistics. Statisticians measure and gather data about the individuals or elements of a sample, then analyze this data to generate descriptive statistics. They can then use these observed characteristics of the sample data, which are properly called “statistics,” to make inferences or educated guesses about the unmeasured (or unmeasured) characteristics of the broader population, known as the parameters.

6. DATA.

Data can be defined as a systematic record of a particular quantity. It is the different values of that quantity represented together in a set. It is a collection of facts and figures to be used for a specific purpose such as a survey or analysis. When arranged in an organized form, can be called information. The source of data ( primary data, secondary data) is also an important factor

TYPES OF DATA

Data may be qualitative or quantitative. Once you know the difference between them, you can know how to use them.

1.Qualitative Data: They represent some characteristics or attributes. They depict descriptions that may be observed but cannot be computed or calculated. For example, data on attributes such as intelligence, honesty, wisdom, cleanliness, and creativity collected using the students of your class a sample would be classified as qualitative. They are more exploratory than conclusive in nature.

2.Quantitative Data: These can be measured and not simply observed. They can be numerically represented and calculations can be performed on them. For example, data on the number of students playing different sports from your class gives an estimate of how many of the total st

.

1,. solution:

Class interval. mid point. F. CF RF. RCF

17….18. 17.5. 5. 5. 15.15. 4.03

19….20. 19.5. 6. 11. 18.18. 8.87

21….22. 21.5. 8. 19. 24.24. 15.32

23….24. 23.5. 7. 26. 21.21. 20.96

25….26. 25.5. 4. 30. 12.12. 24.19

27….28. 28.5. 3. 33. 9.09. 26.61

2a,A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations.

b,What Is Population? A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic. In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study.

c, A discrete variable is a variable that takes on distinct, countable values. Discrete variables have values that are counted.e.g. number of egg in creates, number of visitors in house. e t c.

d,Statistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In other words, it is a mathematical discipline to collect, summarize data. Also, we can say that statistics is a branch of applied mathematics.

e,In computing, data is information that has been translated into a form that is efficient for movement or processing. Relative to today’s computers and transmission media, data is information converted into binary digital form. It is acceptable for data to be used as a singular subject or a plural subject.

1) compute the tables as follows (22,20,19,25,22,17,28,20,22,23,17,18,24,25,22,20,23,25,22,28,29,22,25,27,23,24,17,18,22,29,22,23,24)

a) class interval using sturge rule

b) mid point

c) frequency

d) cumulative frequency (CF)

e) relative frequency( RF)

f) relative cumulative frequency (RCF)

solution:

formular: G=1+3.3logN

G= number of class groups

N=Number of observation

1+3.3log33

1+3.3(1.52)

1+5.016= 6.02

=6.

class interval

range= 28-17 =11

11/6= 1.833= 2( class interval).

Class mid. freq. cum. rela. R.cum.

interval point. uency. freq. freq. freq.

17-18. 17.5. 5. 5. 0.15. 0.15

19-20. 19.5. 6. 11. 0.18. 0.33

21-22. 21.5. 8. 19. 0.24. 0 .57

23-24. 23.5. 7. 26. 0.21. 0.78

25-26. 25.5. 4. 30. 0.12. 0.9

27-28 27.5 3 33 0.09 0.99

total 33. 0.99 midpoint :

lower class + higher class /2

e.g 17+18/2 =35/2= 17.5

frequency = the number of times a set of data appeared.

cumulative frequency = the addition of the frequencies

relative frequency= f/N

e g5/33= 0.15

relative cumulative frequency= the addition of the relative frequency.

2) write a briefly

a) Sample: A sample refers to a smaller manageable version of a larger group. it is that subset containing the characteristics of a larger population.Sample are used in statistical testing when population sizes are too large for the test to include all possible members or observations.A sample should represent the population as a whole.There are two basic types of sample: Random sample; if every entity in the population is identical, then a random sampling is ideal. Startified random sampling: this method of sampling divides the whole population into smaller group called strata. in this method, the participants are given equal opportunity to be selected from the population.

b) Population : in statistics, a population is the pool of individuals from which a statistical sample is drawn for a study thus, any selection of individuals grouped by a population. population parameter is data base on entire population.there are four types of population: finite population, infinite population,existent population, hypothetical population.

c) A continuous variable: this is defined as a variable which can take an uncountable set of value or infinite set of value. for instance,if a variable over a non empty range of the real number is continuous, then it can take on any value in that range.There are types of variable which are: instant variable- can be defined as the distance or level between each category that is equal and static. Ratio variable – is another type of continuous variable it has only one variation from an interval variable.

d) Discrete variable is a variable that takes on distinct countable value. examples are the of workers in an office, the number of steps you take in a day etc

e) Statistics is defined as the study, collection, analysis, interpretation and organisation of data for different ultimate objects. statistics helps a user in gathering and analyzing huge numerical data easily and efficiently

f) Data: it is the formation that has been translated into a form that is efficient for movement or processing there are two classes of data – qualitative and quantitative. qualitative data is a bunch of information that cannot be measured in the form of numbers. Quantitative data can be measured on form of numbers.the two basic types of data are- Primary data – this is the original data that has been collected specially for the purpose in mind it means someone collected the data from the original source first hand,to be used by them. and Secondary data is a research data that has previously been gathered and can be accessed by researchers.

Ogochukwu chukwuka great

2021/241355

greatchukwuka59@gmail.com

QUESTION 1

1 class interval using sturges rule

Sturges rule formula 1+3. 3logn where n is the sum total of observations

n=33

=1+3.3log(33)

=1+3.3*1.518

=6.0

2.) midpoint =average sum of the class limit

17+18/2 = 17.5

19+20/2 = 19.5

21+22/2 = 21.5

23+24/2 = 23.5

25+26/2 = 25.5

27+28/2 = 27.5

3.) frequency

17-18 = 5

19-20 = 6

21-22 = 8

23-24 = 7

25-26 = 4

27-28 = 3

Total = 33

4.)Cumulative frequency

17-18=5

19-20=11

21-22=19

23-24=26

25-26=30

27-28=33

5.)relative frequency

5/33 =0.15

6/33=0.18

8/33 =0.24

7/33=0.21

4/33=0.12

3/33=0.09

6.) relative cumulative frequency

0.15

0.15+0.18=0.33

0.33+0.24=0.57

0.57+0.21=0.78

0.78+0.12=0.9

0.1+0.9=1

Intervals freq midpoint(x) cf. Rf. RFC

17-18. 5. 17.5. 5. 0.15. 0.15

19-20. 6. 19.5. 11. 0.18. 0.33

21-22. 8. 21.5. 19. 0.24. 0.57

23-24. 7. 23.5. 26. 0.21. 0.78

25-26. 4. 25.5. 30. 0.12. 0.9

27-28. 3. 27.5. 33. 0.1. 1

Total. 33. 1

QUESTION 2

1.)Sample

Sample is a portion of the population or can be said to be a subset of the population.

It is a segment of the population which we are interested in and it is seen as a portion of the entire population

2.) population

Population is defined as the entire group of individuals that we are interested in making a statement about. It is the entire set of objects, observations, or scores that have something in common

3.)Continous variable

A continuous variable is one which, within tthe limits the variable ranges, any value is possible. Continuous variable can take any value between a certain set of real numbers

4.)Discrete variables

Discrete variables or data are also known as categorical variables. They are variables or data that exist only as whole numbers and are not divisible

5.) statistics

The word ‘statistics’ refers to the numerical facts such as the number of events occurring in time or the number of people living in a particular area. It also involves the study of ways of collecting, analyzing, and interpreting numerical facts or numerical data

6.)Data

Data could be seen as a collection of facts such as numbers, words, measurement, observations or even just descriptions of things. It could be seen as information in raw or unorganized form(such as alphabet, numbers, or symbols) that refers to, or represent, conditions, ideas, or objects.

Ogochukwu chukwuka great

2021/241355

greatchukwuka59@gmail.com

QUESTION 1

1 class interval using sturges rule

Sturges rule formula 1+3. 3logn where n is the sum total of observations

n=33

=1+3.3log(33)

=1+3.3*1.518

=6.0

2.) midpoint =average sum of the class limit

17+18/2 = 17.5

19+20/2 = 19.5

21+22/2 = 21.5

23+24/2 = 23.5

25+26/2 = 25.5

27+28/2 = 27.5

3.) frequency

17-18 = 5

19-20 = 6

21-22 = 8

23-24 = 7

25-26 = 4

27-28 = 3

Total = 33

4.)Cumulative frequency

17-18=5

19-20=11

21-22=19

23-24=26

25-26=30

27-28=33

5.)relative frequency

5/33 =0.15

6/33=0.18

8/33 =0.24

7/33=0.21

4/33=0.12

3/33=0.09

6.) relative cumulative frequency

0.15

0.15+0.18=0.33

0.33+0.24=0.57

0.57+0.21=0.78

0.78+0.12=0.9

0.1+0.9=1

Intervals freq midpoint(x) cf. Rf. RFC

17-18. 5. 17.5. 5. 0.15. 0.15

19-20. 6. 19.5. 11. 0.18. 0.33

21-22. 8. 21.5. 19. 0.24. 0.57

23-24. 7. 23.5. 26. 0.21. 0.78

25-26. 4. 25.5. 30. 0.12. 0.9

27-28. 3. 27.5. 33. 0.1. 1

Total. 33. 1

QUESTION 2

1.)Sample

Sample is a portion of the population or can be said to be a subset of the population.

It is a segment of the population which we are interested in and it is seen as a portion of the entire population

2.) population

Population is defined as the entire group of individuals that we are interested in making a statement about. It is the entire set of objects, observations, or scores that have something in common

3.)Continous variable

A continuous variable is one which, within tthe limits the variable ranges, any value is possible. Continuous variable can take any value between a certain set of real numbers

4.)Discrete variables

Discrete variables or data are also known as categorical variables. They are variables or data that exist only as whole numbers and are not divisible

5.) statistics

The word ‘statistics’ refers to the numerical facts such as the number of events occurring in time or the number of people living in a particular area. It also involves the study of ways of collecting, analyzing, and interpreting numerical facts or numerical data

6.)Data

Data could be seen as a collection of facts such as numbers, words, measurement, observations or even just descriptions of things. It could be seen as information in raw or unorganized form(such as alphabet, numbers, or symbols) that refers to, or represent, conditions, ideas, or objects.

1).

Class interval midpoint. F. CF RF RCF

17-18. 17.5. 5. 5. 15.15. 15.15

19-20. 19.5. 6. 11. 18.18. 33.3

21-22. 21.5. 8. 19. 24.25. 57.57

23-24. 23.5 7. 26. 21.21. 78.77

25-26. 25.5. 4. 30. 12.12. 90.90

27-28. 27.5. 3. 33. 9.09. 100

Total:. 33

Using sturges rule to calculate the class interval:

According to sturge rule

The class interval is

K=1+3.3logN

K=1+log3.3×33

K=6.01

The range dividing k = 28 – 17/ 6.01

= 1.830

So the class interval is 1.830kg

2). Sample: A sample is defined as a smaller set of data that is chosen and selected from a larger population by using a predefined selection method. It is a science that helps procure information of a given population and it is the easiest way. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations.

Population:. It is the entire group of individuals that we draw a statement about. Population is the entire group of people about which information is desired about their number . A population is a numerical quantity measuring some aspects of a population of scores.

Continuous variables: are variables which can take an uncountable set of values or infinite set of values in a set of information. A continuous variable is a specific kind a quantitative variable used in statistics to describe data that is measurable . It is defined over an interval of values.It represents measurable amounts and is quantitative variable

Discrete variables: it is a quantitative variable whose value is obtained by counting. It takes only a whole number as it’s value. Discrete variables are countable in a finite amount of time. For example, you can count the pages in your book. You can count the money in your bag. It is a variable that deals on counts.

Statistics: is the scientific method of collecting, organising, summarizing, presenting and data analysis. According to Bowley statistics may be rightly called the scheme of averages or numerical statement of facts in any department of enquiry in relation to each other.

Data : data is the information used for calculation, analysis, or planning. It is recognized as statistics and facts gathered and arranged in a systematic order for a study . . It is considered a quantitative measure that helps to represent the actual economy. Data is a systematic record of a particular quantity.

1)CLASS INTERVAL CLASS MARK F CF RCF

17-22 19.5 19 19 57.6%

23-28 25.5 14 33 100%

33

R.F for 17-22=19/33×100/1

=57.6%

R.F for 23-28 = 33/33×100/1

= 100%

2)Sample- This is a procedure by which one or more members of a population are selected from the population.

Population- Population is defined as the entire group about which information is desired. It is also described as a largest collection of entities for which we have an interest at a particular time.

Continous variable-A continous variable is one for which, within the limits the variable ranges, any value is possible. Continous variable can take any value between a certain set of real numbers.

Discrete variable- Discrete variables or data are also known as categorical variables.They are variables or data that exist only as whole numbers and are not divisible.

Statistics- Statistics is concerned with the scientific method of collecting, organising, summarising, presenting and analysing data. It also entails deriving valid conclusions and making reasonable decisions on the basis of analysis.

Data- Data is information in raw form.it could be seen as a collection of facts such as numbers, words, measurements, observations or even description of things.

Question one.

(1) The class interval using sturge rule.

The formula for sturge rule is k=1+3•3logN. Where: k= number of interval. And N= number of observation or frequency.

K= 1+3•3log33 =6•01

17-18.

19-20.

21-22.

23-24.

25-26.

27-28.

(2). Mid-point.

17•5.

19•5.

21•5.

23•5.

25•5.

27•5.

(3) Frequency.

5.

6.

8.

7.

4.

3.

=33.

(4). Cumulative frequency.

5.

11.

19.

26.

30.

33.

=124.

(5). Relative frequency.

15•15.

18•18.

24•24.

21•21.

12•12.

9•09.

=99•99.

(6). Relative cumulative frequency.

4•03.

8•87.

15•32.

20•96.

24•19.

26•61.

=99•98.

Question two.

(1). Sample: Sample can be defined as part or portion of a population and it is taken from the population as a representative of it. However, a sample must be representative of the population in all ramification.

(2). Population: Population is the entire collection of items or individuals which one wishes to examine at a particular time. It is also describe as a largest collection of entities set of object, observation, or scores that have something in common.

(3). Continuous variable: It is a type of variable that assumes any value from a range of values. Continuous variable can take any value between a certain set of real numbers. For example, Bank interest #50•50k, income of a staff #155,000•70k.

(4). Discrete variable: It is a type of variable that is also known as categorical variables, they are variables or data that exit only as whole numbers and are not divisible. It is only represented in whole numbers. For example Number of books, Age of students.

(5). Statistics: Statistics can be defined according to Upton and Cook, as a scientific method for collecting, organizing, summarizing, analysing and presenting data as well as drawing valid inference s or conclusion and making reasonable decision on the basis of such analysis. It also entail derving valid conclusion conclusion and making reasonable decision on the basis of analysis.

(6). Data: it can be defined as a raw or unprocessed information, it is a numerical statement of fact in a specific field of enquiry. Data could be seen as a collection of facts, such as numbers, words, measurements, observation or even just description of things. Data collection is a fundamental aspect of research, data are required for empirical analysis and other forms of analysis.

ADEBAYO EXCEL TEMITAYO

DEPARTMENT OF ECONOMICS

REG NO: 2021/246242

Question One Answers.

Computing the table..

1. The class interval Using Sturge’s rule

K = 1+3.332 × Log N

Where N = Total Number of Observations/ Cases

K= 1+3.332 × Log 33

K = 4.332 × 1.518

K = 6.57 approximately, K = 7

Range = 28 – 17 = 11÷ K = 11÷7 = 1.57 approximately 2.

The Class interval = 2 ( That is, 17-18, 19-20, 21-22,23-24,25-26, 27-28.)

2. Midpoints are 19.75,19.5,21.5,23.5,25.5,27.5 respectively.

3. Frequency: 5,6,8,7,4,3 respectively. Giving a total frequency of 33.

4. Cumulative frequency: 5,11,19,26,30,33 respectively.

5. Relative Frequency: Calculated by actual frequency divided by total frequency e. g 5÷33 = 0.151. The relative frequency are 0.151,0.181,0.242,0.212,0.121,0.090 respectively.

6. Relative cumulative frequency: 15.1%, 18.1%, 24.2%,21.2%,12.1%,9.09% respectively. This is calculated by Actual frequency divided by total frequency multiplied by 100. e.g 5÷33 × 100 = 15.1%

Question Two answers

1.Sample : A sample is a smaller set or subset of data that is chosen and/or selected from a larger population by using a predefined selection method. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations.

2. Population: Population is defined as an entire group about which information is desired. The largest collection of entities for which there is interest at a particular time.

3. Continuous variable: It is a variable that can take on any value within a range or set of real numbers

4. Discrete Variables: They are variables that exist only as whole numbers and are not divisible. It can take on a finite number of numerical values, categories or codes.

5. Statistics : According to Upton and Cook( 2008) , Statistics is a scientific method for collecting, organising, summarizing, analysing and presenting data as well as drawing valid references on the basis of such analysis.

6. Data: It simply means Information. it can come in form of text,observations, figures, images, numbers, graphs, or symbols.

QUESTION ONE

SOLUTION

Sturges rule : This rule enables us to determine the number of classes and the size of the class interval.

K=1+3.3LogN , Where N is the total number of outcome. Therefore

1+3.3Log(33) = 1+3.3(1.518) = 1+5.01 = 6.01, Which is approximately 6, therefore the number of classes will be 6, therefore class interval is 1.

Note: shortened forms ;

F : Frequency

CF: Cumulative Frequency

RF: Relative Frequency

RCF: Relative Cumulative Frequency

Class- Mid- F CF RF RCF

interval point

17-18 17.5 5 5 15.15 15.15

19-20 19.5 6 11 18.18 33.3

21-22 21.5 8 19 24.25 57.57

23-24 23.5 7 26 21.21 78.78

25-26 25.5 4 30 12.12 90.90

27-28 27.5 3 33 9.09 100

Total 33

QUESTION TWO

Brief notes on the following:

Sample

A sample is a part of a population that we usually observe.

Sampling is thereby a procedure by which one or more members of a population are selected from the population. The objective is to make certain observations about the members of the sample and on the basis of this results, to draw valid conclusion about the characteristics of the entire population. Since it is usually impractical to test every member of a population, a sample from the population is typically the best approach available. However a sample must be representative of the population in all ramifications. It is usually difficult to examine all members of the population due to time, cost, and other constraints. So we examine only a portion of the population and try to draw conclusion about the whole using sample estimates.

Population

In a statical problem Population can be defined as the entire group of individuals that we are interested in making a statement about. It is the entire group which information is desired . A portion of a population to be studied/ observed is called a sample . It is also described as a largest collection of entities for which we have interest at a particular time, an entire set of objects, observations or scores that have something in common. To analyze a population, a Census is taken. A population parameter is a numerical quantity measuring some aspect of a population of scores, they are rarely known and are usually estimated by statistics computed in samples.

Continuous Variable

A Continuous Variable is one for which within the limit the variable ranges, any value is possible. Continuous Variables can take any value between a certain set of real numbers. The value given to an observation for a continuous variable can include values as small as instrument of measurement allows.

Discrete variable

Discrete variables are also known as categorical variables. They are variables or data that exists only as whole numbers and are not divisible. A discrete variable can take on a finite number or numerical values, categories or codes.

Statistics

Statistics has to do with numerical facts such as the number of events occurring in time or the number of people living in a particular area. It also involves the study of ways of collecting, analysing and interpreting numerical facts or numerical data. Basically statistics is concerned with the scientific method of collecting, organizing, summarizing, presenting and analyzing data and interpreting data sets so as to determine their essential characteristics. It also entails deriving valid conclusions and making reasonable decisions on the basis of analysis.

Data

Data can be described as a collection of facts, such as numbers, words, measurements, observations, or even just descriptions of things. It could also be seen as information in raw or unorganized form that refer to, or represent condition, ideas, or objects. Data could be qualitative (data that deals with description) and quantitative (data that has to do with numbers). Data collection is the fundamental aspect of research. Data are required for empirical analysis and other forms of analysis.

Types of Data based on their mode of collection: Primary and Secondary data.

Name : Ike Blessing Onyinye

Reg no: 2021/241946

Date:7/02/2023

1: The class interval using sturge rule.

Ans_ Sturge rule k=1+3.322logN

‘N’ is total number of observation= 33 K=1+3.322log33 K=6.04 Approximately=K = 6// K= 6 shows that you have 6 classes//

Step 2: finding the range . The range is the difference between the highest and lowest value . Range =HV – LV Range = 28-17 =11//

Step 3: finding the class interval. Formula= Range /K = 11/6 =1.83 = 2//

CLASS INTERVAL:

17-18, 19-20, 21-22, 23-24, 25-26, 27-28

MIDPOINT 17+18/2=17.5

19+20/2=19.5

21+22/2=21.5

23+24/2=23.5

25+26/2=25.5

27+28/2=27.5

FREQUENCY 5, 6, 8, 7, 4, 3

=TOTAL FREQUENCY= 33//

CUMULATIVE FREQUENCY to find cumulative frequency Formula= CF = F + CF 5 11 19 26 30 33

RELATIVE FREQUENCY

(RF)= FREQUENCY/TOTAL FREQUENCY×100

RF= 5/33 ×100=15.15

= 6/33 × 100=18.18

= 8/33×100 =24.24

=7/33 ×100=21.21

= 4/33×100= 12.12

= 3/33×100=9.09

RELATIVELY CUMULATIVE FREQUENCY :

(R C F) = CUMULATIVE FREQUENCY/TOTAL FREQUENCY ×100

= 5/33×100= 15.15

=11/33× 100=33.33

=19/33×100=57.57

=26/33×100=78.78

=30/33×100=90.90

=33/33×100=100

QUESTIONS TWO

Write a brief note on the following

i, SAMPLE: It is usually difficult to examine all members of the population due to time , cost and other constraints. So we examine only a portion of the population and try to draw conclusions about the whole using samples estimate . The process of the entire population is known as statistical inference.

ii, POPULATION: In a statistical problem, the population is the entire group of individuals that we are interested in making a statement about . Population is defined as the entire group about which information is desired.

iii, CONTINUOUS VARIABLE: A continuous variable is one for which , within the limit the variable range , any value is possible. Continuous variable can take any value between a certain set of real number.

Iv, DISCRETE VARIABLE: Discrete variables data are also known as categorical variables. They are variables or data that exist only as whole number and are not divisible . A discrete variable can take on a finite number of numerical value, categories or codes.

v, STATISTICS: statistics could also be defined as the theory and methods of collecting , organizing , presenting , analysing and interpreting data sets so as to determine their essential characteristics .

vi, DATA : This is a raw information or information in it’s original form . In it’s simplest form , data could be seen as a collection of facts, such as numbers ,words ,measurements , observation or even just descriptions of things .

Name : Ike Blessing Onyinye

Reg no: 2021/241946

Date:7/02/2023

Email: ikeblessingonyinye@gmail.com

1: The class interval using sturge rule

Ans_. Sturge rule = k=1+3.322logN

‘N’ is total number of observation= 33

K=1+3.322log33

K=6.04

Approximately=K = 6//

K= 6 shows that you have 6 classes//

Step2: finding the range .

The range is the difference between the highest and lowest value .

Range =HV-LV

Range = 28-17

=11//

Step3: finding the class interval.

Formula= Range /K

= 11/6

=1.83 = 2//

CLASS INTERVAL:

17-18

19-20

21-22

23-24

25-26

27-28

MIDPOINT

17+18/2=17.5

19+20/2=19.5

21+22/2=21.5

23+24/2=23.5

25+26/2=25.5

27+28/2=27.5

FREQUENCY

5

6

8

7

4

3

TOTAL= 33//

CUMULATIVE FREQUENCY

to find cumulative frequency

Formula= CF = F + CF

5

11

19

26

30

33

RELATIVE FREQUENCY

RF= FREQUENCY/TOTAL FREQUENCY×100/1

RF= 5/33 ×100=15.15

= 6/33 × 100=18.18

= 8/33×100 =24.24

=7/33 ×100=21.21

= 4/33×100= 12.12

= 3/33×100=9.09

RELATIVELY CUMULATIVE FREQUENCY

RCF= CUMULATIVE FREQUENCY/TOTAL FREQUENCY ×100/1

= 5/33×100= 15.15

=11/33× 100=33.33

=19/33×100=57.57

=26/33×100=78.78

=30/33×100=90.90

=33/33×100=100

QUESTIONS TWO

Write a brief note on the following

i, SAMPLE:

It is usually difficult to examine all members of the population due to time , cost and other constraints. So we examine only a portion of the population and try to draw conclusions about the whole using samples estimate . The process of the entire population is known as statistical inference.

ii, POPULATION:

In a statistical problem, the population is the entire group of individuals that we are interested in making a statement about . Population is defined as the entire group about which information is desired.

iii, CONTINUOUS VARIABLE:

A continuous variable is one for which , within the limit the variable range , any value is possible. Continuous variable can take any value between a certain set of real number.

iv, DISCRETE VARIABLE:

Discrete variables data are also known as categorical variables. They are variables or data that exist only as whole number and are not divisible . A discrete variable can take on a finite number of numerical value, categories or codes.

v, STATISTICS:

statistics could also be defined as the theory and methods of collecting , organizing , presenting , analysing and interpreting data sets so as to determine their essential characteristics .

vi, DATA :

This is a raw information or information in it’s original form . In it’s simplest form , data could be seen as a collection of facts, such as numbers ,words ,measurements , observation or even just descriptions of things .

NAME: BASSEY MICHEAL EKANEM

REG NO: 2021/244123

EMAIL: basseymicheal30@gmail.com

ANSWERS.

QUESTION ONE:

1. Using sturge’s rule:

K= 1+3.3LogN. where;

N= Number of observations; which is = 33

K= Number of class intervals?

K= 1+3.3Log33

= 6.01

1. 2. 3. 4. 5. 6.

class Md(x) f. Cf. Rf. Rcf.

intervals

17-18 17.5 5 5 15.2 4.0

19-20 19.5 6 11 18.2 8.9

21-22 21.5 8 19 24.2 15.3

23-24 23.5 7 26 21.2 20.9

25-26 25.5 4 30 12.2 24.2

27-28 27.5 3 33 9.1 26.6

total= 33 124

QUESTION TWO:

1. SAMPLE: A Sample is defined as a smaller and more manageable representation of a larger group. It can also be seen as a fragment, segment or elements chosen from a population. it is also a subset of a larger population that contains characteristics of that population. For example, in the institution of the University of Nigeria, Nsukka,(UNN), the total number of students in all it’s departments can be seen as the population of the UNN students while the students in the department of economics can be seen as a sample of the population of the UNN students.

A sample is used in statistical testing when the population size is too large for all members or observations to be included in the test.

To overcome the restraints of a population, you can sometimes collect data from a subset of your population and then consider it as the general norm. You collect the subset information from the groups who have taken part in the study, making the data reliable. The results obtained for different groups who took part in the study can be extrapolated to generalize for the population.

2. POPULATION: In statistics, population is the entire collection of items or individuals which one uses to examine and draw data from for a statistical study at a particular time. Generally, population refers to the people who live in a particular area at a specific time. But in statistics, population refers to data on your study of interest. It can be a group of individuals, objects, events, organizations, etc. You use populations to draw conclusions. An example of a population would be the entire student body at a school. It would contain all the students who study in that school at the time of data collection.

3. CONTINUOUS VARIABLE: A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. A continuous variable can assume any form of range of value. For instance, measurements of heights of plants, income of a staff, weight of an animal, length of a plant etc. They are measured in continuous scales in meteres, centimeters, millimeters etc and could be 10.4cm, 0r even 10.4573.

4. DISCRETE VALUABLE: A discrete variable is a variable that takes on distinct, countable values. In theory, you should always be able to count the values of a discrete variable. They are variables that can be counted and registered in a whole number. Examples of discrete variables are age of a student, Years of schooling, Number of goals scored in a soccer match, number of registered voters in an election, Votes for a particular politician, Number of times a coin lands on heads after ten coin tosses etc.

5. STATISTICS: Statistics is the scientific study of data collection, analysis, interpretation, presentation and the organizing of the data in a specific way. Statistics also refers to numerical facts such as the number of events occurring in time or the number of people living in a particular area. Statisticians, people who do statistics, are particularly concerned with determining how to draw reliable conclusions about large groups and general events from the behavior and other observable characteristics of small samples. These small samples represent a portion of the large group or a limited number of instances of a general phenomenon.

The two major areas of statistics are known as descriptive statistics, which describes the properties of sample and population data, and inferential statistics, which uses those properties to test hypotheses and draw conclusions. Descriptive statistics include mean (average), variance, skewness, and kurtosis while Inferential statistics include linear regression analysis, analysis of variance (ANOVA), logit/Probit models, and null hypothesis testing.

6. DATA: Data can simply be defined as a collection of facts, such as numbers, words, measurements, observations or even just descriptions of things. It can also be seen as information in raw or unorganized form (such as alphabets, numbers, or symbols) that refer to, or represent conditions, ideas, or objects. It is also seen as an unprocessed information. Data could be qualitative (i. e. data that deals with description) or quantitative (i. e. data that deals with numbers or quantities). Data collection is the base or the foundation upon which research can be done. Data are required for empirical analysis and other forms of analysis.

2021/245588

Question1

Class interval Midpoint F CF RF RCF

17_18 17.5 5 5 15.5 15.15

19_20 19.5 6 11 18.18 3.3

21_22 21.5 8 19 24.24 57.57

23_24 23.5 7 26 21.21 78.78

25_26 25.5 4 30 12.12 90.90

27_28 27.5 3. 33 9.09 100

Total 33

Question 2:

5:statistics, the science of collecting, analyzing, presenting, and interpreting data.

Question1

Class interval Midpoint F CF RF RCF

17_18 17.5 5 5 15.5 15.15

19_20 19.5 6 11 18.18 3.3

21_22 21.5 8 19 24.24 57.57

23_24 23.5 7 26 21.21 78.78

25_26 25.5 4 30 12.12 90.90

27_28 27.5 3. 33 9.09 100

Total 33

Question 2:

5:statistics, the science of collecting, analyzing, presenting, and interpreting data.

Name: Joel chibuikem Kingsley

Matric number:2021/244125

Question1

Class interval Midpoint F CF RF RCF

17_18 17.5 5 5 15.5 15.15

19_20 19.5 6 11 18.18 3.3

21_22 21.5 8 19 24.24 57.57

23_24 23.5 7 26 21.21 78.78

25_26 25.5 4 30 12.12 90.90

27_28 27.5 3. 33 9.09 100

Total 33

Question 2:

1. A sample is defined as a smaller and more manageable representation of a larger group. A subset of a larger population that contains characteristics of that population. A sample is used in statistical testing when the population size is too large for all members or observations to be included in the test.

2.A population is the entire group that you want to draw conclusions about. A sample is the specific group that you will collect data from. The size of the sample is always less than the total size of the population.

3: Continuous variables A variable is said to be continuous if it can assume an infinite number of real values within a given interval. For instance, consider the height of a student. The height can’t take any values. It can’t be negative and it can’t be higher than three metres

4: A discrete variable is a variable whose value is obtained by counting. Examples: number of students present. number of red marbles in a jar. number of heads when flipping three coins. students’ grade level.

5: Statistics is the practice or science of collecting and analysing numerical data in large quantities, especially for the purpose of inferring proportions in a whole from those in a representative sample.

“standard error is a mathematical tool used in statistics to measure variability”

6: Data can come in the form of text, observations, figures, images, numbers, graphs, or symbols. For example, data might include individual prices, weights, addresses, ages, names, temperatures, dates, or distances. Data is a raw form of knowledge and, on its own, doesn’t carry any significance or purpose.

Name: Ezema Miracle oluebube

Reg no: 2021/241316

Dept: Economics

Course: Eco 131

1). The class interval using sturge rule

Sturge rule = K = 1+3.322 log N

K= number of classes

N= total frequency

so, K= 1+3.322 log N

K= 1+3.322 log 33

K= 1+3.322 (1.5185)

K= 1+5

K= 6 that is, 6 classes.

determine the approximate class interval class, using h

h= Range ÷ Number of classes

h= 11÷ 6 = 1.8

the next higher whole number will be taken as the class interval = 2

determining class boundary = 17+2=19

Class boundary = 17-19, 20-22, 23-25, 26-28

2). Mid point

18, 21, 24, 27 respectively,

3). Frequency

8, 11, 11, 3 total =33 respectively,

4). Cumulative frequency

8, 19, 30, 33 total=90 respectively,

5). Relative frequency

24.2, 33.3, 33.3, 9.1 total =99.9 respectively,

6). Relative cumulative frequency

8.9, 21.1, 33.3, 36.7 respectively

Question two

1). Sample

Sample in statistics refers to a smaller, manageable version of a larger group. it is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations. A sample should represent the population as a whole and not reflect any bias toward a specific attribute.

2). Population

Population in statistics is the entire group of individuals that we are interested in making a statement about. In statistics, a population is a set of similar items or events which is of interest for some question or experiment. A statistical population can be a group of existing objects or a hypothetical and potentially infinite group of objects conceived as a generalisation from experience.

3). Continuous variable

Continuous variable is obtained by measuring. it is a variable which can take an uncountable set of values or infinite set of values. for instance, if a variable over a non empty range of the real number is Continuous, then it can take any value in that range.

4). Discrete variable

Discrete variable is a variable whose value is obtained by counting, they are countable in a finite amount of time.

for example, you can count the change in your pocket. it might take time to count, but the point is – it’s still countable .

5). Statistics

Statistics refers to numerical facts such as the number of events occurring in time or the number of people living in a particular area.

Statistics is the science of collection, compilation, tabulation, analysis and interpretation of quantitative data.

6). Data

Data is a collection of facts, such as numbers, measurements, observations, or even just description of things.

example: alphabets, numbers, symbols, which refers to conditions, ideas, or objects.

Name: Ogbedeh Chukwudalu Frances

Reg.no:2021/241352

Email address: franceschukwudalu@gmail.com

Question One:

1:The class interval using sturge rule =

Class interval=range/k

Number of observations =N

Where n=33

i.e=k=1+3.322log33=6

Range/k=highest – lowest/6

=28 -17/6

= 11/6 =1.84

2: Mid-point=26,29,33.5,36.5,41

3: Frequency=5,6,12,7,3=33

4: Cumulative Frequency=5,11,23,30,33=102

5: Relative Frequency=15.15,18.18,36.36,21.21,0.09

6: Relative Cumulative Frequency=4.91,10.78,22.55,29.411,32.35

Question Two:

1: Sample: Sample is defined as parts or portion of a population and it is taken from the population as a representation of it. E.g – The height of students in faculty of social sciences taken to represent the height of students in the department.

2: Population: Population is the entire collection of items or individuals of which one wishes to examine at a particular time.

3: Continuous Variable: Continuous Variable can assume any value from a range of values E.g – Measurement of height of plant, lncome of a staff, weight of an animal or man . They are measured on continuous scale in meters, centi meters, millimeter etc and could be 10.4,10.45.

4:Discrete Variables:This is in the case of the variable that can only be counted and the represent in a whole number. E.g Age of a student, number of seeds per carton.

5: Statistics: Statistics can be defined as a field of study concerns with layout of experiment, collection, calculation, summarization and analystics of data. It also involves drawing of inferences.

6:Data:Data is a numerical statement of fact in a specific field of enquiring of simple numbers which may result from taken measurements. E.g recording height, weight or temperature measurement. It can also be said to be a raw information in it’s original form.

Name-Mbaeze chidera marycynthia

Reg no-10912021HC

Department- Economics

1.according to sturge rule the class interval is k=1+3.3logN, k=1+3.3log33 k=6.01 the table of the data set 1 2 3 4 5 6 class midpoint F CF RF RCF interval 17.18 17.5 55 15 15 15 15 18 20 15.5 11 18 18 33.3 21.22 21.53 19 24 25 57 57 23 34 23 57 26 21 21 78 78 25 26 25 54 30 12 12 90 90 27 28 27 53 33 90 total =133

2. Sample-it is defined as the parts of portion of a population and it is taken from the population as a representatives of it.

b. Population- population is the entire collection of items or individuals of which one wishes to examine at a particular time.

c. Continuous variable- unlike discrete can assume any variable from a range of values e.g measurement of height of class, income of staff, weight of an animal, length of a fruit. They are measures on continuous scale, in meter, cm,mm,etc and could be 10.4-5 or even 10.4573 etc.

d. Discrete variable- this is in the case of variable that can only be counted and be represented in a whole number e.g age of a student, number of seed per carton.

e. Statistics- it refers to numerical facts such as the number of events occurring in a particular time. It is the scientific method of presenting, collecting, organising, summarizing and analysing data.

f. Data- data is a numerical statement of facts in a specific field of enquiry or simply numbers which may result from taking measurement.

2021/248750

Name: Nana Wendezinkede Danielle

Reg Number: 241347

Department: Economics

1)

Soybean Mid-point F C.M R.F. R.C.F

Yield.

17-18 17.5 5 5 15.2 4.0

19-20 19.5 6 11 18.9 8.9

21-22 21.5 8 19 24.2 15.3

23-24 23.5 7 26 21.2 20.9

25-26 25.5 4 30 12.1 24.2

27-28 27.5 3 33 9.09 26.6

33 124

2)

a) Sample: This is the part or portion of a population. It is taken from the population as a representation of it.

b) Population: This is the entire collection of items or individuals which one wishes to examine at a particular time.

c) Continuous Variable: A continuous variable is one for which, within the limits the variable ranges, any value is possible. Continuous variables can take any value between a certain set of real numbers.

d) Discrete Variable: Discrete Variables or data are also known as categorical variables. They are variables or data that exist only as whole numbers and are not divisible. A discrete variable can take on a finite number of numerical values, categories or codes.

e) Statistics: The word ‘statistics’ refers to numerical facts such as the number of events occurring in time or the number of people living in a particular area.

Statistics can be defined as a field of study concerned with layout experiments, collection, calculation, summarisation and analysis of data. It also involves interpretation of results or drawing of inference.

f) Data: This is raw information or information in its original form. In its simplest form, data could be seen as a collection of facts, such as numbers, words, measurements, observations or even just descriptions of things. It could be seen as information in raw or unorganized form ( such as alphabets, numbers or symbols) that refer to or represent conditions, ideas or objects.

Name: ODUMUKO FAVOUR CHINAZAEKPERE Reg.no: 2021/241350

Question I:

1)Sturges rule: it states that K=1+3.322log(N); where N is the number of observations.

K=1+3.322log(N)

K=1+3.322log33

K=1+5.0445

K=6.045

Class interval is 6

Class interval

17-22

23-28

2) Midpoint

19.5

25.5

3) Frequency

19

14

4) Cumulative frequency

19

33

5) Relative frequency

57.6%

42.2%

Question 2:

1) Sample: Sampling is a procedure by which one or more members of a population are selected from the population.

2) Population: Population is the entire group of individuals that we are interested in making a statement about.

3) Continuous variable: It is one for which, within the limits the variable ranges, any value is possible. Continuous variable can take any value between a certain set of real numbers.

4) Discrete variable: It is also known as Categorical variable. They are variables that exit only as whole numbers and are not divisible.

5) Statistics: According to Robert (1994), statistics is a set of procedures for organizing, summarizing, describing, analyzing, interpreting measurement and for drawing conclusion and making inference about what is generally true for an entire group when only a few members of the group are actually measured.

6) Data: Data are the actual pieces of factual information that you collect and record through your study and used for the purpose of analysis.

REG NUMBER: 2021/241933

1i.) Class Interval

using Sturge’s rule, K=1+3.3logN

where K= number of classes, N=total frequency =33

k=1+3.3log33

k=1+3.3(1.518)

k=1+5

k=6

17–18, 19–20, 21–22, 23–24, 25–26, 27–28

ii.) Midpoint = 17.5, 19.5, 21.5, 23.5, 25.5, 27.5

iii.) Frequency = 5, 6, 8, 7, 4, 3

iv.) Cumulative Frequency = 5, 11, 19, 26, 30, 33

v.) Relative Frequency= 15, 18, 24, 21, 12, 9

vi.) Relative Cumulative Frequency = 15, 33, 57, 78, 90, 100

2i.) SAMPLE:A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations. A sample should represent the population as a whole and not reflect any bias toward a specific attribute.

A sample, in other words, is a portion, part, or fraction of the whole group, and acts as a subset of the population. Samples are used in a variety of settings where research is conducted.

ii.) POPULATION

Population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic.

In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped by a common feature can be said to be a population.

iii.) CONTINUOUS VARIABLE

A continuous variable is a specific kind a quantitative variable used in statistics to describe data that is measurable in some way. If your data deals with measuring a height, weight, or time, then you have a continuous variable.

Iv.) DISCRETE VARIABLE

A discrete variable is a kind of statistics variable that can only take on discrete specific values. The variable is not continuous, which means there are infinitely many values between the maximum and minimum that just cannot be attained, no matter what.

v.) STATISTICS

Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data. Statistics is a highly interdisciplinary field; research in statistics finds applicability in virtually all scientific fields and research questions in the various scientific fields motivate the development of new statistical methods and theory. In developing methods and studying the theory that underlies the methods statisticians draw on a variety of mathematical and computational tools.

Statistics are the results of data analysis – its interpretation and presentation. Statistics are often, though they don’t have to be, presented in the form of a table, chart, or graph

vi.) DATA

Data are individual pieces of factual information recorded and used for the purpose of analysis. It is the raw information from which statistics are created.

Both statistics and data are frequently used in scholarly research.

1i.) Class Interval

using Sturge’s rule, K=1+3.3logN

where K= number of classes, N=total frequency =33

k=1+3.3log33

k=1+3.3(1.518)

k=1+5

k=6

17–18, 19–20, 21–22, 23–24, 25–26, 27–28

ii.) Midpoint = 17.5, 19.5, 21.5, 23.5, 25.5, 27.5

iii.) Frequency = 5, 6, 8, 7, 4, 3

iv.) Cumulative Frequency = 5, 11, 19, 26, 30, 33

v.) Relative Frequency= 15, 18, 24, 21, 12, 9

vi.) Relative Cumulative Frequency = 15, 33, 57, 78, 90, 100

2i.) SAMPLE:A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations. A sample should represent the population as a whole and not reflect any bias toward a specific attribute.

A sample, in other words, is a portion, part, or fraction of the whole group, and acts as a subset of the population. Samples are used in a variety of settings where research is conducted.

ii.) POPULATION

Population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic.

In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped by a common feature can be said to be a population.

iii.) CONTINUOUS VARIABLE

A continuous variable is a specific kind a quantitative variable used in statistics to describe data that is measurable in some way. If your data deals with measuring a height, weight, or time, then you have a continuous variable.

Iv.) DISCRETE VARIABLEA discrete variable is a kind of statistics variable that can only take on discrete specific values. The variable is not continuous, which means there are infinitely many values between the maximum and minimum that just cannot be attained, no matter what.

v.) STATISTICS

Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data. Statistics is a highly interdisciplinary field; research in statistics finds applicability in virtually all scientific fields and research questions in the various scientific fields motivate the development of new statistical methods and theory. In developing methods and studying the theory that underlies the methods statisticians draw on a variety of mathematical and computational tools.

Statistics are the results of data analysis – its interpretation and presentation. Statistics are often, though they don’t have to be, presented in the form of a table, chart, or graph

vi.) DATA

Data are individual pieces of factual information recorded and used for the purpose of analysis. It is the raw information from which statistics are created.

Both statistics and data are frequently used in scholarly research.

1.)Class interval:

17-18 ,19-20,21-22,23-24,25-26,27-28

Mid point:

17.5, 19.5, 21.5, 23.5, 25.5, 27.5.

Frequency:

5, 6 ,8, 7, 4, 3

5+6+8+7+4+3=30

Cumulative frequency:

5, 11, 19, 26, 30, 33

Relative frequency

5/33 *100 =15.15%

6/33*100= 18.18%

8/33*100= 24.24%

7/33*100 =21.21%

4/33*100 =12.12%

3/33*100 =9.09%

Relative cumulative frequency

5/33*100= 15.15%

11/33*100= 33.3%

19/33*100= 57.57%

26/33*100= 78.78%

30/33*100= 90.90%

33/33*100= 100%

2. Discuss the followingA sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations.

1. A sample:

Data are measurements or observations that are collected as a source of information.

Ofili Chigozilim George

2021/244130

chigozilimofili@gmail.com

1. Class interval:

17-18 ,19-20,21-22,23-24,25-26,27-28

Mid point:

17.5, 19.5, 21.5, 23.5, 25.5, 27.5.

Frequency:

5, 6 ,8, 7, 4, 3

5+6+8+7+4+3=30

Cumulative frequency:

5, 11, 19, 26, 30, 33

Relative frequency

5/33 *100 =15.15%

6/33*100= 18.18%

8/33*100= 24.24%

7/33*100 =21.21%

4/33*100 =12.12%

3/33*100 =9.09%

Relative cumulative frequency

5/33*100= 15.15%

11/33*100= 33.3%

19/33*100= 57.57%

26/33*100= 78.78%

30/33*100= 90.90%

33/33*100= 100%

2.A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations.

1. A sample:

Data are measurements or observations that are collected as a source of information.

Question no:2

(a). Sample:is defined as a numerical quantity (such as the sample mean)

calculated in a sample.such statistics are used to estimate parameters.

(b). population:it is a group of units (persons, objects,or other items)ennu-

merated in a census or from which a sample is drawn.

(c). continuous variable:it is one for which, within the limits the variable ra-

nges,any value is possible.

(d). Discrete variable:it is also known as categorical variable. They are var-

riable or data that exist only as whole numbers and are not divisible.

(e). Statistics:it is a numerical facts such as the number of events occu-

ring in time or the people living in a particular area.

(f). Data: it is a collection of facts, such as numbers, words, measurem-

ents, observations or even just descriptions of things.

Question no 1.

22,20,19,25,22,17,28,20,22,23,17,18,24,25,

22,20,23,25,22,28,19,22,25,27,23,24,17,18,

22,19,22,23,24.

Solution.

Class interval. Mid point. F. CF. RF. RCF

15-20. 15+20/2. 11. 11. 25.5.

21-26. 19. 30. 44.1

27-31. 13. 43. 30.2

_____

43

NEBOH ODINAKACHUKWU MARIA

ECONOMICS DEPARTMENT

2021/241342

nebohmaria22@gmail.com

Question one

Using sturge rule _K=1+3.3logN

K=1+3.3log(33)= K= 6.011

Class midpoint F. CF RF RCF

17-18. 17.5. 5. 5. . 15.2. 4.9

19-20. 19.5. 6. 11. 18.2. 10.8

22-23. 22.5. 12. 23 36.4. 22.5

24-25. 24.5. 7. 30. 21.2. 29.4

27-28. 27.5. 3. 33. 9.1. 32.4

[33}. (102)

Therefore _RF is the frequency of that class divided by total frequency of all classes while RCF is the CF of that class divided by total cumulative frequency of all classes.

Question two .

1.SAMPLE – It is a part of the population that we actually observed. The objective is to make certain observations about the members of the sample ,and then , on the basis of these results , to draw valid conclusions about the characteristics of the entire population. Since it is usually impractical to test every member of a population, a sample from the population is typically the best approach available .

2. POPULATION – population is the entire group of individual that we are interested in making a statement about or which information is required. It can be a parameter they measures a numerical quantity of some aspect of a population of series. For example ,the mean. It is a measures of central tendency. Population parameters are known and are usually estimated by statistics computed in samples.

3. CONTINUOUS VARIABLES – It is one for which , within the limits the variables ranges, nay value is possible. Continuous variables can take any value between a certain set of real numbers. The value given to an observation for a continuous variables can include values as small as the instrument of measurement allows. It can be classified into three categories:

a. Interval – scale variables.

b. Continuous ordinal variables.

c. Ratio – scale variables.

4. DISCRETE VARIABLES -Discrete variables or data are also known as categories variables. They are variables or data that exist only as whole numbers and are not divisible. A discrete variables can take on a finite number of numerical values, categories or code. Examples: number of tables in a class ,number of biscuit in a carton etc. It can be classified into the categories:

a. Nominal variables.

b. Ordinal variables.

c. Dummy variables.

d. Preference variables.

e. Multiple response variables.

5. STATISTICS – Statistics refers to numerical facts such as the number of events occurring in time or the number of people living in a particular area. It Laos involves the study of ways of collecting, analyzing and interpreting numerical facts or data. There are four steps involves in statistics :

a. Collection of data .

b. Presentation of data .

c. Analysis of data.

d. Interpretation of data .

6.DATA- Data could be seen as a collection of facts, such as numbers,word,measurements,observation or even just descriptions of things. It could also be seen as information in raw or unorganized form(such as alphabets, numbers or symbols) that refers to, or represent, conditions, ideas, or objects. Data is divided into two types :

a. Primary data – Is a data that is collected for the first time through personal experience or evidence and it is used by that agent or organization. It is describe as a raw data or first hand data. The primary data can be collected through survey,interviews, observation NAD focus group.

b. Secondary data – Is a data that has previously being gathered and can be access by researchers. Example: taxed records, social security data,census data etc.

Name: Ameh Emmanuel Chinaecherem

Reg no: 2021/247162

email: emmanuelchinaecherem115@gmail.com

Question 1:

Applying sturge rule

K= 1+3.3LogN

Where K= Number of an interval

N= Number of the observation

Then; K= 1+3.3Log33

K= 6.01

Approximately; K= 6

The range= highest minus the lowest

28-17= 11

Then; 11/6=1.8

Approximately 2

The function of sturge rule is to know the number of intervals.

Class. Mid

Interval point. F. C. F. R. F. R. C.F

17…18 17.5 5 5 15.2 15.2%

19…20 19.5 6 11 18.2 33.4%

21…22 21.5 8 19 24.2 57.6%

23…24 23.5 7 26 21.2 78.8%

25…26 25.5 4 30 12.1 90.8%

27…28 27.5 3 33 9.09 99.8%

33

Question 2

1) sampleA sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations. A sample should represent the population as a whole and not reflect any bias toward a specific attribute.

2) PopulationA population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic.

In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped by a common feature can be said to be a population.

3) Continuous variables

A variable is said to be continuous if it can assume an infinite number of real values within a given interval. For instance, consider the height of a student. The height can’t take any values. It can’t be negative and it can’t be higher than three metres. But between 0 and 3, the number of possible values is theoretically infinite. A student may be 1.6321748755 … metres tall. In practice, the methods used and the accuracy of the measurement instrument will restrict the precision of the variable. The reported height would be rounded to the nearest centimetre, so it would be 1.63 metres. The age is another example of a continuous variable that is typically rounded down.

4) Discrete variables

As opposed to a continuous variable, a discrete variable can assume only a finite number of real values within a given interval. An example of a discrete variable would be the score given by a judge to a gymnast in competition: the range is 0 to 10 and the score is always given to one decimal (e.g. a score of 8.5). You can enumerate all possible values (0, 0.1, 0.2…) and see that the number of possible values is finite: it is 101! Another example of a discrete variable is the number of people in a household for a household of size 20 or less. The number of possible values is 20, because it’s not possible for a household to include a number of people that would be a fraction of an integer like 2.27 for instance.

5) Statistics

The word Statistics is derived from the Greek word ‘Statistique,’ Latin word ‘Status,’ the Italian word ‘Statista,’ and the German word ‘Statistic.’ Statistics is defined as the study, collection, analysis, interpretation, and organization of data for different ultimate objectives. Statistics help a user in gathering and analyzing huge numerical data easily and efficiently. Statistics can be easily defined in two senses: Plural Sense and Singular Sense.

6) Data

Data could be seen as a collection of facts, such as numbers, words, measurements, observations or even just descriptions of things. It could also be seen as information in raw or unorganised form ( such as alphabets, numbers, or symbols) that refer to, or represent, conditions, ideas, or objects. Data could be qualitative (that is; data that deal with description) or quantitative (that is; data that deal with numbers). Data collection is a fundamental aspect of research. Data are required for empirical analysis and other forms of analysis.

Name:Akachukwu Kosisochukwu John

Reg No:2021/244040

Dept:Economics

1. The class interval using sturge rule:

Sturge rule formula= k= 1 + 3.322 logN

Where N= Total number of observations.

K= 1 + 3.322 log33

K= 1 + 3.322(1.5185)

K= 1 + 5.0445

K= 6.0445

K= 6~

Class interval= Range/1 + 3.322 logN

Range=Highest value – Lowest value

Range= 28 – 17 = 11

Class interval= 11/ 1+3.322log33

= 11/6

=1.83

= 2~

Class Interval Mid-point F. C.F. R.F. R.C.F

17 – 18 17.5 5 5 15.15 15.15

19 – 20 19.5 6 11 18.18 33.33

21 – 22 21.5 8 19 24.24 57.57

23 – 24 23.5 7 26 21.21 78.78

25 – 26 25.5 4 30 12.12 90.90

27 – 28 27.5 3 33 9.09 100

Total=

33

Question one:

1, class interval using surge’s rule

K=1+3.3logN

Where k=class interval

N=number of observations:33

K=1+3.3log33= 1+3.3(1.5185)

=6.01= 6 intervals

2 _6,

No y. F M.P CF RF RCF

17_18 5 17.5 5. 15.5. 4.03

19_20 6 19.5 11 18.18 8.87

21_22 8 21.5 19 24.24 15.32

23_24 7 23.5 26 21.21 20.96

25_26 4 25.5 30 12.122 4.9

27_28 3 27.5 33 9.09 26.61

Total 33 124

From the table, F=frequency, M.p=mid point,

Cf=cumulative frequency, RF=relativefrequency: n/£f×100, RCF= relative cumulative frequency: n/£cf×100

Question 2

1) Sample means a subgroup of the members of population chosen for participation in the study. It Include Only a handful of units of population, we can also say it is a subset of the population.

2)Population refers to the collection of all elements possessing common characteristics, that comprises universe. It includes all the units in that group.

3) continues variable alludes to the a variable which assumes infinite number of different values.

4)Discrete variable refers to the variable that assumes a finite number of isolated values

5) statistics is a scientific method of collecting, organising, summarizing, analysing and presentation of data as well as drawing inference

Or making valid conclusion on the basis of such analysis

6) Data could be seen as a collection of facts, such as numbers, words, measurements, observations or even just discription of things. The are information in raw and unorganized form

Name: Obidike kosisochukwu Charles E_mail: kosisochukwuc05@gmail.com

Reg number: 2021/246047

Department: Economics

1. Computing the following as follows Using the sturge rule

Solution.

{Sturge rule} k=1+3.3 log N

K=1+3.3 log 33

K=1+3.3(1.5185)

K=1+5.0

K=6

:no of class= 6

Range =28-17

=11

Class interval=11/6

=1.8. (approximately) =2.

Class interval:=2

17-18 ,19-20,21-22,23-24,25-26,27-28

Mid point:

17.5, 19.5, 21.5, 23.5, 25.5, 27.5.

Frequency:

5, 6 ,8, 7, 4, 3

5+6+8+7+4+3=30

Cumulative frequency:

5, 11, 19, 26, 30, 33

Relative frequency

5/33 *100 =15.15%

6/33*100= 18.18%

8/33*100= 24.24%

7/33*100 =21.21%

4/33*100 =12.12%

3/33*100 =9.09%

Relative cumulative frequency

5/33*100= 15.15%

11/33*100= 33.3%

19/33*100= 57.57%

26/33*100= 78.78%

30/33*100= 90.90%

33/33*100= 100%

1. A sample:

Data are measurements or observations that are collected as a source of information.

Name: Obidike kosisochukwu Charles

E_mail: kosisochukwuc05@gmail.com

Reg number: 2021/246047

Faculty:Social Science

Department: Economics

1. Computing the following

Using the sturge rule

Solution.

{Sturge rule} k=1+3.3 log N

K=1+3.3 log 33

K=1+3.3(1.5185)

K=1+5.0

K=6

:no of class= 6

Range =28-17

=11

Class interval=11/6

=1.8. (approximately) =2.

Class interval: =2

17-18 ,19-20,21-22,23-24,25-26,27-28

Mid point:

17.5, 19.5, 21.5, 23.5, 25.5, 27.5.

Frequency:

5, 6 ,8, 7, 4, 3

5+6+8+7+4+3=30

Cumulative frequency:

5, 11, 19, 26, 30, 33

Relative frequency

5/33 *100 =15.15%

6/33*100= 18.18%

8/33*100= 24.24%

7/33*100 =21.21%

4/33*100 =12.12%

3/33*100 =9.09%

Relative cumulative frequency

5/33*100= 15.15%

11/33*100= 33.3%

19/33*100= 57.57%

26/33*100= 78.78%

30/33*100= 90.90%

33/33*100= 100%

1. A sample:

Data are measurements or observations that are collected as a source of information.

Name: OSITA MARYJANE OLUEBUBE

E_mail:ositamaryjane6@gmail.com

Reg-number:10541245BB

Faculty: Social Science

Department: Economics

Q1.Computing the following

Using the sturge rule

Solution.

{Sturge rule} k=1+3.3 log N

K=1+3.3 log 33

K=1+3.3(1.5185)

K=1+5.0

K=6

;:no of class= 6

Range =28-17

=11

Class interval=11/6

=1.8. (approximately) =2.

Class interval:=2

17-18 ,19-20,21-22,23-24,25-26,27-28

Mid point:

17.5, 19.5, 21.5, 23.5, 25.5, 27.5.

Frequency:

5, 6 ,8, 7, 4, 3

5+6+8+7+4+3=30

Cumulative frequency:

5, 11, 19, 26, 30, 33

Relative frequency

5/33 *100 =15.15%

6/33*100= 18.18%

8/33*100= 24.24%

7/33*100 =21.21%

4/33*100 =12.12%

3/33*100 =9.09%

Relative cumulative frequency

5/33*100= 15.15%

11/33*100= 33.3%

19/33*100= 57.57%

26/33*100= 78.78%

30/33*100= 90.90%

33/33*100= 100%

Q2. Discuss the following:,,,,A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations.

1. A Sample:

2. A Population:A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic. In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study.

A population is simply a complete set of people with a specialized set of characteristics.

3. A continuous variable:

A continuous variable is a specific kind a quantitative variable used in statistics to describe data that is measurable in some way.The continuous variable refers to the numerical variable whose value is attained by measuring. Continuous variables are generally measured on scales such as height, weight, temperature, etc.

4. A discrete variable:

A discrete variable is a variable which exists only as a whole number and is not divisible. It can take a while or finite number of numerical value,categories or codes.For example,the number of people in a room or counting the money you have in ur account.

Discrete variables can also called a categorical variable.

5. Data:

Data is information such as facts and numbers used to analyze something or make decisions. Data can come in the form of text, observations, figures, images, numbers, graphs, or symbols. For example, data might include individual prices, weights, addresses, ages, names, temperatures, dates, or distances.it is a raw form of knowledge and also on it’s own

6.Statistics:

Statistics is a mathematical body of science that pertains to the collection, analysis, interpretation or explanation, and presentation of data ,or as a branch of mathematics. For example, if we consider one math class to be a sample of the population of all math classes, then the average number of points earned by students in that one maths class at the end of the term is an example of a statistic.

In short, statistics is a crucial process which helps to make the decision based on the data.

Solution

K= 1+3.3logN( sturges rule)

K= 1+3.3log33

K=1+3.3(1.5185)

K=1+5.0

K=6 or no of classes=6

Range = 28-17 =11

Class interval = 11/6 = 1.8 = 2

Class-interval. Midpoint. Freq. Cumulative freq. Relative freq. Relative cumulative(freq)

17-18. 17.5. 5. 5. 5/33 *100/1=15.2%. 5/33*100/1=15.2%

19-20. 19.5. 6. 11. 6/33*100/1=18.2%. 11/33*100/1=33.4%

21-22. 21.5. 8. 19. 8/33*100/1=24.2%. 19/33*100/1=57.6%

23-24. 23.5. 7. 26. 7/33*100/1=21.2%. 26/33*100/1=78.8%

25-26. 25.5. 4. 30. 4/33*100/1=12.1%. 30/33*100/1=90.9%

27-28. 27.5. 3. 33. 3/33*100/1=9.1%. 33/33*100/1=100%

33. 100%.

Sample: it’s defined as a smaller and more manageable representation of a large group

Population: it refers to the people who live in a particular area at a specific time. But in statistics, population refers to data on your study of interest.

Continuous variable: it’s defined as a variable which can take an uncountable set of values or infinite set of values.

Discrete variable: it’s a variable that takes on distinct, countable values.

Statistics: it’s the study of the collection analysis, interpretation, presentation, and organization of data. In other words, it’s a mathematical discipline to collect, summarize data.

Data: they’re individual pieces of factual information recorded and used for the purpose of analysis.

REG NO:2021/246499

DEPARTMENT:SOCIAL SCIENCE

UNIT: ECONOMIC EDUCATION

1.

C. I M. P F C. F R. F C. R. F

17-18 17.5 5 5 15.2 4.0

19-20 19.5 6 11 18.2 8.87

21-22 21.5 8 19 24.2 15.3

23-24 23.5 7 26 21.2 20.9

25-26 25.5 4 30 12.1 24.1

27-28 27.5 3 33 9.1 26.6

33 124

2. A) Sample: Sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations.

B) Population: Population is the entire set of items from which you draw data for a statistical study. It can be a group of individuals, a set of items, etc. It makes up the data pool for a study.

Generally, population refers to the people who live in a particular area at a specific time.

C) Discrete Variable: Discrete variables are countable in a finite amount of time. For example, you can count the change in your pocket. You can count the money in your bank account. A discrete variable is a kind of statistics variable that can only take on discrete specific values. The variable is not continuous, which means there are infinitely many values between the maximum and minimum that just cannot be attained, no matter what.

D) Continuous Variable: A variable is said to be continuous if it can assume an infinite number of real values within a given interval.Quantitative variable may be continuous if they are typically obtained by measuring or counting, respectively. For instance, consider the height of a student. The height can’t take any values.

E) Statistics: Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.In other words, it is a mathematical discipline to collect, summarize data. Also, we can say that statistics is a branch of applied mathematics.

F) Data: Data are measurements or observations that are collected as a source of information.It is the raw information from which statistics are created. Data are individual pieces of factual information recorded and used for the purpose of analysis.

Name : Arubaleze Raluchukwu Marie-Zita

Department: Economics

Reg No : 2021/24310

1. A table showing plots in a soyabean field given two sprays of pesticides.

Class Intervals Mid-point Frequency Cumulative Relative

(x) Frequency Frequency

17-18 17.5 5 5 15.5

19-20 19.5 6 11 18.18

21-22 21.5 8 19 24.24

23-24 23.5 7 26 21.21

25-26 25.5 4 30 12.12

27-28 27.5 3 33 9.09

Total 30

Relative Cumulative Frequency

15.15

33.33

57.58

78.79

90.91

100

Workings:

A. Relative Cumulative

I (5÷33)×100 =15.15

ii (6÷33)×100 =18.18

iii (8÷33)×100 = 24.24

iv (7÷33)×100 = 21.21

v (4÷33)×100 = 12.12

vi (3÷33)×100 = 9.09

B. Relative Cumulative Frequency

I (5÷33)×100 = 15.15

ii (11÷33)×100 =33.33

iii (19÷33)×100 = 57.58

iv (26÷33)×100 = 78.79

v (30÷33)×100 = 90.91

vi (33÷33)×100 = 100

2. Write a brief note on the following:

1. Sample: A sample is a part of a population that is used to represent a population.

2. Population: This is the total number of an entire collection of items or individuals which a person wishes to examine at a particular time.

3. Continuous Variable: This is a type of variable that assumes any value from a range of values.

4. Discrete variable: This is a type of variable that can only be counted and be represented in a whole number.

5. Statistics: Statistics is a field of study concerned with the lay out of experiment, collection, calculation, tabulation, summarization and analysis of data.

6. Data: Data is an unprocessed information or raw information in its original form.

1a. Class interval

17-18

19-20

21-22

23-24

25-26

26-28

1b. Midpoint

17.5

19.5

21.5

23.5

25.5

27.5

1c. Frequency

5

6

8

7

4

3

Total=33

1d. Cumulative frequency

5

11

19

26

30

33

1e. Relative frequency

15.2

18.2

24.2

21.2

12.1

9.1

1f. Relative Cumulative frequency

15.2

33.3

57.5

78.7

90.9

100

2a. Sample: This is defined as a part or portion of a population and it is taken from the population as a representation of it.

2b. Population: This is the entire collection of items or individuals which one wishes to examine at a particular time.

2c. Continuous variable: This is a variable which can take an uncountable set of values or infinite set of values. It takes on any value within a range and and the number of possible values within the range is infinite.

2d. Discrete variable: It is also known as categorical variable. They are variables that can be counted and represented in a whole number. Example; Age of students, number of seeds.

2e. Statistics: Statistics refers to numerical facts such as the number of events occuring in time or the number of people living in a particular area. It also involves the study of ways of collecting, analyzing and interpreting numerical facts or numerical data.

2f. Data: This is a numerical statement of facts in a specific field of enquiry or simply numbers which may result from taking measurements. Example; recording heights weights or temperature.

Name: Arthur Philip David

Reg no: 2021/241939

Interval,????????(????) ???? ????f. ???????? ????????????

17−18 17.5 5 5 16.6 4.4

19−20 19.5 5 10 16.6 8.9

21- 22 21.5 7 17 56.6 15.1

23−24 23.5 6 23 20 20.5

25−26. 25.5 4 27 13.3 24.1

27−28 27.5 3 30 10 26.7

30 112 133.1 99.7

Sturge rule

K=1 + 3.3logN

SAMPLE:

A sample is defined as a smaller and more manageable representation of a larger group.

Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations.

POPULATION:

Population is the whole number of people or inhabitants in a country or region. : the total of individuals occupying an area or making up a whole

CONTINUOUS VARIABLE:

A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values.

DISCRETE VARIABLE:

A discrete variable is a variable whose value is obtained by counting.

STATISTICS:

Statistics for economics concerns itself with the collection, processing, and analysis of specific economic data. It helps us understand and analyze economic theories and denote correlations between variables such as demand, supply, price, output etc.

DATA:

Data something that hasn’t be process…

Data in economics refers to a set of given information

NAME:UDEH BEATRICE CHINAZA

REG.NO:2021/244045

22, 20, 19, 25, 22, 17, 28, 20, 22, 23, 17

18, 24, 25, 22, 20, 23, 25, 22, 28, 19, 22

25, 27, 23, 24, 17, 18, 22, 19, 22, 23, 24

Compute the table as follows:

The class interval using sturge rule

Mid-point

Frequency

Cumulative Frequency

Relative Frequency

Relative Cumulative Frequency

Solution

1) Using sturges rule to find class interval =

K=1+3.3logN

K is the no of intervals

N is the no of observations

K=1+3.3log33

K=6.01

Class interval midpoint freq. CF RF RCF

17-22 19.5 19 19 57.6 36.53

23-28 25.5 14 33 42.42 63.46

Total= 33 52

QUESTION TWO

Write a brief note on the following:

Sample

Population

Continuous Variable

Discrete variable

Statistics

Data

i) Sample is defined as the part or portion of a population and its taking from the population as a representation of it.

ii) Population is the total number of collection of an items or individual on which somebody wishes to examine at a particular time.

iii) Continous variable is any variable that can assume any value from a range of values.

iv) Discrete variable is any variable that can be counted only and presented as a whole number.

v) Statistics can be defined as the field of study concerning the layout of experiment, connection, calculation, summarization and analysis of data.

vi) Data is a numerical statement of facts in a specific means of enquire.

Reg no: 2021/241311

QUESTION 1:

Using sturge rule

Step a: find range= 28-17 = 11

Step b: Determine the number of classes (k), class size

K= 1+3.322(log N)

K=1+3.322(log 33)

K=1+ 3.22(1.518)

K=1+5.081

K=6.081 approximately 6

Step c: calculate the class interval

C.I = range ÷ class size (k)

C.I = 11÷ 6= 1.8 approximately 2

Kg. M.D F. R.F. C.F R.C.F

17-18. 17.5 5. 5 / 33 ×100= 15.15 5. 4.03

19-20. 19.5 6. 6 / 33× 100= 18.18 11. 8.87

21-22. 21.5 8 8 / 33 x 100=24.24 19. 15.32.

23-24. 23.5 7. 7/ 33 × 100=21.21 26. 20.96

25-26. 25.5 4 4 / 33 × 100=12.12. 30. 24.19

27-28. 27.5 4 3 / 33 × 100=9.09 33. 26.61

33 124

QUESTION 2:

1 SAMPLE:

It is really difficult examine all members of the population due to time cost and other constraints. So we examine only a portion of the population and try to draw conclusion about the whole sample estimates.

In a broader sense, sampling is a procedure by which one or more members of a population as selected from the population. The objective is to make certain observation about the members of the sample, and then, on the basis of these results, draw valid conclusions about the characteristics of the entire population.

2POPULATION:

Population is defined as the entire group about which information desired. It is describe as the largest collection of entities for which we have an interest at a particular time, the entire set of object, observations or scores that have something in common.

3 CONTINUOUS VARIABLE:

Continuous variable is one for which, within the limits variable rangers, any value is positive. Continuous variable can take any value between a second set of real numbers. The value given to an observation before a continuous variable can include values as small as the instrument 4 measurement allows. For example, the variable “time to solve an algebra problem” is continuous says it could take 2 minutes, 2.3 minutes, 5 minutes etc. To finish the problem. Other examples of continuous variables include height, time, and temperature.

4 DISCRETE VARIABLE

Discrete variables or data are also known as categorical variables. You are variable or data that the exists only has whole number and are not divisible. A discrete variable can take a finite number or numerical value categories or codes.

5 STATISTICS:

The word statistics refers 2 numerical facts such as the number of events occurring in time order number of people living in particular area. It also involves the study of ways of collecting, analysing and interpreting numerical facts or numerical data. Basically, statistics is concerned with the statistic method of collecting, organising ,summarising ,presenting and analysing data. According to Upton and Cook (2008) , statistics is the statistic method of collecting, organising, summarising, analysing and presenting data as well as drawing valid inference or conclusion and making reasonable decisions on the basis of such analysis.

6 DATA:

Data in a simplified form could be seen as measurements of observations that are collected as a source of information.

NAME – ONUOHA SAMUEL CHIEMEZUO

MATRIC NO-2021/241353

DEPARTMENT – ECONOMICS

1) solutions = No of observations =33

Using Sturges rule

K= 1+ 3.3 log N

K= 1+3.3 log 33

K= 1 + 3.3(1.5185)

K= 1 + 5.0

K= 6

No of classes =6

Range = 28-17

=11

Class interval =11÷6= 1.8

1.8=2

Class interval. Mid point F C. F. R. F

17-18. 17.5 5. 5. 5/33×100/1=15.2%.

19-20. 19.5 6. 11. 6/33×100/1=18.2%

21-22. 21.5. 8. 19. 8/33×100/1=24.2%

23-24. 23.5. 7. 26. 7/33×100/1=21.2%

25-26. 25.5. 4. 30. 4/33×100/1=12.1%

27-28 27.5 3. 33. 3/33×100/1=9.1%

33. 100%

R.C.F

5/33×100/1=15.2%

11/33×100/1=33.4%

19/33×100/1=57.6%

26/33×100/1=78.8%

30/33×100/1=90.9%

33/33×100/1=100%

2). – SAMPLE

Sample can simply be defined as a smaller, managerable version of a larger group. It is said to be a subset containing the characteristics of a larger population. Samples are used in statistical, testing when population sizes are too large for the test to include all possible members or observations.

-POPULATION

Population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristics.

-CONTINUOUS VARIABLE

A continuous variable is defined as a variable which can take an uncountable set of value or infinite set of values. For instance, If a variable over a non empty range of the real numbers is continuous, then it can take on any value in that range.

-DISCRETE VARIABLE

These are variable that assumes only a finite number of values. For example, raco categorized as non-hispanic white, Hispanic, blank Asian other.

-STATISTICS

This is the practice or science of collecting and analysing numerical data in large quantities, especially for the purpose of interfering proportions in a while from those in a representative sample.

-DATA

Data are measurement or observations that are collected as a source of information.

QUESTION 1:

Using sturge rule

Step a: find range= 28-17 = 11

Step b: Determine the number of classes (k), class size

K= 1+3.322(log N)

K=1+3.322(log 33)

K=1+ 3.22(1.518)

K=1+5.081

K=6.081 approximately 6

Step c: calculate the class interval

C.I = range ÷ class size (k)

C.I = 11÷ 6= 1.8 approximately 2

Kg. M.D F. R.F. C.F R.C.F

17-18. 17.5 5. 5 / 33 ×100= 15.15 5. 4.03

19-20. 19.5 6. 6 / 33× 100= 18.18 11. 8.87

21-22. 21.5 8 8 / 33 x 100=24.24 19. 15.32.

23-24. 23.5 7. 7/ 33 × 100=21.21 26. 20.96

25-26. 25.5 4 4 / 33 × 100=12.12. 30. 24.19

27-28. 27.5 4 3 / 33 × 100=9.09 33. 26.61

33 124

QUESTION 2:

1 SAMPLE:

It is really difficult examine all members of the population due to time cost and other constraints. So we examine only a portion of the population and try to draw conclusion about the whole sample estimates.

In a broader sense, sampling is a procedure by which one or more members of a population as selected from the population. The objective is to make certain observation about the members of the sample, and then, on the basis of these results, draw valid conclusions about the characteristics of the entire population.

2POPULATION:

Population is defined as the entire group about which information desired. It is describe as the largest collection of entities for which we have an interest at a particular time, the entire set of object, observations or scores that have something in common.

3 CONTINUOUS VARIABLE:

Continuous variable is one for which, within the limits variable rangers, any value is positive. Continuous variable can take any value between a second set of real numbers. The value given to an observation before a continuous variable can include values as small as the instrument 4 measurement allows. For example, the variable “time to solve an algebra problem” is continuous says it could take 2 minutes, 2.3 minutes, 5 minutes etc. To finish the problem. Other examples of continuous variables include height, time, and temperature.

4 DISCRETE VARIABLE

Discrete variables or data are also known as categorical variables. You are variable or data that the exists only has whole number and are not divisible. A discrete variable can take a finite number or numerical value categories or codes.

5 STATISTICS:

The word statistics refers 2 numerical facts such as the number of events occurring in time order number of people living in particular area. It also involves the study of ways of collecting, analysing and interpreting numerical facts or numerical data. Basically, statistics is concerned with the statistic method of collecting, organising ,summarising ,presenting and analysing data. According to Upton and Cook (2008) , statistics is the statistic method of collecting, organising, summarising, analysing and presenting data as well as drawing valid inference or conclusion and making reasonable decisions on the basis of such analysis.

6 DATA:

Data in a simplified form could be seen as measurements of observations that are collected as a source of information.

QUESTION 1:

Using sturge rule

Step a: find range= 28-17 = 11

Step b: Determine the number of classes (k), class size

K= 1+3.322(log N)

K=1+3.322(log 33)

K=1+ 3.22(1.518)

K=1+5.081

K=6.081 approximately 6

Step c: calculate the class interval

C.I = range ÷ class size (k)

C.I = 11÷ 6= 1.8 approximately 2

Kg. M.D F. R.F. C.F R.C.F

17-18. 17.5 5. 5 / 33 ×100= 15.15 5. 4.03

19-20. 19.5 6. 6 / 33× 100= 18.18 11. 8.87

21-22. 21.5 8 8 / 33 x 100=24.24 19. 15.32.

23-24. 23.5 7. 7/ 33 × 100=21.21 26. 20.96

25-26. 25.5 4 4 / 33 × 100=12.12. 30. 24.19

27-28. 27.5 4 3 / 33 × 100=9.09 33. 26.61

33 124

QUESTION 2:

1 SAMPLE:

It is really difficult examine all members of the population due to time cost and other constraints. So we examine only a portion of the population and try to draw conclusion about the whole sample estimates.

In a broader sense, sampling is a procedure by which one or more members of a population as selected from the population. The objective is to make certain observation about the members of the sample, and then, on the basis of these results, draw valid conclusions about the characteristics of the entire population.

2 POPULATION:

Population is defined as the entire group about which information desired. It is describe as the largest collection of entities for which we have an interest at a particular time, the entire set of object, observations or scores that have something in common.

3 CONTINUOUS VARIABLE:

Continuous variable is one for which, within the limits variable rangers, any value is positive. Continuous variable can take any value between a second set of real numbers. The value given to an observation before a continuous variable can include values as small as the instrument 4 measurement allows. For example, the variable “time to solve an algebra problem” is continuous says it could take 2 minutes, 2.3 minutes, 5 minutes etc. To finish the problem. Other examples of continuous variables include height, time, and temperature.

4 DISCRETE VARIABLE

Discrete variables or data are also known as categorical variables. You are variable or data that the exists only has whole number and are not divisible. A discrete variable can take a finite number or numerical value categories or codes.

5 STATISTICS:

The word statistics refers 2 numerical facts such as the number of events occurring in time order number of people living in particular area. It also involves the study of ways of collecting, analysing and interpreting numerical facts or numerical data. Basically, statistics is concerned with the statistic method of collecting, organising ,summarising ,presenting and analysing data. According to Upton and Cook (2008) , statistics is the statistic method of collecting, organising, summarising, analysing and presenting data as well as drawing valid inference or conclusion and making reasonable decisions on the basis of such analysis.

6 DATA:

Data in a simplified form could be seen as measurements of observations that are collected as a source of information.

Question Two

1) Sample: it is usually difficult to examine all members of the population due to time, cost and other constraints. So we examine only a portion of the population and try to draw conclusion about the whole using sample estimates.

2) population: is the entire group of individuals that we are interested in making a statement about.

3) Continuous variable: is one for which, within the limits the variable ranges, any value is possible. Continuous variable can take any value between a certain set of real numbers. For example, the variable “time to solve an algebra problem” is continuous since it could take 2 minutes, 2.14 minutes, 5 minutes etc.

4) Discrete variable or data are also known as categorical variables. They are variables or data that exist only as whole numbers and are not divisible.

5) Statistics refers to numerical facts such as the number of events occurring in time or the study of ways of collecting, analyzing, and interpreting numerical facts or numerical data.

6) Data could be seen as a collection of facts, such as numbers, words, measurements, observations or even just descriptions of things. It could also be seen as information in raw or unorganized form (such as alphabet, numbers, or symbols) that refer to, or represent, conditions, ideas, or objects.

1)Sturge rule

K=1+3.3logN

1+3.3log(33)

1+5.01

6.01

Class interval Freq mid points C.F R.F RCF

17-18 5 17.5 5 15.15 4.03

19-20 6 19.5 11 18.18 8.87

21-22 8 21.5 19 24.24 15.32

23-24 7 23.5 26 21.21 20.97

25-26 4 25.5 30 12.12 24.2

27-28 3 27.5 33 9.1 26.61

2) Sample; This is a part or portion of a population. It is taken from a population as a representation of it. A sample must be a representative of the population in all ramifications.

b) Population; This is the entire group of which information is desired. It is also the entire collection of items or individuals which one wishes to examine at a particular time.

c) Continuous variable; This variable is one for which within the limits the variable ranges,Continuous variable can take any value between a certain set of real numbers.

d)Discrete variable; These are variables or data are also known as categorical variables. They are variables or data that only exist as a whole number and are not divisible.

e)Statistics; Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data

f) Data; It can be described as the collection of facts such as numbers, words, observations, or description of things. It could also be seen as information in raw or organized form.

Solution to number ( 1)

C-i m-p. F. Cf. Rf. Rcf

17-18. 17.5. 5. 5. 15.15. 4.0

19-20. 19.5. 6. 11. 18.18. 8.87

21-22. 21.5. 8. 19. 24.24. 15.32

23-24. 23.5. 7. 26. 21.21. 20.96

25-26. 25.5. 4. 30. 12.12. 24.19

27-28. 27 .5. 3. 33. 9.09. 26.6

The brief short note of the following are

(A) A sample refers to a smaller manageable version if a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations.A sample is a subset of individuals from a larger population. Sampling means selecting the group that you will actually collect from in your research for example if you are researching the opinions of students in your University, you could survey a Sample of 100 students

When you conduct research about a group of people ,it is rarely possible to group of data From every person in that group.instead you select a sample. The sample is the group of individuals who will actually participate in the research.

To draw valid conclusion from your results, you have to carefully decide how you will select a sample that is representative of the group as a whole.

There are two primary types of sampling methods that you can use in your research

(1) probability sampling involves Random selection, allowing you to make strong statistical interference about the whole group it is sub divided into 4

Simple random sampling, cluster sampling, systematics sampling, stratified random sampling

(2) Non probability sampling involves non random selection based on convenience or other criteria, allowing you to easily collect data it is sub divided into 4

Convenience sampling, judgemental/ purposive sampling , snowball sampling, quota sampling

IMPORTANT Of SAMPLE

1 reduced cost and time

2 reduced resource deloyment

3 accuracy of data

4 intensive and exhaustive data

5 apply properties to a larger population

( B ) POPULATION

A population is the complete set group of individuals wether that group comprises a nationa or a group of people with a common characteristics. In statistics a population is the pool of individuals from which a statistical sample is drawn for a study . This, any selection of individuals grouped by a common feature can be said to be a population

key TAKE AWAY

1 in ordinary usage, a population is a distinct group of individuals with shared citizenship identity or characteristics

2 in statistics, a population is a representative sample of a larger group of people or even things with one or more characteristics in common

3 the u.s census is perhaps the most ambitious survey in existence, given that it entails a door-to – door. Canvas of the entire population rather than a sample group study

4 population surveys larger and small inform many if not most decisions by government and business.

(C) CONTINUOUS VAVRIABLES

CONTINUOUS VAVRIABLES can be described as numbers that may assume one of infinite values between any two values of reference. For example there is an infinite number of decimal between them. Using decimals, one may try to list all values between 1and 2, such as

1,1,1,1,2,1.3,1.4,1,1 .5, 1.6, 1 .7, 1.8, 1 .9

The interval between the values above is 0.1 how ever, there is no limit to the numbers that can appear after a decimal point. Thus , even between 1 and 1.1, there is an infinite possibility of values . In the interval 1and 1.1

The Body mass is an example of a continuous variable.even though one can define a values for body mass, for example with there numbers after the decimal point ( eg 5.542kg) this value can always be more accurate incorporating infinite digits after the point

( D ) DISCRETE VARIABLE

Is a variable that may assume only a countable and usually finite , number of values

As opposed to a continuous variable a discrete variable can assume only a finite number of real values within a given interval an example of a discrete variable would be the score given by a judge to a gymnast in competition. The range is 0 to10 and score is always given to one decimal (eg a score of 8.5

TYPES OF DISCRETE VARIABLE ARE

1 dichotomous variable

2 categorical variable ( or nominal variable

3 ordinal variable

Discrete variable have values that are counted

Discrete variable represent counts ( eg the number of objects in a collection)

( E )STATISTICS

Statistics is the study of the the collection analysis, interpretation, presentation, and organization of data. In other words , it is a mathematical discipline to collect summarize data . Also , we can say that statistics is a branch of applied mathematics.How ever , there are two important and basic ideas involved in statistics, they are uncertainty and variation. The uncertainty and variation in different fields can be determined by the probability that plays an important role in statistics

Example

To find the mean of the marks obtained by each student in the class whose strength is 50. The average value here is the statistics of the mark obtained.

TYPES O F STATISTICS

1 descriptive and inferential

1 descriptive statistics in the case of descriptive statistics, the data or collection of data is describe in summary but in the case of inferential stats it is used to explain the descriptive one . Both these types have been used to large scale

Scope of stastistics

Stats is used in many sectors such psychology, geology, sociology, weather forecasting, probability and much more the goal of statistics is to gain under standing from the data , it focuses on application and hence, it is distinctively considered as a mathematical science

MTHODS IN STATISTICS

The methods involve collecting summerizing analysis, and interpreting variable numerical data. Here are some of the methods are provided below

1 data collection

2 data summarizing

3 statistics analysis.

(F) DATA

Data are individual pieces of factual information recorded and used for the purpose of analysis. It is the raw information from which statistics are created . Statistics are the results of data analysis. It is interpretation and presentation.

Data is classified into majorly four categories. Nominal data., Ordinal data , discrete data. Continuous data data is used to create new information or knowledge for example ,census data provides data about the number of people within a particular area with variable such as gender, age, income, etc

TYPES OF DATA

1. Qualitative data they represent some characteristics or attributes. They depict description that may be observed but cannot be computed or calculated

2 quantitative data. These can be measured and not simple observed. They can be numerically represented and calculations can be performed on them

DATA COLLECTION

1 primary data. These are the data that are collected for the first time by an investigator for a specific purpose

2 secondary data they are the data that are sourced from some place. That has originally collected it . This means that this

Kind of data has already been collected by some researchers or investigator in the past and is available either in published or unpublished form

3 Discrete data These are data that can take only certain specific values rather than a range of valuesb

4 Continuous data. These are data that can take values between a certain range with the highest and lowest values.

NAME: ANAGHARA ESTHER CHIBUZOR

DEPT: ECONOMICS

MATRIC.NO: 2021/241940

Email: anagharachibuzor205@gmail.com

Course code: Eco 131.

SAMPLING AND OTHER ISSUES.

Q1 : Compute the following in a frequency distribution table.., 22,20,19,25,22,17,28,20,22,23,17,18,24,25,22,20,23,25,22,28,19,22,25,27,23,24,17,18,22,19,22,23,24

Using:

Class interval.

Mid-point.

Frequency.

Cumulative frequency.

Relative frequency.

Cumulative relative frequency.

Class M.P F C.F R.F C.R.F

17-18 17.5 5 5 5/33*100=15.15 15.15

19-20 19.5 6 11 6/33*100=18.18 33.33

21-22 21.5 8 19 8/33*100=24.24 57.57

23-24 23.5 7 26 7/33*100=21.21 78.78

25-26 25.5 4 30 4/33*100=12.12 90.9

27-28 27.5 3 33 3/33*100=9.09 99.99

STATISTICS

Statistics, the science of collecting, analyzing, presenting, and interpreting data. Governmental needs for census data as well as information about a variety of economic activities provided much of the early impetus for the field of statistics. Currently the need to turn the large amounts of data available in many applied fields into useful information has stimulated both theoretical and practical developments in statistics .

DATA

Data are individual pieces of factual information recorded and used for the purpose of analysis. It is the raw information from which statistics are created. Statistics are the results of data analysis – its interpretation and presentation.

POPULATION

Population is the pool of individuals from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped by a common feature can be said to be a population. In statistics, population is a set of similar items or events which is of interest for some question or experiment.

SAMPLE

Sample refers to a smaller manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations.

DISCRETE VARIABLE.

This is a variable that can only take on discrete specific values. The variable is not continous which means there a infinitely many minimum that cannot be attained no matter what.

CONTINUOUS VARIABLE.

A variable is said to be continous if it can assume an infinite number of real values within a given interval. For instance, consider the height of a student, the height can’t take any values .

NAME: ORJI EVAN CHINAZA.

REG NO: 2021/242394.

DEPARTMENT: EDUCATION.

FACULTY: ECONOMICS EDUCATION.

COURSE: INTRODUCTION TO ECONOMICS STATISTICS.

CI. MP. F. CF. RF. CRF

17-18. 17.5. 5. 5. 15.2. 4.03

19-20. 19.5. 6. 11. 18.2. 8.87

21-22 21.5. 8. 19. 24.2. 15.32

23-24. 23.5. 7. 26. 21.2. 20.96

25-26. 25.5. 4. 30. 12.1. 24.19

27-28. 27.5. 3. 33. 9.09. 26.61

33. 124

RF

A) 5÷33 ×100=15.2

B) 6÷33 ×100=18.18

18.2

C) 8÷33×100=24.24

24.2

D) 7÷33×100=21.21

21.2

E) 4÷33×100=12.12

12.1

F) 3÷33×100=9.09

C R F

a) 5÷124×100=4.03. b) 26÷124×100=20.96

c) 11÷124×100=8.87. d) 30÷124×100=24.19

e) 29÷124×100=15.32. f) 33÷124×100=26.61

* SAMPLE: Sampling is a procedure by which one or more members of a population are selected from the population. Since it is usually impractical to test every member of a population, a sample from the population is typically the best approach available.

*POPULATION: Population is defined as an entire group of individual that we are interested in making a statement about or it’s a group about which information is desired.

*CONTINUOUS VARIABLE: A continuous variable is one for which, within the limits the variable ranges, any value is possible. Continuous variable can take any value between a certain set of real numbers.

*DISCRETE VARIABLES: Discrete variable or data are also known as categorical variables. They are variables or data that exist only as a whole numbers and are not divisible.

*STATISTICS: The word ‘statistics’ refers to numerical facts such as the number of events occurring in time or the number of people living in a particular area.

*DATA: Data in it’s simplest form, data could be seen as a collection of facts, such as numbers, words, measurement, observations or even just descriptions of things. It could also be seen as information in raw or unorganized form such as alphabets, symbols, numbers etc.

NAME: ORJI EVAN CHINAZA.

REG NO: 2021/242394.

DEPARTMENT: EDUCATION.

FACULTY: ECONOMICS EDUCATION.

COURSE: INTRODUCTION TO ECONOMICS STATISTICS.

CI. MP. F. CF. RF. CRF

17-18. 17.5. 5. 5. 15.2. 4.03

19-20. 19.5. 6. 11. 18.2. 8.87

21-22 21.5. 8. 19. 24.2. 15.32

23-24. 23.5. 7. 26. 21.2. 20.96

25-26. 25.5. 4. 30. 12.1. 24.19

27-28. 27.5. 3. 33. 9.09. 26.61

33. 124

RF

A) 5÷33 ×100=15.2

B) 6÷33 ×100=18.18

18.2

C) 8÷33×100=24.24

24.2

D) 7÷33×100=21.21

21.2

E) 4÷33×100=12.12

12.1

F) 3÷33×100=9.09

C R F

a) 5÷124×100=4.03. b) 26÷124×100=20.96

c) 11÷124×100=8.87. d) 30÷124×100=24.19

e) 29÷124×100=15.32. f) 33÷124×100=26.61

* SAMPLE: Sampling is a procedure by which one or more members of a population are selected from the population. Since it is usually impractical to test every member of a population, a sample from the population is typically the best approach available.

*POPULATION: Population is defined as an entire group of individual that we are interested in making a statement about or it’s a group about which information is desired.

*CONTINUOUS VARIABLE: A continuous variable is one for which, within the limits the variable ranges, any value is possible. Continuous variable can take any value between a certain set of real numbers.

*DISCRETE VARIABLES: Discrete variable or data are also known as categorical variables. They are variables or data that exist only as a whole numbers and are not divisible.

*STATISTICS: The word ‘statistics’ refers to numerical facts such as the number of events occurring in time or the number of people living in a particular area.

*DATA: Data in it’s simplest form, data could be seen as a collection of facts, such as numbers, words, measurement, observations or even just descriptions of things. It could also be seen as information in raw or unorganized form such as alphabets, symbols, numbers etc.

Nnanyere Success Ihechukwu

2021/241956

Department of Economics

Question 1

Class Midpoint. Freq. CF. RF. Rel.Cum

interval. (x) . Frequency

17- 18. 17.5. 5. 5. 15.2 . 15.1%

19 – 20 19.5. 6. 11. 18.2. 36. 7%

21 – 22. 21.5. 8. 19. 24.2. 57.6%

23 – 24. 23.5. 7. 26. 21.2. 78.8%

25 – 26. 25.5. 4. 30. 12.1 90.9%

27-. 28. 27.5. 3. 33. 9.1. 100%

Question 2

1. Sample

In statistics, sample is defined as a smaller and more manageable representation of a larger group. It is also a subset of a larger population that contains characteristics of that population. A sample is used in statistical testing when the population size is too large for all members or observations to be included in the test

2. Population

In statistics, population is the entire set of items from from which you draw data for statistical study. It can be a group of individuals,a set of items,etc. It makes up the data pool for study.

Generally, population refers to the group of people who occupy at a particular place or area at a specific time. But, in statistics, population refers to data on your study of interest. It can be a group of individuals, objects,events, organizations etc. Population is used to draw conclusions.

3. Continuous Variable

It is a specific kind of quantitative variable used in statistics to describe data that is measurable in some way. A continuous variable deals with measuring a height, weight,or time. It also comes in the form of decimals or fractions. Continuous variable is a variable that takes on any value within a range,and the number of possible values within that range is infinite.

4. Discrete Variable

It is also known as categorical variable.it is a variable that exist only as whole number and are not divisible. A discrete variable can take a finite number of numerical values, categories or codes.

5. Statistics

It is the science that deals with the collection, classification, analysis and interpretation of numerical facts or data, and that by use of mathematical theories of probability,imposes order and regularity on aggregates of more or less disparate elements. It is also the Development and application of methods to the collection, Analysis and interpretation of observed information from planned investigation

6. Data

They are information, especially facts or numbers,collected to be examined and considered and used to help decision making.

It is also classified into two namely

Qualitative data and

Quantitative data

Where qualitative data is descriptive, referring to things that can be observed not measured

While quantitative data refers to anything that can be counted and measured. It refers to numerical data.

Nnanyere Success Ihechukwu

2021/241956

Department of Economics

Question 1

Class Midpoint. Freq. CF. RF. Rel.Cum

interval. (x) . Frequency

17- 18. 17.5. 5. 5. 15.2 . 15.1%

19 – 20 19.5. 6. 11. 18.2. 36. 7%

21 – 22. 21.5. 8. 19. 24.2. 57.6%

23 – 24. 23.5. 7. 26. 21.2. 78.8%

25 – 26. 25.5. 4. 30. 12.1 90.9%

27-. 28. 27.5. 3. 33. 9.1. 100%

Question 2

1. Sample

In statistics, sample is defined as a smaller and more manageable representation of a larger group. It is also a subset of a larger population that contains characteristics of that population. A sample is used in statistical testing when the population size is too large for all members or observations to be included in the test

2. Population

In statistics, population is the entire set of items from from which you draw data for statistical study. It can be a group of individuals,a set of items,etc. It makes up the data pool for study.

Generally, population refers to the group of people who occupy at a particular place or area at a specific time. But, in statistics, population refers to data on your study of interest. It can be a group of individuals, objects,events, organizations etc. Population is used to draw conclusions.

3. Continuous Variable

It is a specific kind of quantitative variable used in statistics to describe data that is measurable in some way. A continuous variable deals with measuring a height, weight,or time. It also comes in the form of decimals or fractions. Continuous variable is a variable that takes on any value within a range,and the number of possible values within that range is infinite.

4. Discrete Variable

It is also known as categorical variable.it is a variable that exist only as whole number and are not divisible. A discrete variable can take a finite number of numerical values, categories or codes.

5. Statistics

It is the science that deals with the collection, classification, analysis and interpretation of numerical facts or data, and that by use of mathematical theories of probability,imposes order and regularity on aggregates of more or less disparate elements. It is also the Development and application of methods to the collection, Analysis and interpretation of observed information from planned investigation

6. Data

They are information, especially facts or numbers,collected to be examined and considered and used to help decision making.

It is also classified into two namely

Qualitative data and

Quantitative data

Where quantitative data refers to numerical data,that is something that can be counted and measured.

While quantitative data is descriptive, referring to things that can be observed not measured.

NAME: OBODOZIE PASCHALINE CHIAMAKA

DEPARTMENT: ECONOMICS EDUCATION

COURSE TITLE: ECO 131

REG NUMBER: 11213141IA

SOLUTION FOR NUMBER ONE

C.I M.P. F. C.F. R.F. RCF

17-18 17.5 5 5 15.2 4.03

19-20 19.5 6 11 18.2 8.87

21-22 21.5 8 19 24.2 15.32

23-24 23.5 7 26 21.2 20.96

25-26 25.5 4 30 12.1 24.19

27-28 27.5 3 33 9.09 26.61

=33 =124

NUMBER TWO

SAMPLE : It can be defined as tte point or population and its taken as a population and its representation.

It is a subset containing the characteristics of a larger population. Samples are used when population sizes are too large for the test to include all possible members or observations.

TYPES TO SAMPLING

SIMPLE RANDOM SAMPLING

It is ideal if every entity in the population is identical.If the researcher don’t care whether their sample subject are all male or all female or a combination of both sexes in some form.

STRATIFIED RANDOM SAMPLING

Thess type of sampling also referred to as proportional random sampling or quota random sampling. It divides the overall population into small groups.

CLUSTER SAMPLING

Cluster sampling also involves dividing the population into subgroups, but each subgroup should have similar characteristics to the whole sample. Instead of sampling individuals from each subgroup, you randomly select entire subgroups.

SYSTEMATIC SAMPLING

Systematic sampling is similar to simple random sampling, but it is usually slightly easier to conduct. Every member of the population is listed with a number, but instead of randomly generating numbers, individuals are chosen at regular intervals.

POPULATION

It can be defined as the entire collection of similar items , individual or event in which one uses one wishes to examine at a particular time.its is the collection of people who have something in common

TYPES OF POPULATION

FINITE POPULATION

The finite population is also known as a countable population in which the population can be counted. In other words, it is defined as the population of all the individuals or objects that are finite

INFINITE POPULATION

The infinite population is also known as an uncountable population in which the counting of units in the population is not possible. Example of an infinite population is the number of germs in the patient’s body is uncountable

EXISTENT POPULATION

The existing population is defined as the population of concrete individuals. In other words, the population whose unit is available in solid form is known as existent population. Examples are books, students etc.

HYPOTHETICAL POPULATION

The population in which whose unit is not available in solid form is known as the hypothetical population. A population consists of sets of observations, objects etc that are all something in common.

CONTINUOUS VARIABLE

A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range of plant ,income of a staff, weight if animals, weight of man, length of a plant .

TYPES OF CONTINUOUS VARIABLE

There are two types of continuous variables namely interval and ratio variables.

Instant variable

Ratio variable

INSTANT VARIABLE

A variable can be defined as the distance or level between each category that is equal and static. For example, what is the average day time temperature in Bangalore during the summer?

RATIO VARIABLE

Ratio variable is another type of continuous variable. This type of variable has only one variation from an interval variable. The only difference is that the ratio between the scores gives information regarding the relationship between the responses.

DISCRETE VARIABLE

It is in the case of a variable that can only be counted and they represent the whole number.It is use to describe a variable that can only take in a finite number of values and it is nt continuous

Examples are: the number of people in a room , whether it is raining or not , the point scored in a football game.

Types of Discrete Variable

There are four Types of Discrete Variable:

Dichotomous variables

Categorical variables (or nominal variables)

Ordinal variables

Nominal variables

DICHOTOMOU VARIABLES

Dichotomous variables are those that can be divided into two groups. The groups can be based on anything, but they are usually either on or off, true or false, positive or negative.

CATEGORICAL VARIABLES

Categorical variables are a type of data that can be divided into groups. They are often used to group data by characteristics such as race, gender, or income level..

ORDINAL VARIABLES

An ordinal variable is a type of data that is assigned a rank or order. Ordinal variables are often used in surveys and questionnaires to collect data about people’s preferences and opinion

NOMINAL VARIABLES

Nominal variables are those that can be classified into non-numeric categories. Examples of nominal variables include gender, religious affiliation, and country of origin. Nominal variables are often used in social science research to measure factors such as beliefs, attitudes, and values.

STATISTICS

Statistics is the study of science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.

Types of Statistics

Basically, there are two types of statistics.

Descriptive Statistics

Inferential Statistics

DESCRIPTIVE STATISTICS

It is the collection of data is described in sumary,it involves observing and describing the behavior of a subject without influencing it in any way .

INFERENTIAL STATISTICS

Inferential statistics can be defined as a field of statistics that uses analytical tools for drawing conclusions about a population by examining random samples. The goal of inferential statistics is to make generalizations about a population. Inferential statistics helps to develop a good understanding of the population data by analyzing the samples obtained from it. It helps in making generalizations about the population by using various analytical tests and tools.

DATA

Data can be defined as a systematic record of a particular quantity. It is the different values of that quantity represented together in a set. it is the unmerical statement of fact in a specific field of enquiry.

TYPES OF DATA.

PRIMARY DATA

Primary data is one which an investigator collects for the first time for a particular purpose. Further, this data is ‘pure’ in the sense that there haven’t been any statistical operations performed on them, plus they are also original.

SECONDARY DATA

Secondary data (also known as second-party data) refers to any dataset collected by any person other than the one using it.

Secondary data sources are extremely useful. They allow researchers and data analysts to build large, high-quality databases that help solve business problems.

NAME: OGBODO KINGSLEY OBINNA

REG NO: 2021/243698

EMAIL: ogbodokingsley26@gmail.com

QUESTION ONE

The following yields (kg) were obtained from plots in a soyabean field given two sprays of pesticides.

22, 20, 19, 25, 22, 17, 28, 20, 22, 23, 17

18, 24, 25, 22, 20, 23, 25, 22, 28, 19, 22

25, 27, 23, 24, 17, 18, 22, 19, 22, 23, 24

Compute the table as follows:

The class interval using sturge rule

Mid-point

Frequency

Cumulative Frequency

Relative Frequency

Relative Cumulative Frequency

ANSWER:

Class interval F Mid-point CF RF RCF

17–18 5 17.5 5 15 15

19–20 6 19.5 11 18 33

21–22 8 21.5 19 24 57

23–24 7 23.5 26 21 78

25–26 4 25.5 30 12 90

27–29 3 27.5 33 9 100

QUESTION TWO

Write a brief note on the following:

Sample

Population

Continuous Variable

Discrete variable

Statistics

Data

ANSWER

A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations. A sample should represent the population as a whole and not reflect any bias toward a specific attribute.

There are several sampling techniques used by researchers and statisticians, each with its own benefits and drawbacks.

Types of sampling

1. Simple Random Sampling

Simple random sampling is ideal if every entity in the population is identical. If the researchers don’t care whether their sample subjects are all male or all female or a combination of both sexes in some form, simple random sampling may be a good selection technique.

2. Stratified Random Sampling

This type of sampling, also referred to as proportional random sampling or quota random sampling, divides the overall population into smaller groups. These are known as strata. People within the strata share similar characteristics.

Conclusion

In conclusion, a sample is a subset of a population that is used to represent the characteristics of the entire population. Sampling is essential in research and data analysis to make inferences about a population based on a smaller group of individuals. There are different types of sampling, such as probability sampling, non-probability sampling, and others, each with its own advantages and disadvantages.

POPULATIONA population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic.

In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped by a common feature can be said to be a population. A sample may also refer to a statistically significant portion of a population, not an entire population.

In statistical inference, a subset of the population (a statistical sample) is chosen to represent the population in a statistical analysis. Moreover, the statistical sample must be unbiased and accurately model the population (every unit of the population has an equal chance of selection). The ratio of the size of this statistical sample to the size of the population is called a sampling fraction. It is then possible to estimate the population parameters using the appropriate sample statistics.

CONTINUOUS VARIABLEA discrete variable is a type of statistical variable that can assume only fixed number of distinct values and lacks an inherent order.

Also known as a categorical variable, because it has separate, invisible categories. However no values can exist in-between two categories, i.e. it does not attain all the values within the limits of the variable. So, the number of permitted values that it can suppose is either finite or countably infinite. Hence if you are able to count the set of items, then the variable is said to be discrete.

A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range.

CONTINUOUS VARIABLE EXAMPLE

Continuous variables would take forever to count. In fact, we would get to forever and never finish counting them. For example, take an age. We can’t count “age”. Because it would literally take forever. For example, it could be 37 years, 9 months, 6 days, 5 hours, 4 seconds, 5 milliseconds, 6 nanoseconds, 77 picoseconds…and so on.

DISCRETE VARIABLE

Examples of Discrete Variable

1.Number of printing mistakes in a book.

2.Number of road accidents in New Delhi.

3.Number of siblings of an individual.

STATISTICS

Statistics Definition: Statistics is a branch that deals with every aspect of the data. Statistical knowledge helps to choose the proper method of collecting the data and employ those samples in the correct analysis process in order to effectively produce the results. In short, statistics is a crucial process which helps to make the decision based on the data.

EXAMPLE

An example of statistical analysis is when we have to determine the number of people in a town who watch TV out of the total population in the town. The small group of people is called the sample here, which is taken from the population.

Types of Statistics

The two main branches of statistics are:

1. Descriptive Statistics

2. Inferential Statistics

Descriptive Statistics – Through graphs or tables, or numerical calculations, descriptive statistics uses the data to provide descriptions of the population.

Inferential Statistics – Based on the data sample taken from the population, inferential statistics makes the predictions and inferences.

Both types of statistics are equally employed in the field of statistical analysis.

CHARACTERISTICS OF STATISTICS

The important characteristics of Statistics are as follows:

1. Statistics are numerically expressed.

2. It has an aggregate of facts

3. Data are collected in systematic order

4. It should be comparable to each other

5. Data are collected for a planned purpose

Importance of Statistics.

The important functions of statistics are:

1. Statistics helps in gathering information about the appropriate quantitative data.

2. It depicts the complex data in graphical form, tabular form and in diagrammatic representation to understand it easily.

3. It provides the exact description and a better understanding.

4. It helps in designing the effective and proper planning of the statistical inquiry in any field.

5. It gives valid inferences with the reliability measures about the population parameters from the sample data.

6. It helps to understand the variability pattern through the quantitative observations.

DATA

Data can be defined as a systematic record of a particular quantity. It is the different values of that quantity represented together in a set. It is a collection of facts and figures to be used for a specific purpose such as a survey or analysis. When arranged in an organized form, can be called information. The source of data ( primary data, secondary data) is also an important factor.

Types of Data

Data may be qualitative or quantitative. Once you know the difference between them, you can know how to use them.

Qualitative Data: They represent some characteristics or attributes. They depict descriptions that may be observed but cannot be computed or calculated. For example, data on attributes such as intelligence, honesty, wisdom, cleanliness, and creativity collected using the students of your class a sample would be classified as qualitative. They are more exploratory than conclusive in nature.

Quantitative Data: These can be measured and not simply observed. They can be numerically represented and calculations can be performed on them. For example, data on the number of students playing different sports from your class gives an estimate of how many of the total students play which sport. This information is numerical and can be classified as quantitative.

Data Collection

Depending on the source, it can classify as primary data or secondary data. Let us take a look at them both.

Primary Data

These are the data that are collected for the first time by an investigator for a specific purpose. Primary data are ‘pure’ in the sense that no statistical operations have been performed on them and they are original. An example of primary data is the Census of Nigeria.

Secondary Data

They are the data that are sourced from someplace that has originally collected it. This means that this kind of data has already been collected by some researchers or investigators in the past and is available either in published or unpublished form. This information is impure as statistical operations may have been performed on them already. An example is an information available on the Government of Nigeria.

QUESTION ONE

1).. Sturge’s rule = 1+3.322logN

Where N = total number of distribution…….= 33

The class interval = 1+3.322log(33)

= 1+3.322(1.5185)

=1+5.0445

K=6.0445~6

Range= highest value_lowest value

28_17 =11

Class interval= Range/k

=11/6 =1.8 = 2.

Class interval = 2

2)…Class midpoint = (lower class limit + upper class limit) / 2

= 15 and 25 respectively

3)…. Frequency = 33

4)…. Cumulative frequency = 44

5)… Relative frequency = 1

6)… Relative cumulative frequency =99.9%

QUESTION TWO

1) SAMPLE : Sample is a part of population that we actually observe . It is the largest collection of entities for which we have an interest at a particular time. Sample is also defined as a smaller and more manageable representation of a larger group. A subset of a larger population that contains characteristics of that population. A sample is used in statistical testing when the population size is too large for all members or observations to be included in the test.

2). POPULATION: Population is the pool of individuals from which a statistical sample is drawn for a study. It is the entire group of individuals that we are interested in making a statement about. A population definition gives a clear statement of those included … Here are some examples below:

_All UNN students

_ All universities in Nigeria

3) . CONTINUOUS VARIABLE : A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. For instance, if a variable over a non-empty range of the real numbers is continuous, then it can take on any value in that range….and considering the height of a student, the height can’t take any values

4). DISCRETE VARIABLE : Discrete variable are Variables that can only take on a finite number of values and are not divisible…All quantitative variables are discrete. Discrete variables are also known as categorical variables.

Categories of discrete variables:

*Nominal variables

*Ordinal variables

*Dummy variables

*Preference variables. And

* Multiple response variables

5) . STATISTICS : Statistics is the practice or science of collecting and analysing numerical data in large quantities, especially for the purpose of inferring proportions in a whole from those in a representative sample. It is also the study of Data Collection, Analysis, Interpretation, Presentation, and organizing in a specific way.

6 ) . DATA : Data are measurements or observations that are collected as a source of information. An example of data is information collected for a research paper. An example of data is an email. There are different types of data in Statistics, that are collected, analysed, interpreted and presented. The data are the individual pieces of factual information recorded, and it is used for the purpose of the analysis process. The two processes of data analysis are interpretation and presentation.

NAME :OMEKE JUDITH EBUBECHUKWU

REG NO:2021/243691

COURSE CODE :Eco 131

COURSE TITLE:INTRODUCTION TO ECONOMIC STATISTICS

1)using sturges rule to get the class interval

Formula:K=1+3.3logN

K=1+3.3log(33)

K=1+5.01

K=6.01

Class interval Frequency M.D C.F R.F R.C.F

17-18 5 17.5 5 15.15 4.03

19-20 6 19.5 11 18.18 8.87

21-22 8 21.5 19 24.24 15.32

23-24 7 23.5 26 21.21 20.92

25-26 4 25.5 30 12.12 24.2

27-28 3 27.5 33 9.1 26.61

Total. 33 124

2)i)Sample:Sample is a part or portion of a population and it is taken from the population as a representative of it .It is a procedure where one or more member of a population are selected from the population.A sample must be a representative of a population in all ramifications.

Haphazard sample and Random sample are the two ways of selecting sample .

ii)Population:This is the entire collection of items or individual which one wishes to examine at a particular time .It can also be said to be the total number of item or individual at a particular place in time .

iii)Continuous variable:This type of variable can assume any value from a range of value e.g measurement of height of plant,income of staff ,bank interest rate,weight of an animal etc.There are measured on continuous scale in meter ,centimeters,mm and it could be 9.4,9.45,9.457.

iv)Discrete variable:This is the case of a variable that can only be counted and represented in a whole number e.g age of a student ,number of seed per carton,number of visitors etc.

v)Statistic:Thus can be defined as a field of study that concern with a layout of experiment,collection,tabulation,summarization and analysis of data .It is also involved in interpretation of result or drawing of inference.

Statistics methods are:

a)Descriptive method :it is a scientific method that involves observing and describing the behavior of the subject without influencing it in any way .

b)parametric inferential method :it’s a mathematical inference method that consider the underline assumption on the shade of the probability distribution of the population.

c)Non parametric inferential method :Its a mathematical inferential method that does not consider the underline assumption on the shade of probability distribution.

vi)Data:Data is a numerical statement of fact in a specific field of enquiry or simply numbers which may result from taking measurements.Data is a raw information in it original form .

Types of data:

a)Primary data:it’s a data that is collected for the first time through personal experience or evidence.It is also classified as raw data or first hand data .

b)Secondary data :is a data that has previously been gathered and an be accessed by researcher.

Name: Oroko Chinagorom Vivian. Department: Social Science Education. Unit: Education Economics. Registration number:11046850ic. Course code:Eco 131. Year:2021/2022. Date: March,2023. (1)Class interval using sturge rule:it function is just to know the number of interval which is 6.01 approximately 6.meaning our class interval mustn’t exceed 6.for example:17-18,19-20,21-22,23-24,25-26,27-28. If yours exceed this, then you are wrong, that what the guideline sturge rule is trying to tell us. Class interval are:17-18,19-20,21-22,23-24,25-26,27–28. (2) Mid-point is:17.5,19.5,21.5,23.5, 25.5,27.5. (3) Frequency :5,6,8,7,4,3.then add the numbers to get the total number of frequency which is 5+6+8+7+4+3=33.(4) Cumulative frequency:5,11,19,26,30,33.then add the numbers to get the total number of cumulative frequency which is 5+11+19+26+30+33=124.(5) Relative frequency:15.2,18.2,24.2,21.2,12.1,9.09. (6)Relative cumulative frequency:4.03,8.87,15.32,20.96,24.19,26.61. To get relative frequency, pick out the numbers from frequency, divide it by total number of frequency and times it by 100, for example 5/33×100=15.2).To get relative cumulative frequency, pick out the numbers from cumulative frequency, divide by total number of cumulative frequency and times by 100, for example (5/124×100=4.03). Question 2, Answers: SAMPLE:In statistics, a sample is anything less than the entire population. If the population is one million doodleflips, then any number of doodleflips less than or equal to 999,999 is a sample. So, 12 would be a sample as would 3,765. Statisticians distinguish samples on many dimensions, the main one being whether a sample is random (all members of the population has the same chance of being included in the sample) or one of convenience (different members of the population have different chances of being included in sample). In general, samples that are closer to the size of the population are more representative than smaller samples are. (For example, a sample of one less than the whole population is almost always very similar to the population.). POPULATION: population is defined as the entire group about which information is desired.it also described as a largest collection of entities for which we have an interest at a particular time;an entire set of objects, observations,or scores that have something in common.to analyse a population a census is taken. CONTINUOUS VARIABLE:a continuous variables is a variable that has infinite number of possible values because it’s change is constant.a person’s age, height, weight, number of siblings, income of continuous data are not restricted to define separate values,but can occupy any value over a continuous range. DISCRETE VARIABLE: it one with numerical value which are”discrete”in that they can only have separated numerical values, typically interfere, which aren’t close to each other when looking at the range, example: survey a group of people and count, for each person,the number of fingers with rings on them.the values are 0,1,2…………..10 and there can’t be intermediate value. STATISTICS: Statistics is a science which deals with collection, tabulation,analysis and interpretation of the data.it is also an item of data or something calculated from a data set.it must not depend on any unknown values,so the mean of a sample minus the mean of a population is not a statistics.(unless you really do know the mean of the population),but the mean and the standard of deviation of the sample are examples of statistics.the topic statistics may be the act of using information to produce references about a population. DATA:data could be seen as a collection of facts,such as numbers,words, measurements, observations or even just descriptions of things.it could also be seen as information in raw or unorganized form(such as alphabets, numbers,or symbols) that refers to,or represent, conditions, ideas or objects.data could be qualitative (i.e.data that deals with numbers).

Name: Oroko Chinagorom Vivian.

Department: Social Science Education.

Unit: Education Economics.

Registration number:11046850ic.

Course code:Eco 131.

Year:2021/2022.

Date: March,2023.

(1)Class interval using sturge rule:it function is just to know the number of interval which is 6.01 approximately 6.meaning our class interval mustn’t exceed 6.for example:17-18,19-20,21-22,23-24,25-26,27-28. If yours exceed this, then you are wrong, that what the guideline sturge rule is trying to tell us.

Class interval are:17-18,19-20,21-22,23-24,25-26,27–28. (2) Mid-point is:17.5,19.5,21.5,23.5,

25.5,27.5. (3) Frequency :5,6,8,7,4,3.then add the numbers to get the total number of frequency which is 5+6+8+7+4+3=33.(4) Cumulative frequency:5,11,19,26,30,33.then add the numbers to get the total number of cumulative frequency which is 5+11+19+26+30+33=124.(5) Relative frequency:15.2,18.2,24.2,21.2,12.1,9.09.

(6)Relative cumulative frequency:4.03,8.87,15.32,20.96,24.19,26.61. To get relative frequency, pick out the numbers from frequency, divide it by total number of frequency and times it by 100, for example 5/33×100=15.2).To get relative cumulative frequency, pick out the numbers from cumulative frequency, divide by total number of cumulative frequency and times by 100, for example (5/124×100=4.03).

Question 2,

Answers: SAMPLE:In statistics, a sample is anything less than the entire population. If the population is one million doodleflips, then any number of doodleflips less than or equal to 999,999 is a sample. So, 12 would be a sample as would 3,765.

Statisticians distinguish samples on many dimensions, the main one being whether a sample is random (all members of the population has the same chance of being included in the sample) or one of convenience (different members of the population have different chances of being included in sample).

In general, samples that are closer to the size of the population are more representative than smaller samples are. (For example, a sample of one less than the whole population is almost always very similar to the population.).

POPULATION: population is defined as the entire group about which information is desired.it also described as a largest collection of entities for which we have an interest at a particular time;an entire set of objects, observations,or scores that have something in common.to analyse a population a census is taken.

CONTINUOUS VARIABLES:a continuous variables is a variable that has infinite number of possible values because it’s change is constant.a person’s age, height, weight, number of siblings, income of continuous data are not restricted to define separate values,but can occupy any value over a continuous range.

DISCRETE VARIABLES: it one with numerical value which are”discrete”in that they can only have separated numerical values, typically interfere, which aren’t close to each other when looking at the range, example: survey a group of people and count, for each person,the number of fingers with rings on them.the values are 0,1,2…………..10 and there can’t be intermediate value.

STATISTICS: Statistics is a science which deals with collection, tabulation,analysis and interpretation of the data.it is also an item of data or something calculated from a data set.it must not depend on any unknown values,so the mean of a sample minus the mean of a population is not a statistics.(unless you really do know the mean of the population),but the mean and the standard of deviation of the sample are examples of statistics.the topic statistics may be the act of using information to produce references about a population.

DATA:data could be seen as a collection of facts,such as numbers,words, measurements, observations or even just descriptions of things.it could also be seen as information in raw or unorganized form(such as alphabets, numbers,or symbols) that refers to,or represent, conditions, ideas or objects.data could be qualitative (i.e.data that deals with numbers).

NAME: Nwobodo kosisochukwu Susan

Course:Eco 131

Reg no:246698

Education Economics

Questions no 2

Sample:

Sample is the part of population that we actually observe it can be seen as the proportion from which information is derived

Population:

Population is the entire group of individuals that we are interested in making a statement about.it is your zone of interest.

Continuous variable/discrete

In mathematics and statistics,a quantitative variable may be continuous or discrete if they are typically obtained by measuring or counting, respectively.

Statistics:

It is the discipline that concerns the collection, organization, analysis, interpretation,and presentation of data.

Data:

Data are individual pieces of factual information recorded and used for the purpose of analysis.they are collected,analyzed and summarized for presentation and interpretation

No 1 answer

C.I. MP. F. CF. RF. RCF

17_18. 17.5. 5. 5. 15.15. 4.0

19_20. 19.5. 6. 11. 18.18. 18.87

21_22. 21.5. 8. 19. 24.24. 15.32

23_24. 23.5. 7. 26. 21.21. 20.96

25_26. 25.5. 4. 30. 12.12. 24.19

27_28. 27.5. 3. 33. 9.09. 26.6

NAME: Nwobodo kosisochukwu Susan

Course:Eco 131

Reg no:246698

Questions no 2

Sample:

Sample is the part of population that we actually observe it can be seen as the proportion from which information is derived

Population:

Population is the entire group of individuals that we are interested in making a statement about.it is your zone of interest.

Continuous variable/discrete

In mathematics and statistics,a quantitative variable may be continuous or discrete if they are typically obtained by measuring or counting, respectively.

Statistics:

It is the discipline that concerns the collection, organization, analysis, interpretation,and presentation of data.

Data:

Data are individual pieces of factual information recorded and used for the purpose of analysis.they are collected,analyzed and summarized for presentation and interpretation

No 1 answer

C.I. MP. F. CF. RF. RCF

17_18. 17.5. 5. 5. 15.15. 4.0

19_20. 19.5. 6. 11. 18.18. 18.87

21_22. 21.5. 8. 19. 24.24. 15.32

23_24. 23.5. 7. 26. 21.21. 20.96

25_26. 25.5. 4. 30. 12.12. 24.19

27_28. 27.5. 3. 33. 9.09. 26.6

1. Using struge’s rule

K=1+33logN

K= 1+33log(33)

K=1+33(1.518)

K=1+5.01

K=6.01

Class interval midpoint F CF RF RCF

17-18 17.5 5 5 15.15 4.03

19-20 19.5 6 11 18.18 8.87

21-22 21.5 8 19 24.24 15.32

23-24 23.5 7 26 21.21 20.97

25-26 25.5 4 30 12.12 24.19

27-28 27.5 3 33 9.09 26.61

Total 33 124

2. Sample:A sample is a smaller set of data that a researcher chooses or selects from a larger population using a pre-defined selection method. These elements are known as sample points, sampling units, or observations.

Population:a population is the pool of individuals or items from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped by a common feature can be said to be a population.

Continuous variable:Continuous variables can assume any numeric value and can be meaningfully split into smaller parts. Consequently, they have valid fractional and decimal values. When you see decimal places for individual values, you’re looking at a continuous variable.

Examples of continuous data include weight, height, length, time, and temperature.

Discrete variable: Discrete variables can only assume specific values that you cannot subdivide. Typically, you count them, and the results are integers. For example, if you work at an animal shelter, you’ll count the number of cats.

For example, you might count 20 cats at the animal shelter. These variables cannot have fractional or decimal values. You can have 20 or 21 cats, but not 20.5! Natural numbers have discrete values.

Statistics:Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.

Data:Data are the facts and figures that are collected, analyzed, and summarized for presentation and interpretation

Name: Agbo Eberechukwu Eunice

Reg no : 2021/241938

Department: Economics

1)Compute the table above using sturges rule/ formular

K=1+3.3log N

K=number of the intervals

N=number of the observations

K=1+3.3 log (48)

K=6.5

Age. Mid (x). F. CF. RF. RCF

17-18. 17.5. 5. 5 15.15 4.03

19-20. 19.5. 6. 11. 18.18. 8.87

21-22. 21.5. 8. 19. 24.24. 15.32

23-24. 23.5. 7. 26. 21.21. 20.97

25-26. 25.5. 4. 30. 12.12. 24.19

27-28. 27.5. 3. 33. 9.09. 26.61

F=33.cf=124

F=33.

CF=6+5=11, 11 +8=19, 19 +7=26, 26+4=30

30 +3=33

RF=f/total observations*100/1

;5/33*100/1=15.15, 6/33 *100/1=18.18,8/33*100/1=24.24 etc

RCF=CF/total observations*100/1

5/124*100/1=4.03,11/124*100/1=8.87,

19/124*100/1 =15.32,26/124*100/1=20.94,30/124*100/1=24.19,33/124*100/1=26.61

2) a) Sample: Sampling is a procedure by which one or more members of a population are selected from the population.It is a smaller set of data that a researcher chooses or selects from a larger population using a pre- defined selection method. These elements are known as sample points, sampling units,or observations. Creating a sample is an efficient method of conducting research. Researching the whole population is often impossible,costly and time consuming. Hence, examining the sample provides insights the researcher CA apply to the entire population.

b) Population: Population is the complete or entire set group of individuals, that we are interested in making a statement about whether that group of people with common characteristic. In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped by a common feature can be said to be a population .

c) Continuous variable: A continuous variable is a specific kind a quantitative variable use in statistics to describe data that is measurable in some way. If ur data deals with measuring height, weight or time, then you have a continuous variable.

d) Discrete variable: This is a type of statistical variable that can assume only fixed number of distinct values and lacks an inherent order. It is also known as categorical variable, because it has separate, invisible categories.However no values can exist in-between two categories.i.e it does not attain all values within the limits of the variable. So the number of the permitted values that it can suppose is either finit or countable. It is said to be discrete if countable.

e) Statistics : These are numerical statements or quantitative data in scenario placed in relation to each other. It involves the study of collecting, analyzing and interpreting numerical facts or numerical data. It is the scientific method of collecting, organizing, Summarizing, presenting and analysing data.

f) Data : Data can be defined as a systematic record of a particular quantity.It is a collection of facts and figures to be used for a specific purpose such as a survey or analysis.

Name:Elochukwu chigozie Victor

Reg no: 2021/241954

Solution

1)K= 1+3.3logN( sturgas rule)

K= 1+3.3log33

K=1+3.3(1.5185)

K=1+5.0

K=6 or no of classes=6

Range = 28-17 =11

Class interval = 11/6 = 1.8 = 2

Class-interval. Midpoint. Freq. Cumulative freq. Relative freq. Relative cumula(freq)

17-18. 17.5. 5. 5. 5/33 *100/1=15.2%. 5/33*100/1=15.2%

19-20. 19.5. 6. 11. 6/33*100/1=18.2%. 11/33*100/1=33.4%

21-22. 21.5. 8. 19. 8/33*100/1=24.2%. 19/33*100/1=57.6%

23-24. 23.5. 7. 26. 7/33*100/1=21.2%. 26/33*100/1=78.8%

25-26. 25.5. 4. 30. 4/33*100/1=12.1%. 30/33*100/1=90.9%

27-28. 27.5. 3. 33. 3/33*100/1=9.1%. 33/33*100/1=100%

33. 100%

.

2a)Sample: it’s defined as a smaller and more manageable representation of a large group

2b)Population: it refers to the people who live in a particular area at a specific time. But in statistics, population refers to data on your study of interest.

2c)Continuous variable: it’s defined as a variable which can take an uncountable set of values or infinite set of values.

2d)Discrete variable: it’s a variable that takes on distinct, countable values.

2e)Statistics: it’s the study of the collection analysis, interpretation, presentation, and organization of data. In other words, it’s a mathematical discipline to collect, summarize data.

2f)Data: they’re individual pieces of factual information recorded and used for the purpose of analysis.

NAME: OSIM, PHILIP BASSEY

REG. NO:2021/241942

DEPARTMENT: ECONOMIC

Class interval: 17-18, 19-20, 21-22, 23-24, 25-26, 27-28.

Mid-point: 17.5, 19.5, 21.5, 23.5, 25.5, 27.5

Frequency: 5, 6, 8, 7, 4, 3=33

Cumulative frequency: 5, 11, 19, 26, 30, 33=124

Relative frequency: 15.15, 18.18, 24.24, 21.21, 12.12, 9.09

Relative cumulative frequency: 4.03, 8.87, 15.32, 20.96, 24.19, 26.61= 99.98

(2) write a brief note on the following

SAMPLEA sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations. A sample should represent the population as a whole and not reflect any bias toward a specific attribute.

There are several sampling techniques used by researchers and statisticians, each with its own benefits and drawbacks.

POPULATIONA population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic.

In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped by a common feature can be said to be a population. A sample may also refer to a statistically significant portion of a population, not an entire population. For this reason, a statistical analysis of a sample must report the approximate standard deviation, or standard error, of its results from the entire population. Only an analysis of an entire population would have no standard error.

CONTINUOUS VARIABLE

A continuous variable is a variable that can take on any value within a range. A continuous variable takes on an infinite number of possible values within a given range.

Because the possible values for a continuous variable are infinite, we measure continuous variables (rather than count), often using a measuring device like a ruler or stopwatch. Continuous variables include all the fractional or decimal values within a range.

Examples of continuous variables include:

I. The time it takes sprinters to run 100 meters

II. The size of real estate lots in a city

III.The weight of baby elephants

IV.The body temperature of patients with the flu

V. The deployment altitude of skydivers

None of these variables are countable. Each of them could take on an infinite number of values within a range.

DISCRETE VARIABLEA discrete variable is a variable that takes on distinct, countable values. In theory, you should always be able to count the values of a discrete variable.

Examples of discrete variables include:All of these variables take a finite number of values that you can count. They are examples of discrete variables.

I. Years of schooling

II. Number of goals made in a soccer match

III. Number of red M&M’s in a candy jar

IV. Votes for a particular politician

V. Number of times a coin lands on heads after ten coin tosses

STATISTICS

Statistics is the art and science of gathering, organizing, analyzing and drawing conclusions from data. And without rudimentary knowledge of how it works, people can’t make informed judgments and evaluations of a wide variety of things encountered in daily life.

Statistics refers to a discipline of applied mathematics that deals with gathering, describing, analyzing, and drawing conclusions from numerical data.

Statistics is about using small sample size groups, and observing their behavior to derive accurate conclusions about larger groups and general occurrences.

DATA

Data are the facts and figures that are collected, analyzed, and summarized for presentation and interpretation.

Data are measurements or observations that are collected as a source of information. There are a variety of different types of data, and different ways to represent data.

The number of people in Australia, the countries where people were born, number of calls received by the emergency services each day, the value of sales of a particular product, or the number of times Australia has won a cricket match, are all examples of data.

NAME: OSIM PHILIP BASSEY

REG. NO: 2021/241942

DEPARTMENT: ECONOMIC

Class interval: 17-18, 19-20, 21-22, 23-24, 25-26, 27-28.

Mid-point: 17.5, 19.5, 21.5, 23.5, 25.5, 27.5.

Frequency: 6, 6, 8, 7, 4, 2 =33

Cumulative frequency: 6, 12, 20, 27, 31, 33= 129

Relative frequency: 18.18, 18.18, 24.24, 21.21, 12.12, 6.06

Relative cumulative frequency: 4.65, 9.30, 15.50, 20.93, 24.03, 25.58= 99.99

(2) write a brief note on the following

SAMPLEA sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations. A sample should represent the population as a whole and not reflect any bias toward a specific attribute.

There are several sampling techniques used by researchers and statisticians, each with its own benefits and drawbacks.

POPULATIONA population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic.

In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study. Thus, any selection of individuals grouped by a common feature can be said to be a population. A sample may also refer to a statistically significant portion of a population, not an entire population. For this reason, a statistical analysis of a sample must report the approximate standard deviation, or standard error, of its results from the entire population. Only an analysis of an entire population would have no standard error.

CONTINUOUS VARIABLE

A continuous variable is a variable that can take on any value within a range. A continuous variable takes on an infinite number of possible values within a given range.

Because the possible values for a continuous variable are infinite, we measure continuous variables (rather than count), often using a measuring device like a ruler or stopwatch. Continuous variables include all the fractional or decimal values within a range.

Examples of continuous variables include:

I. The time it takes sprinters to run 100 meters

II. The size of real estate lots in a city

III.The weight of baby elephants

IV.The body temperature of patients with the flu

V. The deployment altitude of skydivers

None of these variables are countable. Each of them could take on an infinite number of values within a range.

DISCRETE VARIABLEA discrete variable is a variable that takes on distinct, countable values. In theory, you should always be able to count the values of a discrete variable.

All of these variables take a finite number of values that you can count. They are examples of discrete variables.

Examples of discrete variables include:

I. Years of schooling

II. Number of goals made in a soccer match

III. Number of red M&M’s in a candy jar

IV. Votes for a particular politician

V. Number of times a coin lands on heads after ten coin tosses

STATISTICS

Statistics is the art and science of gathering, organizing, analyzing and drawing conclusions from data. And without rudimentary knowledge of how it works, people can’t make informed judgments and evaluations of a wide variety of things encountered in daily life.

Statistics refers to a discipline of applied mathematics that deals with gathering, describing, analyzing, and drawing conclusions from numerical data.

Statistics is about using small sample size groups, and observing their behavior to derive accurate conclusions about larger groups and general occurrences.

DATA

Data are the facts and figures that are collected, analyzed, and summarized for presentation and interpretation.

Data are measurements or observations that are collected as a source of information. There are a variety of different types of data, and different ways to represent data.

The number of people in Australia, the countries where people were born, number of calls received by the emergency services each day, the value of sales of a particular product, or the number of times Australia has won a cricket match, are all examples of data.

NAME: UGWUOGBU CASMIR CHIBUIKE.

REG NO.: 2021/241962.

EMAIL: ugwuogbucasmir@gmail.com.

DEPT.: ECONOMICS.

QUESTION ONE.

The following yields (kg) were obtained from plots in a soyabean field given two sprays of pesticides.

22, 20, 19, 25, 22, 17, 28, 20, 22, 23, 17

18, 24, 25, 22, 20, 23, 25, 22, 28, 19, 22

25, 27, 23, 24, 17, 18, 22, 19, 22, 23, 24

Compute the table as follows:

(i) THE CLASS INTERVAL USING STURGE RULE: k = 1+3.3logn= 1+3.3log33, => Class interval (k) =6.011 ≈6.

Class size= Range/K.

Class size= 28-17/6, = 11/6=1.83, therefore Class size is≈ 2.

(ii) MID-POINT (X): 17.5, 19.5, 21.5, 23.5, 25.5, 27.5.

(iii) FREQUENCY: 5, 6, 8, 7, 4, 3.=33

(iv) CUMULATIVE FREQUENCY: 5, 11, 19, 26, 30, 33.

(v) RELATIVE FREQUENCY: 15.15, 18.18, 24.24, 21.21, 12.12, 9.09.

(vi) RELATIVE CUMULATIVE FREQUENCY: 15.15, 33.33, 57.57, 78.78, 90.90, 100.

QUESTION TWO (2).

Write a brief note on the following:

(A) SAMPLE: Sampling is a statistical procedure that is mostly concerned with the selection of the individual observation; it helps us to make statistical inferences about the population. Sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations.

(B) POPULATION: In statistics, the population is the entire group of individuals that we are mostly interested in making a statement about. Hence, a population is the pool of individuals from which a statistical sample is drawn for a study. It is the entire group about which information is desired. This can also be seen as a largest collection of entities for which we have an interest at a particular time; an entire set of objects, observations, or scores that have something in common. A cencus must be taken in order to analyse a population. And a Census is a head to head count or total count of every entity or object or item in the population.

(C) CONTINUOUS VARIABLES: This is the type of variables in which the limits ranges from any possible value. A variable is said to be continuous if it can assume an infinite number of real values within a given interval. A continuous variable is defined as a variable which can take an uncountable set of values or infinite set of values. A variable holding any value between its maximum value and its minimum value is what we call a continuous variable; otherwise, it is called a discrete variable.

(D) DISCRETE VARIABLE: These types of variables or data exist only as whole numbers, and are not divisible. A discrete variable is a variable that takes on distinct, countable values. It can take on a finite number of numerical values, categories or codes. There are five classes of discrete variables: Norminal, Ordinal, Dummy, Preference, and Multiple response variables. Norminal variables: they’re said to be measured only on Norminal scale. Ordinal variables: they are said to be measured only on ordinal scale. Dummy variables: In regression analysis, a dummy variable is one that takes the values 0 or 1 to indicate the absence or presence of some categorical effect that may be expected to shift the outcome. Preference variable: these are the variables whose values are either in increasing or decreasing order. Multiple response variables: they’re those which can assume more than one value. As opposed to a continuous variable, a discrete variable can assume only a finite number of real values within a given interval.

(D) STATISTICS: This refers to numerical facts such as the number of events occurring in time or the number of people living in a particular area. Statistics is the branch of mathematics for collecting, analysing and interpreting data. Statistics can be used to predict the future, determine the probability that a specific event will happen, or help answer questions about a survey. It is the development and application of methods to the collection analysis and interpretation of observed information or data from planned investigations.

(E) DATA: Data can be seen as the smallest units of factual information that can be used as a basis for calculation, reasoning, or discussion. In its simplest form, data could be seen as a collection of facts, such as numbers, words, measurements, observations or even just descriptions of things. It could also be seen as information in raw or unorganized form such as alphabets, numbers, or symbols that refer to or represent, conditions, ideas, or objects. Data could be qualitative (e.i. data that deal with description) or quantitative (e.i, data that deal with numbers). Data collection is a fundamental aspect of research. Data are required for empirical analysis and other forms of analysis. We have:

*Primary Data: They are data collected originally for the first time. The data are primary for a person who has secured them from the onset by survey. Primary data are collected directly by the user. They are observed and collected from first- hand experience. One of the benefits of primary data is the flexibility that it offers. Primary data gives you the opportunity to collect the exact data you want, not necessarily what is available. That is, primary data allows you to manufacture your own data the way you desire them and how they suit your purpose. However, this freedom comes with a very exorbitant cost. It takes a lot of time, effort and resources to collect meaningful primary information or data.

*Secondary Data: Secondary data: These are data collected on behalf of another and which is processed to a certain extent. Assuming the data were taken from a person or institution that has originally collected them, the person or institution becomes the primary source. It can only be called secondary data if the data were provided by some persons or institutions who has not originally collected them.

Solutions

1. According to sturge rule

The class interval is

K=1+3.3logN

K=1+log3.3×33

K=6.01

2.

1. Sample:

Sample is a part or portion of a population and it is taken from the population as a representation of the population. It is the portion of a population where information is gathered, i.e the part of the population that we usually observe because it is difficult to examine all members of the population due to time, cost and other constraints.

For example the height of students in the faculty of social sciences taken to represent the heights of students in all the departments

2. Population:

Population is the entire collection of items or individuals of which one wishes to examine at a particular time. It is also the largest collection of entities for which we have an interest at a particular time: an entire set of objects, observations, or scores that have something in common.

For example the number of all males between the ages of 25 and 29 in Enugu state.

3. Continuous Variable:

A continuous variable is a variable which can take an uncountable or infinite set of values. Continuous Variables are derived by measurements on a continuous scale, and as a result can assume any value from a range of values. For example measurements of heights of a family which is measured on a centimeter or a millimeter scale and could be 10.4-5mm or 10.4573 mm.

4. Discrete Variable:

A discrete variable also called a categorical variable is a variable which exists only as a whole number and is not divisible. It can take a whole or finite number of numerical values, categories or codes. For example the smage if a child or the number of people in a room.

5. Statistics:

The word ‘statistics’ refers to numerical facts such as the number of events occurring in a particular time. It is the scientific method of collecting, organizing, summarizing, presenting and analysing data. It is also the theory and methods of collecting, organizing, presenting, analysing and interpreting data sets so as to determine their essential characteristics.

It is the development and application of methods to the collection, analysis, and interpretation of observed data from planned investigations.

6. Data:

Data is a numerical statement of facts in a specific field of enquiry or simply numbers which may result from taking measurement. It could also be qualitative i.e. data that deals with description. Data are required for empirical analysis and other forms of analysis. Data are of two types: primary data which are data collected originally for the first time by a person who secures them by survey for his own personal use, and secondary data which are data collected by someone else from a person that originally collected them and which are processed to some extent.

3.

Class Mid F RF CF RCF

interval

17-18 17.5 5 15.15 5 15.15

19-20 19.5 6 18.18 11 3.3

21-22 21.5 8 24.24 19 57.57

23-24 23.5 7 21.21 26 78.78

25-26 25.5 4 12.12 30 90.90

27-28 27.5 3 9.09 33 100

Total 33

Name: Raymond Chiamaka Sylvia

Reg no:2021/243700

Email:sylviachiamaka208@gmail.com

1.The class interval using sturge rule

Sturge formula= K=1+3.322log N

where N is the total number of observations.

K=1+3.222log 33

K=1+3.222(1.5185)

K=1+5.0445

K=6.0445~6

C. interval mid p. Freq. C.F. R.F. R.C.F

17_18. 17.5. 5. 5. 15.15. 4.03

19_20. 19.5. 6. 11. 18.18. 8.87

21_22. 21.5. 8. 19. 24.24 15.32

23_24. .23.5. 7. 26. 21.21. 20.96

25_26. 25.5. 4. 30. 12.12. 24.19

27_28. 27.5. 3. 33. 9.09. 26.61

2.What is a Sample?

A sample is defined as a smaller and more manageable representation of a larger group. A subset of a larger population that contains characteristics of that population. A sample is used in statistical testing when the population size is too large for all members or observations to be included in the test.

The sample is an unbiased subset of the population that best represents the whole dataA discrete variable is a variable that takes on distinct, countable values. In theory, you should always be able to count the values of a discrete variable.

2.What is population?

Population is the group of people from which a statistical sample is taken in statistics. Therefore, a population is any collection of people who have something in common. A statistically substantial subset of a population, rather than the complete population, may be referred to as an example or sample. In addition to this, a statistical analysis of a sample needs to provide an estimate of the standard deviation, or the standard error, of its findings from the total population. Only a whole or complete population analysis would have zero standard error.

3.What is a Discrete Variable?

Examples

Examples of discrete variables include:

Years of schooling

Number of goals made in a soccer match

Number of red M&M’s in a candy jar

Votes for a particular politician

Number of times a coin lands on heads after ten coin tosses

All of these variables take a finite number of values that you can count. They are examples of discrete variables.

4.What is a Continuous Variable?

A continuous variable is a variable that can take on any value within a range. A continuous variable takes on an infinite number of possible values within a given range.

Because the possible values for a continuous variable are infinite, we measure continuous variables (rather than count), often using a measuring device like a ruler or stopwatch. Continuous variables include all the fractional or decimal values within a range.

Examples

Examples of continuous variables include:

The time it takes sprinters to run 100 meters

The size of real estate lots in a city

The weight of baby elephants

The body temperature of patients with the flu

The deployment altitude of skydivers

5.What is Data ?

Data can be defined as a systematic record of a particular quantity. It is the different values of that quantity represented together in a set. It is a collection of facts and figures to be used for a specific purpose such as a survey or analysis. When arranged in an organized form, can be called information. The source of data ( primary data, secondary data) is also an important factor.

6 What is Statistics?

Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data. Statistics is a highly interdisciplinary field; research in statistics finds applicability in virtually all scientific fields and research questions in the various scientific fields motivate the development of new statistical methods and theory. In developing methods and studying the theory that underlies the methods statisticians draw on a variety of mathematical and computational tools.

Class Mid F RF CF RCF

interval

17-18 17.5 5 15.15 5 15.15

19-20 19.5 6 18. 18 11 3.3

21-22 21.5 8 24.24. 19 57.57

23-24 23.5 7 21.21 26. 78.78

25-26 25.5 4 12.12 30 90.90

27-28 27.5 3 9.09 33 100

Total 33

Class Mid F RF CF RCF

interval

17-18 17.5 5 15.15 5 15.15

19-20 19.5 6 18.18 11 3.3

21-22 21.5 8 24.24 19 57.57

23-24 23.5 7 21.21 26 78.78

25-26 25.5 4 12.12 30 90.90

27-28 27.5 3 9.09 33 100

Total 33

2.

1. Sample:

Sample is a part or portion of a population and it is taken from the population as a representation of the population. It is the portion of a population where information is gathered, i.e the part of the population that we usually observe because it is difficult to examine all members of the population due to time, cost and other constraints.

For example the height of students in the faculty of social sciences taken to represent the heights of students in all the departments

2. Population:

Population is the entire collection of items or individuals of which one wishes to examine at a particular time. It is also the largest collection of entities for which we have an interest at a particular time: an entire set of objects, observations, or scores that have something in common.

For example the number of all males between the ages of 25 and 29 in Enugu state.

3. Continuous Variable:

A continuous variable is a variable which can take an uncountable or infinite set of values. Continuous Variables are derived by measurements on a continuous scale, and as a result can assume any value from a range of values. For example measurements of heights of a family which is measured on a centimeter or a millimeter scale and could be 10.4-5mm or 10.4573 mm.

4. Discrete Variable:

A discrete variable also called a categorical variable is a variable which exists only as a whole number and is not divisible. It can take a whole or finite number of numerical values, categories or codes. For example the smage if a child or the number of people in a room.

5. Statistics:

The word ‘statistics’ refers to numerical facts such as the number of events occurring in a particular time. It is the scientific method of collecting, organizing, summarizing, presenting and analysing data. It is also the theory and methods of collecting, organizing, presenting, analysing and interpreting data sets so as to determine their essential characteristics.

It is the development and application of methods to the collection, analysis, and interpretation of observed data from planned investigations.

6. Data:

Data is a numerical statement of facts in a specific field of enquiry or simply numbers which may result from taking measurement. It could also be qualitative i.e. data that deals with description. Data are required for empirical analysis and other forms of analysis. Data are of two types: primary data which are data collected originally for the first time by a person who secures them by survey for his own personal use, and secondary data which are data collected by someone else from a person that originally collected them and which are processed to some extent.

SOLUTIONS:

1. According to sturge rule

The class interval is

K=1+3.3logN

K=1+log3.3×33

K=6.01

NAME: AUGUSTINE OKECHI CHUKWU

MATRIC NO : 2021/244766

DEPARTMENT: ECONOMICS

FACULTY: SOCIAL SCIENCE

COURSE : ECO 131

Solution

K= 1+3.3logN( sturgas rule)

K= 1+3.3log33

K=1+3.3(1.5185)

K=1+5.0

K=6 or no of classes=6

Range = 28-17 =11

Class interval = 11/6 = 1.8 = 2

Class-interval. Midpoint. Freq. Cumulative freq. Relative freq. Relative cumula(freq)

17-18. 17.5. 5. 5. 5/33 *100/1=15.2%. 5/33*100/1=15.2%

19-20. 19.5. 6. 11. 6/33*100/1=18.2%. 11/33*100/1=33.4%

21-22. 21.5. 8. 19. 8/33*100/1=24.2%. 19/33*100/1=57.6%

23-24. 23.5. 7. 26. 7/33*100/1=21.2%. 26/33*100/1=78.8%

25-26. 25.5. 4. 30. 4/33*100/1=12.1%. 30/33*100/1=90.9%

27-28. 27.5. 3. 33. 3/33*100/1=9.1%. 33/33*100/1=100%

33. 100%.

Sample: it’s defined as a smaller and more manageable representation of a large group

Population: it refers to the people who live in a particular area at a specific time. But in statistics, population refers to data on your study of interest.

Continuous variable: it’s defined as a variable which can take an uncountable set of values or infinite set of values.

Discrete variable: it’s a variable that takes on distinct, countable values.

Statistics: it’s the study of the collection analysis, interpretation, presentation, and organization of data. In other words, it’s a mathematical discipline to collect, summarize data.

Data: they’re individual pieces of factual information recorded and used for the purpose of analysis.

Name: Ozuluigbo Hope Ekenedilchukwu

Reg no: 2021/247448

Department: Economics

Email address: hopedili2023@gmail.com

1. According to sturge rule

The class interval is

K=1+3.3logN

K=1+log3.3×33

K=6.01

The table of the data set:

1 2 3 4 5 6

Class midpoint F CF RF RCF

Interval

17-18 17.5 5 5 15.15 15.15

19-20 19.5 6 11 18.18 33.3

21-22 21.5 8 19 24.25 57.57

23-24 23.5 7 26 21.21 78.78

25-26 25.5 4 30 12.12 90.90

27-28. 27.5 3 33 9.09 100

total 33

Answers to question 2:For example the height of students in the faculty of social sciences taken to represent the heights of students in all the departments

1. Sample:

Sample is a part or portion of a population and it is taken from the population as a representation of the population. It is the portion of a population where information is gathered, i.e the part of the population that we usually observe because it is difficult to examine all members of the population due to time, cost and other constraints.

2. Population:

Population is the entire collection of items or individuals of which one wishes to examine at a particular time. It is also the largest collection of entities for which we have an interest at a particular time: an entire set of objects, observations, or scores that have something in common.

For example the number of all males between the ages of 25 and 29 in Enugu state.

3. Continuous Variable:

A continuous variable is a variable which can take an uncountable or infinite set of values. Continuous Variables are derived by measurements on a continuous scale, and as a result can assume any value from a range of values. For example measurements of heights of a family which is measured on a centimeter or a millimeter scale and could be 10.4-5mm or 10.4573 mm.

5. Statistics:The word ‘statistics’ refers to numerical facts such as the number of events occurring in a particular time. It is the scientific method of collecting, organizing, summarizing, presenting and analysing data. It is also the theory and methods of collecting, organizing, presenting, analysing and interpreting data sets so as to determine their essential characteristics.

It is the development and application of methods to the collection, analysis, and interpretation of observed data from planned investigations.

6. Data:

Data is a numerical statement of facts in a specific field of enquiry or simply numbers which may result from taking measurement. It could also be qualitative i.e. data that deals with description. Data are required for empirical analysis and other forms of analysis. Data are of two types: primary data which are data collected originally for the first time by a person who secures them by survey for his own personal use, and secondary data which are data collected by someone else from a person that originally collected them and which are processed to some extent.

Name: Okeke Ruth Ngozi

Reg No: 2021/244119

Course Code: Eco 131

Department: Economics

Faculty: Social Sciences

1. K= 1+ 3.3logN ( Sturges Rule)

K= 1+3.3log33

K= 1+3.3 ( 1.5185)

K= 1+5.0

K= 6. ( Number of Classes = 6)

Range= 28-17 = 11

Class Interval =11/6 = 1.8

Class Interval = 2

Class Interval Mid- Point Frequency

17- 18 17.5 5

19- 20 19.5 6

21-22 21.5 8

23-24 23.5 7

25-26 25.5 4

27-28 27.5 3

Total = 33

Cum.Freq. Relative Freq. Relative Cum. Freq

5 15.2 15.2 %

11 18.2 33.4 %

19 24.2 57.6 %

26 21.2 78.8 %

30 12.1 90.9 %

33 9.1 100 %

Total= 100

(2) 1. Sample: This can be defined as a part or portion of a population and is taken as a representation of it. This process of generalising the results in our sample to that of the entire population is known as statistical inference.

ln other words sampling is a procedure by which on or more members of a population are selected from the population. The objective is to make certain observations about the members of the sample, and then on the basis of these results, to draw valid conclusions about the characteristics of the entire population. A sample statistics is defined as a numerical quantity ( such as the sample mean) Calculated in a sample and the are used to estimate parameters.

2. Population: The population is the entire group of individuals that we are interested in making a statement about. population is define as the entire group about which information is desired. It is also described as a largest collection of entities for which we have an interest at a particular time; an entire set of objects, observations or scores that have something in common to analyse a population census is taken. A census is a total count of every entire object or item in the population. A population parameter is a numerical quantity measuring some aspect of a population of scores.

3. Continuous Variable: This is a specific kind of quantitative variable used in statistics to describe data that is measurable in some way. If your data deals with measuring a height, weight,or time, then you have a continuous variable. Continuous variable can take on an unlimited number of values between the lowest and highest points of measurement. Continuous variable include such things as speed and distance. Continuous data are very desirable in inferential statistics, however they tend to be less useful in data mining and are frequently recorded into a discrete data or sets.

Discrete Variable: Discrete Variable or data are also known as categorical variables. They are variables or data that exist only as whole number s and are not divisible. A discrete Variable can take on a finite number of numerical values, categories or codes.

Discrete Variables can be classified into categories:

i. Nominal variable

ii. Ordinal variables

iii. Dummy Variables from quantitative Variable

iv. Multiple response Variables

v. Preference Variables

Discrete Variables are countable in a finite amount of time. For example, you can count the change in you pocket. You can count the money in your bank account

Statistics: The term statistics is derived from the New Latin Word ” Statisticum Collegium” which means ‘ Council of State ‘ and from an Italian word ‘ Statista which means “statesman or politician”. This refers to the numerical facts such as the number of event occuring in time or number of people living in a particular area. It also the study of ways of collecting, analyzing and interpreting numerical facts or numerical data. Statistics is concerned with the scientific method of collecting, organising, summarizing, presenting and analysing data

According to Horace Secrist ( n. d), statistics may be defined as the aggregate of facts affected to a marked extent by multiplying of causes, numerically expressed, enumerated or estimated according to a reasonable standard of accuracy, collected in a systematic manner, for a predetermined purpose and placed in relation to each other.

According to Upton and Cook 2008, Statistics is a scientific method of collecting, organising, summarizing, analysing and presenting data as well as drawing valid inferences or conclusions and making reasonable decisions on the basis of such analysis.

According to Bowley ( n. d) ‘ Statistics may be rightly called the scheme of averages or numerical statement of facts in any department of enquiry in relation to each other ‘.

According to Croxton and Cowden (n.d) defines ” Statistics as the science of collection, presentation, analysis and interpretation of numerical data. According to this definition there are four basic steps involved which are:

a. collection of data

b. Presentation of data

c. Analysis of data

d. Interpretation of data

6. Data: Data could be seen as a collection of facts, such as numbers, words, measurements, observations or even just description of things used by an individual that collected the raw information. This is seen as information in raw or organised form ( such as alphabets, numbers, or symbols) that refer to, or represent conditions,ideas or objects.

Data could be qualitative I. e data that deals with description or quantitative I. e data that deal with numbers. Data are required for empirical analysis and other forms of analysis.

Azubuike Emmanuel Ayomide 2021/241308

Sturges rule = 1+3.3 Log(n)

=. 1+3.3 Log(33)

=. 1+3.3(1.518)

=. 1+ 5.01= 6.01

1.) Class Interval. Midpoint F. Cf. R.F. R.C.F

17-18. 17.5. 5. 5. 15.15. 15.15

19-20. 19.5. 6. 11. 18.18. 33.3

21-22. 21.5. 8. 19. 24.24. 57.57

23-24. 23.5. 7. 26. 21.21. 78.78

25-26. 25.5. 4. 30. 12.12. 90.90

27-28. 27.5. 3. 33. 9.09. 100

2.) Sample: This is a procedure by which one or more members of a population are selected from the population, so as to make certain observations about the members of the sample and then, on the basis of these results, draw valid conclusions about characteristics of the entire population. We generally have five types; Random, Systematic, Convenience, Cluster and Stratified samples.

b.) Population: This is an entire group or largest collection of entities for which we have an interest at a particular time i.e entire set of observations, objects or scores that have something in common. It is analyzed by census; which is the total count of every item in the population.

c.) Continuous Variable: In this variable any value is possible as long as it’s within the limit of variable ranges; i.e it can take any value between a set of real numbers. It’s generally classified into; Interval-Scale, Continuous Ordinal, Ratio-Scale variables.

d.) Discrete Variable: They are categorical variables that only exist as whole numbers and are not divisible; they are classified into Nominal, Ordinal, Dummy Variables from Quantitative Variables, Preference Variables and Multiple Response Variables.

Class interval F MD CF RF RCF

17-18 5 17.5 5 15.2 0.15

19-20 6 19.5 11 18.2 0.33

21-22 8 21.5 19 24.2 0.56

23-24 7 23.5 26 21.2 0.79

25-26 4 25.5 30 12.1 0.91

27-28 3 27.5 33 9.1 1.0

1)A sample refers to a smaller, manageable version of a larger group. It is a subset containing the characteristics of a larger population. Samples are used in statistical testing when population sizes are too large for the test to include all possible members or observations. A sample should represent the population as a whole and not reflect any bias toward a specific attribute.

2)A population is the complete set group of individuals, whether that group comprises a nation or a group of people with a common characteristic.

In statistics, a population is the pool of individuals from which a statistical sample is drawn for a study.

3)In mathematics and statistics, a quantitative variable may be continuous or discrete if they are typically obtained by measuring or counting, respectively. If it can take on two particular real values such that it can also take on all real values between them (even values that are arbitrarily close together), the variable is continuous in that interval. 4) If it can take on a value such that there is a non-infinitesimal gap on each side of it containing no values that the variable can take on, then it is discrete around that value.In some contexts a variable can be discrete in some ranges of the number line and continuous in others.

5)Statistics (from German: Statistik, orig. “description of a state, a country”) is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as “all people living in a country” or “every atom composing a crystal”. Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.

6)In its simplest form,data could be seen as a collection of facts, such as numbers, words, measurements, observations or even just descriptions of things.

NAME: Ezema miracle chidera

MATRIC NO: 241317

DEPARTMENT: Economics

COURSE: Eco 131

Solution

K= 1+3.3logN( sturgas rule)

K= 1+3.3log33

K=1+3.3(1.5185)

K=1+5.0

K=6 or no of classes=6

Range = 28-17 =11

Class interval = 11/6 = 1.8 = 2

Class-interval. Midpoint. Freq. Cumulative freq. Relative freq. Relative cumula(freq)

17-18. 17.5. 5. 5. 5/33 *100/1=15.2%. 5/33*100/1=15.2%

19-20. 19.5. 6. 11. 6/33*100/1=18.2%. 11/33*100/1=33.4%

21-22. 21.5. 8. 19. 8/33*100/1=24.2%. 19/33*100/1=57.6%

23-24.