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

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.

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.

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

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 : 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.

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.

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:. 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

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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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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

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: 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.

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

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.

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: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.

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.

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.

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

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.

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.

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.

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: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

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: 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.

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

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.

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.

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.

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
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: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:

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.

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.

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:

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: FELIX FAVOUR CHIDUMEBI
Reg No: 2021/241943
Email: felixfavour419@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

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: 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.

Using sturge rule
K= 1+3.3Log(n)

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.

(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.

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.

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.

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

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

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

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.

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.

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

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
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.

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:::
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.

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.