Comparative Statistical Analysis between PRAN Foods Limited and Akij Foods and Beverage Limited on Customer Satisfaction in the Dhaka University Area

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Table of Contents
Chapter 01…………………………………………….3
Introduction…………………………………………..3
1.1 Origin of the Report:...............................................................................................................4
1.2 Purpose of the Study:..............................................................................................................5
1.3 Objectives of the Report: ........................................................................................................6
1.4 Methodology:..........................................................................................................................7
1.5 Limitations of the Report:.......................................................................................................8
Chapter 02........................................................................9
Theoretical Overview .......................................................9
2.1 Statistics:.....................................................................................................................................10
2.2 Statistics: Basic Concepts ...........................................................................................................11
2.3 Types of Statistics:......................................................................................................................16
2.4 Importance of Statistics in Different Fields:...............................................................................18
2.5 Statistical data analysis: ..............................................................................................................21
2.6 Describing data by tables and graphs..........................................................................................21
2.7 Measures of Location:.................................................................................................................26
2.8 Displaying and Exploring Data:..................................................................................................29
Chapter 03......................................................................31
Companys Profile...........................................................31
3.1Company Overview: PRAN Foods Limited................................................................................32
3.2 Company Overview: AKIJ Food and Beverage Limited............................................................34
Chapter 04......................................................................36
Questionnaire Analysis..................................................36
4.1 Questionnaire: ........................................................................................................................37
4.2 Findings on the Questionnaire: ...............................................................................................38
Chapter 05......................................................................54

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Statistical Analysis:Perspective of PRAN Company.....54
5.1 Arithmetic Mean of Sales and Profits:....................................................................................55
5.2 Calculation of Median, Mode and Quartiles of Sales: ............................................................57
5.3 Calculation of Median, mode and quartiles of profits:...........................................................59
5.4 Calculating Mean deviation ....................................................................................................61
5.5 Calculating Variance and Standard Deviation of sales and profit ..........................................62
5.6 Calculating Coefficient of variation of sales and profits.........................................................62
5.7 Software Coefficient of Skewness:.........................................................................................63
5.8 Pearson’s Coefficient of Skewness:.........................................................................................64
5.9 Correlation and Regression Analysis:......................................................................................65
Chapter 06......................................................................69
Statistical Analysis: Perspective of Akij Foods and
Beverage Limited ...........................................................69
6.1 Arithmetic Mean of Sales and Profits.....................................................................................70
6.2 Calculation of Median, Mode and Quartiles of Sales: ............................................................72
6.3 1st
and 3rd
Quartiles .................................................................................................................73
6.4 Calculation of Median, mode and quartiles of profits:...........................................................74
6.5 Mean Deviation and Standard Deviation and Coefficient of Variation of Sales and Profits: .76
6.6 Calculating Coefficient of variation of sales and profits .........................................................78
6.7 Software Coefficient of Skewness:..........................................................................................79
6.8 Pearson’s Coefficient of Skewness: ........................................................................................80
6.9 Correlation and Regression Analysis:......................................................................................81
6.10 Calculation of coefficient of determination..........................................................................82
Chapter 07......................................................................85
Comparative Analysis ....................................................85
Chapter 08......................................................................89
Conclusion .....................................................................89
Reference............................................................................................................................91
Websites:.............................................................................................................................91

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Chapter 01
Introduction

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1.1 Origin of the Report:
Now a day’s education is not just limited to books and classrooms. In today’s world,
education is the tool to understand the real world and apply knowledge for the betterment of
the society as well as business. From education the theoretical knowledge is obtained from
courses of study, which is only the half way of the subject matter. Practical knowledge has no
alternative. The perfect coordination between theory and practice is of paramount importance
in the context of the modern business world in order to resolve the dichotomy between these
two areas. Therefore, for the B.B.A. program we are assigned to prepare a report on
“Comparative Statistical Analysis between PRAN Foods Limited and Akij Foods and
Beverage Limited on Customer Satisfaction in the Dahaka University area” as a part of the
fulfillment of course requirement. The report was prepared under the supervision of
Mohammed Abdullah Al Mamun, Lecturer of Dept. of Finance, University of Dhaka. We are
very much thankful to her for assigning us with such type of practical work that has enhanced
our knowledge and experience.

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1.2 Purpose of the Study:
The purpose of the report is to make Comparative Statistical Analysis between PRAN Foods
Limited and Akij Foods and Beverage Limited on Customer Satisfaction in the Dahaka
University area. The study attempts to find out the both company’s sells and customer
satisfaction ability by studying describe data sets by graphical or numerical methods,
correlations, and many other important issues. The study also aims at showing how the
companies deal with all these issues and observing the real life activities, showing the
appropriate findings.

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1.3 Objectives of the Report:
Primary objective:
 The primary objective of the report is the completion of our course F-107 and submit
the term paper to complete our course.
Specific objectives:
 To gather knowledge about basic concepts of statistics.
 To get practical knowledge by surveying shop stores.
 To learn the environment of present corporate world.
 To enlarge our communication ability.
 To compare about customer satisfaction ability in different organizations.
 To know how to collect information.
 To gain an overview over PRAN Foods Limited.
 To gain an overview over Akij Foods and Beverage Limited.
 To provide with findings on the basis of the study.

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1.4 Methodology:
For smooth and accurate study everyone needs to follow some rules & regulations. The study
concerned information was collected from two sources:
Primary Sources:
Information was collected from primary sources in these ways:
1. By self survey of the respective shop store.
2. By talking face to face with shopkeepers and sales manager.
Secondary Sources:
Data were collected from secondary sources by the following ways:
1. Different trustworthy and reliable websites worked as our prime secondary sources of
data.
2. Books, texts and publications.

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1.5 Limitations of the Report:
While preparing this report, we have faced some problems. The main problem was to co-
ordination all the group members. Moreover, during data collection we faced several
problems.
Budgeted time limitation:
It was one of the main constraints that hindered to cover all aspects of the study.
Validity and Reliability:
Validity and reliability of the obtained information depends on the responses from the
respondents.
Inappropriateness and Scarcity of Evidence:
Actually, Inappropriateness and Scarcity of evidence lacked our proper representation of
Comparative Statistical Analysis of the study.
In spite of many limitations, we have become successful in preparing the report with
sufficient adornment of flawlessness.

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Chapter 02
Theoretical Overview

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2.1 Statistics:
Statistics is a very broad subject, with applications in a vast number of different fields. In
generally one can say that statistics is the methodology for collecting, analyzing, interpreting
and drawing conclusions from information. Putting it in other words, statistics is the
methodology which scientists and mathematicians have developed for interpreting and
drawing conclusions from collected data. Everything that deals even remotely with the
collection, processing, interpretation and presentation of data belongs to the domain of
statistics, and so does the detailed planning of that precedes all these activities.
Statistics consists of a body of methods for collecting and analyzing data. Statistics Defined:
•Singular sense: Statistics in singular sense means a subject or scientific discipline.
•Plural sense: Statistics in plural sense means statistical data. This data must carry answers
to questions like what? Where? When?
So, Statistics can be defined as a body of methods for obtaining and analyzing numerical data
in order to make better decisions in an uncertain world.
From above, it should be clear that statistics is much more than just the tabulation of numbers
and the graphical presentation of these tabulated numbers. Statistics is the science of gaining
information from numerical and categorical or qualitative data. Statistical methods can be
used to find answers to the questions like:
• What kind and how much data need to be collected?
• How should we organize and summarize the data?
• How can we analyse the data and draw conclusions from it?
• How can we assess the strength of the conclusions and evaluate their uncertainty?
That is, statistics provides methods for
1. Design: Planning and carrying out research studies.
2. Description: Summarizing and exploring data.

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3. Inference: Making predictions and generalizing about phenomena represented by
the data.
Furthermore, statistics is the science of dealing with uncertain phenomenon and events.
Statistics in practice is applied successfully to study the eﬀectiveness of medical treatments,
the reaction of consumers to television advertising, the attitudes of young people toward sex
and marriage, and much more. It’s safe to say that nowadays statistics is used in every ﬁeld of
science.
Examples:
If we consider the following problems, we will find the nature of statistics.
–Agricultural problem: Is new grain seed or fertilizer more productive?
–Medical problem: What is the right amount of dosage of drug to treatment?
–Political science: How accurate are the gallops and opinion polls?
–Economics: What will be the unemployment rate next year?
–Technical problem: How to improve quality of product?
2.2 Statistics: Basic Concepts
In order to perform a statistical analysis, need to know some basic concepts of statistics.
From this point of view we are going to discuss about Sample and population,statistic and
parameter, variables , level of measurement and so on.
Sample and Population
Population and sample are two basic concepts of statistics. Population can be characterized as
the set of individual persons or objects in which an investigator is primarily interested during
his or her research problem. Sometimes wanted measurements for all individuals in the
population are obtained, but often only a set of individuals of that population are observed;
such a set of individuals constitutes a sample. This gives us the following definitions of
population and sample.

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Population:
Population is the collection of all individuals or items under consideration in a statistical
study. The term often refers to a group of people, as in the following examples:
 All registered voters in a county;
 All members of the International Labour Union;
 All Americans who played golf at least once in the past year;
Sample:
Sample is that part of the population from which information is collected. The following
examples will help us to understand the concept of sample:
 All electronics products produced last Tuesday by the Walton Company Limited;
 All daily maximum temperatures in July for major U.S. cities;
Pictorial Presentation:
The following picture depicts the nature of population and sample:
Fig 2.1 : Population and Sample
Statistic and Parameter:
Usually the features of the population under investigation can be summarized by numerical
parameters. Hence the research problem usually becomes as on investigation of the values of

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parameters. These population parameters are unknown and sample statistics are used to make
inference about them. That is, a statistic describes a characteristic of the sample which can
then be used to make inference about unknown parameters.
Parameter: A parameter is an unknown numerical summary of the population.
Statistic: A statistic is a known numerical summary of the sample which can be used to make
inference about parameters.
Example : Parameters and Statistics
If we consider the research problem of finding out what percentage of 18-30 year-olds are
going to movies at least once a month, we will find the parameter and statistic in the
following way:
• Parameter: The proportion p of 18-30 year-olds going to movies at least once a month.
• Statistic: The proportion ˆp of 18-30 year-olds going to movies at least once a month
calculated from the sample of 18-30 year-olds.
Data Types:Variables
Developing a good understanding of the kinds of data and data measurement is necessary
because the kind of data one is analyzing essentially dictates the type of statistical analysis.
A characteristic that varies from one person or thing to another is called a variable, i.e, a
variable is any characteristic that varies from one individual member of the population to
another. Examples of variables for humans are height, weight, number of siblings, sex,
marital status, and eye color.
Types of Variables:
Variables can be classified as either numerical (quantitative) or categorical (qualitative) and
is presented below:

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Fig 2.2 : Types of variables
i)Qualitative/Categorical Variables:
Categorical data is data that can be sorted according to a category and each value is from a
set of non-overlapping values. Examples of categorical data would include eye color (green,
brown, blue, etc.) and managerial level (supervisor, mid-level, executive).
Categorical variables are typically measured on a nominal scale.
i)Quantitave/Numerical data:
Quantitave/Numerical data is data that is on a numerical scale of some sort. Quantitative
variables can be classified as either discrete or continuous.
 Discrete data is typically when there’s a limited number of response values and
not an infinite number of response values. For example responses on a five-point
scale can be any of the five values but cannot be 3.1 or 3.6 or 4.2, etc.
 Continuous data is when the response can take on any value within the range of
variable. For example responses to the question of “what’s your GPA on a 4.0
scale?” could take on not just 1, 2, 3, or 4 but also 3.17, 3.83, 2.94, etc.
Numerical data is measured on an ordinal, interval, or ratio scale.
Data Type:Levels of Measurement/Scales
Besides being classified as either qualitative or quantitative, variables can be described
according to the scale on which they are defined. The scale of the variable gives certain
structure to the variable and also defines the meaning of the variable.
Variables
Quantitative
(Numerical)
Discrete Continuous
Qualitative
(Categorical)

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Scales for Qualitative Variables:
The categories into which a qualitative variable falls may or may not have a natural ordering.
For example, occupational categories have no natural ordering. If the categories of a
qualitative variable are unordered, then the qualitative variable is said to be defined on a
nominal scale, the word nominal referring to the fact that the categories are merely names. If
the categories can be put in order, the scale is called an ordinal scale. Based on what scale a
qualitative variable is defined, the variable can be called as a nominal variable or an ordinal
variable.
Examples of ordinal variables are education (classified e.g. as low, high) and “strength of
opinion” on some proposal (classified according to whether the individual favors the
proposal, is indifferent towards it, or opposites it), and position at the end of race (first,
second, etc.).
Scales for Quantitative Variables:
Quantitative variables, whether discrete or continuos, are defined either on an interval scale
or on a ratio scale.
If one can compare the differences between measurements of the variable meaningfully, but
not the ratio of the measurements, then the quantitative variable is defined on interval scale.
If, on the other hand, one can compare both the differences between measurements of the
variable and the ratio of the measurements meaningfully, then the quantitative variable is
defined on ratio scale. In order to the ratio of the measurements being meaningful, the
variable must have natural meaningful absolute zero point, i.e, a ratio scale is an interval
scale with a meaningful absolute zero point.
For example, temperature measured on the Certigrade system is a interval variable andthe
height of person is a ratio variable.

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Fig 2.3 : Pictorial Presentation of Scales for Quntitative Variables.
2.3 Types of Statistics:
There are two broad categories of statistics. They are descriptive and inferential statistics and
are depicted in the following chart:
Fig 2.4 : Types of Statistics.
i)Descriptive Statistics:
In a simple sense, the branch of statistics devoted to the summarization and description of
data is called descriptive statistics. Descriptive statistics consist of methods for organizing
and summarizing information. Descriptive statistics includes the construction of graphs,
charts, and tables, and the calculation of various descriptive measures such as averages,
measures of variation, and percentiles.
Statistics
Descriptive Inferential
Estimation
Modeling
Relationships
Hyposthesis
Testing

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Descriptive statistics summarize population data numerically or graphically by deriving
 Statistics pertaining to central tendency such as the mean, median, or mode;
 Statistics pertaining to dispersion around the central tendency such as the range or
standard deviation;
 Statistics or graphs depicting the shape of a distribution;
ii) Inferential Statistics:
The branch of statistics concerned with using sample data to make an inference about a
population of data is called inferential statistics. Inferential statistics consist of methods for
drawing and measuring the reliability of conclusions about population based on information
obtained from a sample of the population. Inferential statistics includes methods like point
estimation, interval estimation and hypothesis testing which are all based on probability theory.
Inferential statistics allow one to infer population parameters based upon sample statistics and
to model relationships within the data. The categories of inferential statistics are
 Estimation is the group of statistics which allow for the estimation about population
values based upon sample data. The two types of statistics in this category are
population parameter estimates and confidence intervals.
 Modeling allows us to develop mathematical equations which describe the
interrelationships between two or more variables.
 Hypothesis testing allows us to test for whether a particular hypothesis we’ve
developed is supported by a systematic analysis of the data.
Example: Descriptive and Inferential Statistics
Consider event of tossing dice. The dice is rolled 100 times and the results are forming the
sample data. Descriptive statistics is used to grouping the sample data to the following table:
Outcome of the roll Frequencies
1 10
2 20
3 18
4 16
5 11

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Inferential statistics can now be used to verify whether the dice is a fair or not.
Descriptive and inferential statistics are interrelated. It is almost always necessary to use
methods of descriptive statistics to organize and summarize the information obtained from a
sample before methods of inferential statistics can be used to make more thorough analysis of
the subject under investigation. Furthermore, the preliminary descriptive analysis of a sample
often reveals features that lead to the choice of the appropriate inferential method to be later
used.
Sometimes it is possible to collect the data from the whole population. In that case it is
possible to perform a descriptive study on the population as well as usually on the sample.
Only when an inference is made about the population based on information obtained from the
sample does the study become inferential.
2.4 Importance of Statistics in Different Fields:
Statistics plays a vital role in every fields of human activity. Statistics has important role in
determining the existing position of per capita income, unemployment, population growth
rate, housing, schooling medical facilities etc. In a country. Now statistics holds a central
position in almost every field like Industry, Commerce, Trade, Physics, Chemistry,
Economics, Mathematics, Biology, Botany, Psychology, Astronomy etc. So, application of
statistics is very wide. Now we discuss some important fields in which statistics is commonly
applied.
2.4.1 Business:
Statistics play an important role in business. A successful businessman must be very quick
and accurate in decision making. He knows that what his customers wants, he should
therefore, know what to produce and sell and in what quantities. Statistics helps businessman
to plan production according to the taste of the costumers, the quality of the products can also
be checked more efficiently by using statistical methods. So, all the activities of the
businessman based on statistical information. He can make correct decision about the
location of business, marketing of the products, financial resources etc.

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2.4.2 In Economics:
Statistics play an important role in economics. Economics largely depends upon statistics.
National income accounts are multipurpose indicators for the economists and administrators.
Statistical methods are used for preparation of these accounts. In economics research
statistical methods are used for collecting and analysis the data and testing hypothesis. The
relationship between supply and demands is studies by statistical methods, the imports and
exports, the inflation rate, the per capita income are the problems which require good
knowledge of statistics.
2.4.3 In Mathematics:
Statistical plays a central role in almost all natural and social sciences. The methods of
natural sciences are most reliable but conclusions draw from them are only probable, because
they are based on incomplete evidence. Statistical helps in describing these measurements
more precisely. Statistics is branch of applied mathematics. The large number of statistical
methods like probability averages, dispersions, estimation etc… is used in mathematics and
different techniques of pure mathematics like integration, differentiation and algebra are used
in statistics.
2.4.4 In Banking:
Statistics play an important role in banking. The banks make use of statistics for a number of
purposes. The banks work on the principle that all the people who deposit their money with
the banks do not withdraw it at the same time. The bank earns profits out of these deposits by
lending to others on interest. The bankers use statistical approaches based on probability to
estimate the numbers of depositors and their claims for a certain day.
2.4.5 In State Management (Administration):
Statistics is essential for a country. Different policies of the government are based on
statistics. Statistical data are now widely used in taking all administrative decisions. Suppose
if the government wants to revise the pay scales of employees in view of an increase in the
living cost, statistical methods will be used to determine the rise in the cost of living.
Preparation of federal and provincial government budgets mainly depends upon statistics
because it helps in estimating the expected expenditures and revenue from different sources.
So statistics are the eyes of administration of the state.

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2.4.6 In Accounting and Auditing:
Accounting is impossible without exactness. But for decision making purpose, so much
precision is not essential the decision may be taken on the basis of approximation, know as
statistics. The correction of the values of current asserts is made on the basis of the
purchasing power of money or the current value of it.
In auditing sampling techniques are commonly used. An auditor determines the sample size
of the book to be audited on the basis of error.
2.4.7 In Natural and Social Sciences:
Statistics plays a vital role in almost all the natural and social sciences. Statistical methods are
commonly used for analyzing the experiments results, testing their significance in Biology,
Physics, Chemistry, Mathematics, Meteorology, Research chambers of commerce, Sociology,
Business, Public Administration, Communication and Information Technology etc.
2.4.8 In Astronomy:
Astronomy is one of the oldest branches of statistical study, it deals with the measurement of
distance, sizes, masses and densities of heavenly bodies by means of observations. During
these measurements errors are unavoidable so most probable measurements are founded by
using statistical methods.
Example: This distance of moon from the earth is measured. Since old days the astronomers
have been statistical methods like method of least squares for finding the movements of stars.
So, in fine, in the light of the above mentioned points it can be easily assumed the importance
of statistics in our everyday life.

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2.5 Statistical data analysis:
The goal of statistics is to gain understanding from data. Any data analysis should contain
following steps:
Fig 2.5 : Process of statistical data analysis..
2.6 Describing data by tables and graphs
Techniques used to describe a set of data are called Describing data. To describe data by
tables and graphs we generally use the following described techniques.
2.6.1 Frequency Table:
The first procedure to organize and summarize a set of data is a frequency table. The number
of observations that fall into particular class (or category) of the qualitative variable is called
Begin
Formulate the research problem
Define population and sample
Collect the data
Do descriptive data analysis
Use appropriate statistical methods
to solve the research problem
Report the results
End

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the frequency (or count) of that class. A table listing all classes and their frequencies is called
a frequency distribution or frequency table.
2.6.2 Relative Frequency:
In addition of the frequencies, we are often interested in the percentage of a class. We find
the percentage by dividing the frequency of the class bythe total number of observations and
multiplying the result by 100. The percentage of the class, expressed as a decimal, is usually
referred to as the relative frequency of the class.
A table listing all classes and their relative frequencies is called a relative frequency
distribution. The relative frequencies provide the most relevant information as to the pattern
of the data. One should also state the sample size, which serves as an indicator of the
creditability of the relative frequencies. Relative frequencies sum to 1 (100%).
Example: Let the blood types of 40 persons are as follows
O O A B A O A A A O B O B O O A O O A A A A AB A B A A O O A O O A A A O A O
O AB
Summarizing data in a frequency table:
Blood Frequency Relative Frequency
O 16 .40
A 18 .45
B 4 .10
AB 2 .05
Total 40 1
2.6.3 Cumulative frequency:
A cumulative frequency (cumulative relative frequency) is obtained by summing the
frequencies (relative frequencies) of all classes up to the specific class. In a case of qualitative

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variables, cumulative frequencies make sense only for ordinal variables, not for nominal
variables.
Summarizing data in a cumulative frequency table:
Blood Frequency Cumulative Frequency
O 16 16
A 18 34
B 4 38
AB 2 2
Total 40 40
Data Presentation:
The qualitative data are presented graphically either as a pie chart or as a horizontal or
vertical bar graph. Nominal data is best displayed by pie chart and ordinal data by horizontal
or vertical bar graph.
2.6.4 Data Presentation: Pie Chart
A pie chart is a disk divided into pie-shaped pieces proportional to the relative frequencies of
the classes. To obtain angle for any class, we multiply the relative frequencies by 360
degrees, which corresponds to the complete circle.
Pictorial Presentation: Pie Chart

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Fig 2.6 : Pie Chart.
2.6.5 Data Presentation: Bar Chart
A horizontal bar graph displays the classes on the horizontal axis and the frequencies (or
relative frequencies) of the classes on the vertical axis. The frequency (or relative frequency)
of each class is represented by vertical bar whose height is equal to the frequency (or relative
frequency) of the class. In a bar graph, its bars do not touch each other. At vertical bar graph,
the classes are displayed on the vertical axis and the frequencies of the classes on the
horizontal axis.

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Fig 2.7 : Bar Chart.
2.6.6 Histogram:
Another common graphical presentation of quantitative data is a histogram.
 In histogram,the classes are placed on the horizontal axis.
 A rectangle is drawn above each class interval with its height corresponding to
the interval’s frequency, relative frequency, or percent frequency
 Unlike a bar graph, a histogram has no natural separation between rectangles of
adjacent classes
Fig 2.8 : Histogram.

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2.6.7 Frequency Polygon:
Frequency polygons are a graphical device for understanding the shapes of distributions.
They serve the same purpose as histograms, but are especially helpful for comparing sets of
data. Frequency polygons are also a good choice for displaying cumulative frequency
distributions.
Fig 2.9: Frequency Polygon.
2.7 Measures of Location:
Descriptive measures that indicate where the center or the most typical value of the variable
lies in collected set of measurements are called measures of center. The median and the mean
apply only to quantitative data, whereas the mode can be used with either quantitative or
qualitative data.
2.7.1 Mean
The mean of a data set is the average of all the data values.As we said, the sample mean is
the point estimator of the population mean m.
Properties of the Arithmetic Mean:
a. Every set of interval-level and ratio-level data has a mean.
b. All the values are included in computing the mean.
c. A set of data has a unique mean.
d. The mean is affected by unusually large or small data values.

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e. The arithmetic mean is the only measure of central tendency where the
sum of the deviations of each value from the mean is zero.
2.7.2 Geometric Mean:
The geometric mean is a type of mean or average, which indicates the central tendency or
typical value of a set of numbers by using the product of their values (as opposed to the
arithmetic mean which uses their sum). The geometric mean is defined as the nth root of the
product of n numbers.
For instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their
product; that is sqrt{2cdot 8}=4. As another example, the geometric mean of the three
numbers 4, 1, and 1/32 is the cube root of their product (1/8), which is 1/2; that is
sqrt[3]{4cdot 1cdot 1/32}=1/2.
Formula:
GM = ((X1)(X2)(X3)........(XN))1/N
where
X = Individual growth factor
N = Sample size (Number of observations)
2.7.3 Median:
The median of a data set is the value in the middle when the data items are arranged in
ascending order or decending order.
 Whenever a data set has extreme values, the median is the preferred measure of
central location
 The median is the measure of location most often reported for annual income and
property value data
 A few extremely large incomes or property values can inflate the mean
2
1
PointMedian


n
Here, n=number of observations
Median:Grouped Data
Formula: 𝑀𝑒𝑑𝑖𝑎𝑛 = 𝐿 +
𝑓
2
−𝑓 𝑚 −1
𝑓 𝑚
× 𝑖 𝑚

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Where,
𝑓 = Number of frequency
𝑓𝑚−1=Frequency of pre-median class
𝑓𝑚 = Frequency of median class
im=Class interval
L = The lower class boundary of median class
2.7.4 Mode:
The mode of a data set is the value that occurs with greatest frequency.
 The greatest frequency can occur at two or more different values
 If the data have exactly two modes, the data are bimodal
 If the data have more than two modes, the data are multimodal
Mode:Grouped Data
𝑀𝑜𝑑𝑒 = 𝐿 + [
𝑓 𝑚 −𝑓 𝑚 −1
𝑓 𝑚 −𝑓 𝑚 −1 +(𝑓 𝑚 −𝑓 𝑚 +1)
]*im
Where,
L = The lower class boundary of modal class
fm = The Frequency of the modal class
𝑓𝑚−1 = The previous frequency of the modal class
𝑓𝑚+1 = The next frequency of the modal class
im=Class interval
2.7.5 Variance:
The degree to which numerical data tend to spread about an average value is called the
dispersion or variation of the data. It is often desirable to consider measures of variability
(dispersion), as well as measures of location. The formula to measure variance is ---
𝑆2
=
(𝑋 − 𝑋)2
𝑛 − 1

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2.7.6 Standard Deviation:
The standard deviation of a data set is the positive square root of the varianceIt is measured in
the same units as the data, making it more easily interpreted than the variance.Most
commonly used measure of variation in business application. The equation to find standard
deviation.
𝑆 =
(𝑋 − 𝑋)2
𝑛 − 1
2.7.7 Coefficient of Variation:
 Measure of relative dispersion
 Always have a %
 CV is the standard deviation expressed as percent of the mean
 Used to compare two or more groups
 Weakness: CV is undefined if the mean is zero or if data are negative.
 Thus, CV is used only for variables whose values are X>=0
Formula: 𝐶𝑉 𝑋 =
𝑆 𝑋
𝑋
2.8 Displaying and Exploring Data:
Median is the value of the data set arranged either in ascending or descending order. By
extending the idea of Median we can think of values which divides the data set into four or
hundred equal parts. Hence we can get
 Quartiles: The values that divides the data set into four equal parts are called
quartiles
 Percentiles: A percentile provides information about how the data are spread over
the interval from the smallest value to the largest value.
The pth percentile of a data set is a value such that at least p percent of the items take on this
value or less and at least (100 - p) percent of the items take on this value or more
2.8.1 Coefficient of Skewness:
The coefficient of skewness is a measure of the symmetry of a distribution. There are two
formulae for determining the coefficient of skewness:

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The formula developed by Karl Pearson is
𝑆𝐾 =
3( 𝑋 − 𝑀𝑒)
𝑠
Here, 𝑋 = 𝑀𝑒𝑎𝑛
𝑀𝑒 = 𝑀𝑒𝑑𝑖𝑎𝑛
𝑠 = 𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛
The software formula for determining coefficient of skewness is
𝑠𝑘 =
𝑛
(𝑛 − 1) × (𝑛 − 2)
(
𝑌 − 𝑌
𝑆
)3

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Chapter 03
Companys Profile

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3.1Company Overview: PRAN Foods Limited
PRAN Foods Limited is the Bangladeshi food-products corporation based in Dhaka,
Bangladesh., founded in 1981. It is the largest food and nutrition company of Bangladesh, It
is the largest exporter of processed agro products with the compliance of HALAL & HACCP
to more than 100 countries. The Company's principal activity is the manufacture and sale of
Juice, Snacks, Soft Drink, cakes and dairy products.
3.1.1 Brief History:
PRAN stands for Program for Rural Advancement Nationally. “PRAN” is currently the most
well known household name among the millions of people in Bangladesh and abroad also.
Since its inception in 1980, PRAN Group has grown up in stature and became the largest fruit
and vegetable processor in Bangladesh. It also has the distinction of achieving prestigious
certificate like ISO 9001:2000. PRAN, the largest exporter of processed food from
Bangladesh, had a vision of creating a huge demand globally of those agro based products
produced by native farmers. The key was to process the agro products and increase shelf-life
thereby. Starting successful journey to export market in 1996, PRAN currently exports to
over 106 countries.
Highlights of the Company:
1. Type of Company : Private
2. Type of industry : Food Processing
3. Founded : 17 March 1981
4. Founders : Maj Gen (Retd.) Amjad Khan
Chowdhury
5. Headquarters : PRAN-RFL Center, 105, Progoti
Sarani, Middle Badda, Dhaka 1212,
Bangladesh.
6. Area served : South Asia, Africa, North America, Europe,
Middle East
7. Key People : Maj Gen (Retd.) Amjad Khan Chowdhury
(CEO)

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8. Employees : 58,000
9. website : http://www.pranfoods.net
3.1.2 Mission of the Company:
The mission of the PRAN Foods Limited is to “Poverty and hunger are curses.”
3.1.3 Vision of the Company:
The vision of the PRAN Foods Limited is “Improving Livelihood.”
3.1.4 Products of the Company:
PRAN takes a comprehensive approach to all kinds of agro processed food products,
considering all of the ways their lives can be enriched through ensuring hygienic and quality
food products. This organization have many types of products:
 Juice
 Drinks
 Mineral Water
 Bakery
 Carbonated Soft Drink
 Snacks
 Culinary
 Confectionary
 Biscuits
 Dairy.

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3.2 Company Overview: AKIJ Food and Beverage Limited
Akij is a one of the largest Bangladeshi industrial conglomerates. The industries under this
conglomerate include Textiles, Tobacco, Cement, Ceramics, Printing and Packaging,
Pharmaceuticals, Consumer products etc. Akij also provides services in Healthcare,
Information and Communication Technology.
3.2.1 Brief History:
The company Akij Food & Beverage Limited (AFBL), a unit of Akij group, came into
business in year 2006. It has come with the best food & beverage in Bangladesh. It
incorporates manufacturing of variety sort of snack and beverage products and selling them
to the local market as well as some of the international market.
Highlights of the Company:
1. Type of Company : Private
2. Type of industry : Food Processing
3. Founded : 2006
4. Founders : Sheikh Akij Uddin
5. Headquarters : Krishnapura, Dhamrai , Dhaka .
6. Employees : 27,000
7. website : http://www.akijfood.com
3.2.2 Mission of the Company:
The mission of the Akij Food & Beverage Limited is to “to earn a respected position in food
and beverage sector”
3.2.3 Vision of the Company:
The vision of the Akij Food & Beverage Limited is. Discovering and understanding the
desires and needs of community, whiles working in harmony with our consumers, employees
and business partner. ”

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3.2.4 Products of the Company:
Akij Food & Beverage Limited has categorized its products in products line and each line
incorporates various brands to captive the market. This organization’s products are
 Juice
 Drinks
 Mineral Water
 Carbonated Soft Drink
 Snacks
 Dairy.

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Chapter 04
Questionnaire Analysis

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4.1 Questionnaire:
1. How many types of products do you sell in your shop?
a) 1 to 5 b) 5 to 10 c) 10 to 15 d) above 15
2. Who are the key customers of your shop?
a) varsity students b) teachers c) school children d) common people
3. In which time period most of your customers gather in your shop for buying food?
a) at morning b) at noon c) in the evening d) at night
4. When buying food, which brands you give more preference?
a) PRAN Foods and Beverage b) Akij Foods c) Haque Foods d) others
5. In comparison, dealing with which brand you get transportation facility in retailing
purpose?
a) PRAN Foods and Beverage b) Akij Foods
6. Which of the brands in comparison get extra preferences by the customers?
a) PRAN Foods and Beverages b) Akij Foods
7. Do customers directly urge for any specific brand’s product? If so, then which of the
following brand is it?
a) Yes, PRAN Foods and Beverage b) Yes, Akij foods c) both d) none
8. Which of the following foods manufacturing brands provide its sellers with extra
benefits?
a) PRAN Foods and Beverage b) Akij Foods c) none
9. Cold drinks of which brands have drawn customer choices and satisfaction as well?
a) PRAN Foods and Beverage b) Akij Foods c) both d) none
10. Selling which products of the following brands do you get more profit?
11. Which of the following brands are seemed to be manufacturing more innovative and
delicious food items?
12. Which of the following brand’s products are comparatively more costly?
13. Which of the following brand’s food products are still in demand in spite of its being
costly?
14. According to your sell and demand of the customers, which of the brands is more
successful in the foods market of Bangladesh?

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15. How much marks (X) will you provide to PRAN Foods and Beverage on 100?
a) X<20 b) X<50 c) X<75 d) X>75
16. How much marks (Y) will you provide to Akij Foods on 100?
a) Y<20 b) Y<50 c) Y<75 d) Y>75
So, this is the questionnaire that was used to get the findings out and this is the only part of
this appendix.
4.2 Findings on the Questionnaire:
In this section the through findings are going to be presented on the questionnaire built to
fulfill the purpose of the study. It is important to grasp the idea that the study has been done
on the basis of thirty reliable samples. Whatever important and necessary things we have
found from the sample collection is necessary to be expressed. That’s why, here below all
the findings have been presented with necessary tables, charts and short explanations.
1.How many types of products do you sell in your shop?
The answers that the study gets from the respondents show a concentration at the class of
“Above 15” having a frequency of 26 and a relative frequency of 86.67%
Options Frequency Relative Frequency
0-5 1 3.33%
5-10 1 3.33%
10-15 2 6.67%
Above 15 26 86.67%
For a better show and easy grasping of the whole information, the representation of this
table in a chart is the following:

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Figure 4.1 : Types of products sold in the shops.
2.Who are the key customers of your shop?
Varsity students 23 76.67%
Teachers 4 13.33%
School children 1 3.33%
Common people 2 6.67%
“Varsity Students” having a frequency of 23 and a relative frequency of 76.67%
0
5
10
15
20
25
30
0-5 10-May 15-Oct Above 15
FrequencyandRelativeFrequency
Options
Frequency
Relative Frequency

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Figure 4.2 : Key customers.
3.In which time period most of your customers gather in your shop for buying food?
Options Frequency Relative frequency
At morning 20 66.67%
At noon 5 16.67%
In the evening 3 10.00%
At night 2 6.67%
“At morning” having a frequency of 20 and a relative frequency of 66.67%
0
5
10
15
20
25
Varsity
students
Teachers School
children
Common
people
Options
Frequency
Relative Frequency

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Figure 4.3 : Time of gathering customers in the shop.
4.When buying food, which brands you give more preference?
Options Frequency Relative frequency
PRAN Foods Limited 25 83.33%
Akij Foods and Beverage
Limited
2 6.67%
Haque Foods 1 3.33%
Others 2 6.67%
“PRAN Foods Limited” having a frequency of 25 and a relative frequency of 83.33%
0
2
4
6
8
10
12
14
16
18
20
At
morning
At noon In the
evening
At night
Options
Frequency
Relative frequency

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Figure 4.4 : Preferences of food items.
5.In comparison, dealing with which brand you get transportation facility in retailing purpose?
PRAN Foods Limited 15 50%
Limited
15 50%
The answers that the study gets from the respondents show a concentration at both of the
classes having an equal frequency of 15 and a relative frequency of 50%
0
5
10
15
20
25
PRAN
Foods
Limited
Akij
Foods
and
Beverage
Limited
Haque
Foods
Others
Options
Frequency
Relative frequency
0
2
4
6
8
10
12
14
16
Frequency Relative
Frequency
Options
PRAN Foods Limited
Limited

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Figure 4.5 : Transportation facilities provided by the following company.
6.Which of the brands in comparison get extra preferences by the customers?
Limited
9 30%
“PRAN Foods Limited” having a frequency of 21 and a relative frequency of 70%
Figure 4.6 : Extra preferences by the customers.
7.Do customers directly urge for any specific brand’s product? If so, then which of the following
brand is it?
Yes, PRAN Foods Limited 10 33.33%
Limited
8 26.67%
Both 10 33.33%
0
5
10
15
20
25
Frequency Relative
Frequency
Options
PRAN Foods Limited
Limited

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None 2 6.67%
The answers that the study gets from the respondents show a greater concentration both in
the first class and third having a frequency of 10 and a relative frequency of 33.33%%.
Figure 4.7 : Customers demand for specific food items of PRAN and Akij Foods and
Beverage Limited
8.Which of the following foods manufacturing brands provide its sellers with extra benefits?
Limited
7 23.33%
None 17 56.67%
“None” having a frequency of 17 and a relative frequency of 56.67%
0
1
2
3
4
5
6
7
8
9
10
Yes, PRAN Foods LimitedAkij Foods and Beverage LimitedBoth None
Options
Frequency
Relative Frequency

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Figure 4.8 : Providing sellers with extra benefits.
9. Cold drinks of which brands have drawn customer choices and satisfaction as well?
Limited
6 20.00%
Both 9 30.00%
None 11 36.67%
“None” having a frequency of 11 and a relative frequency of 36.67%
0
2
4
6
8
10
12
14
16
18
PRAN Foods
Limited
Akij Foods
and
Beverage
Limited
None
Options
Frequency
Relative Frequency

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Figure 4.8 : Most successful company From customers view.
10. Selling which products of the following brands do you get more profit?
Limited
12 40%
“PRAN Foods Limited” having a frequency of 18 and a relative frequency of 60%
0
2
4
6
8
10
12
PRAN
Foods
Limited
Akij
Foods
and
Beverage
Limited
Both None
Options
Frequency
Relative Frequency

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Figure 4.9 : Most profitable Company between PRAN and akij.
11. Which of the following brands are seemed to be manufacturing more innovative and
delicious food items?
Limited
12 40.0%
“PRAN Foods Limited” having a frequency of 18 and a relative frequency of 60%. For a
better show and easy grasping of the whole information, the representation of this table in
a chart is the following:
0
2
4
6
8
10
12
14
16
18
Frequency Relative
Frequency
Options
PRAN Foods Limited
Limited

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Figure 4.10 : Analysis on manufacturing most innovative and delicious food items.
12. Which of the following brand’s products are comparatively more costly?
Limited
15 50%
The answers that the study gets from the respondents show a concentration at both of the
classes having a frequency of 15 and a relative frequency of 50%.
0
2
4
6
8
10
12
14
16
18
Frequency Relative
Frequency
Options
PRAN Foods Limited
Limited

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Figure 4.11: Comparative analysis on cost of products.
13. Which of the following brand’s food products are still in demand in spite of its being costly?
Limited
12 40%
“PRAN Foods Limited” having a frequency of 18 and a relative frequency of 60%.
0
2
4
6
8
10
12
14
16
Frequency Relative
Frequency
Options
PRAN Foods Limited
Limited

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Figure 4.12 : Most demandable brand being costly.
14. According to your sell and demand of the customers, which of the brands is more successful
in the foods market of Bangladesh?
Limited
12 33.33%
“PRAN Foods Limited” having a frequency of 18 and a relative frequency of 66.67%.
0
2
4
6
8
10
12
14
16
18
20
Frequency Relative Frequency
Options
PRAN Foods Limited
Limited

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For a better show and easy grasping of the whole information, the representation of this table
in a chart is the following:
Figure 4.13 : Analysis on success in the food market between Akij and PRAN.
15. How much marks (X) will you provide to PRAN Foods and Beverage on 100?
X<20 1 3.33%
X<50 7 23.33%
X<75 10 33.33%
X>75 12 40.00%
“X>75” having a frequency of 12 and a relative frequency of 40.00%
in a chart is the following
0
2
4
6
8
10
12
14
16
18
Frequency Relative
Frequency
FRequencyandRelativeFrequency
Options
PRAN Foods Limited
Limited

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:
Figure 4.14 : Analysis on the marks got by PRAN Foods and Beverage Limited.
16. How much marks (Y) will you provide to Akij Foods on 100?
Y<20 2 7%
Y<50 5 17%
Y<75 14 47%
Y>75 9 30%
“Y<75” having a frequency of 14 and a relative frequency of 47%.
in a chart is the following
0
2
4
6
8
10
12
X<20 X<50 X<75 X>75
Options
Frequency
Relative Frequency

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Figure 4.15 : Analysis on the marks got by Akij Foods and Beverage Limited
0
2
4
6
8
10
12
14
Y<20 Y<50 Y<75 Y>75
Options
Frequency
Relative Frequency

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Chapter 05
Statistical Analysis:Perspective of PRAN Company

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Application of Statistical Techniques on the variables concerning PRAN
Foods Limited:
All the necessary applications of statistical techniques concerning the thirty variables of
PRAN Foods Limited have been provided step by step in this chapter. The analysis
comparing with Akij Foods and Beverage Limited has been provided in the analysis section.
5.1 Arithmetic Mean of Sales and Profits:
In the survey of PRAN Foods Limited, we have come across with 30 sample sites and here
are the respective sales which have been presented by X, the independent variable and the
respective profits which have been presented by Y, the dependent variable. So, from here we
can find:
Variable X= Independent Variable
Variable Y= Dependent Variable
Sample Sales (X) Profit (Y)
1 150 21
2 170 23
3 210 28
4 120 14
5 200 28
6 210 27
7 100 18
8 120 13
9 90 15
10 160 19
11 190 23
12 170 26
13 210 28
14 220 30
15 178 20
16 190 27
17 210 24
18 188 26
19 197 22
20 120 17
21 160 23
22 174 20
23 150 23
24 149 20
25 190 27
26 180 21
27 175 22
28 179 20

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Fig 5.1 : Variables of PRAN Foods Limited.
So, this is the thirty variables table on which we are going to concentrate to find out the arithmetic
mean.
The Calculation of Arithmetic Mean:
As described previously, here the accumulation of the values of the independent variable (X)
has been divided by the number of the sample sites to find out the arithmetic mean 𝑋.
Simultaneously, the accumulation of the values of the dependent variable (Y) has been
divided by the number of the sample sites to find out the arithmetic mean 𝑌.
Here,
𝑋 =
𝑋
𝑛
=
5130
30
=171 Tk.
𝑌 =
𝑌
𝑛
=
679
30
= TK. 22.63333
Here, also the Stem-and-Leaf Display of Profits (Y) has been provided for the appropriate
representation of the data. So, the arithmetic mean of the sales is tk. 171 and the arithmetic
mean of the profit is tk. 22.63333.
Here below the presentation of sales in the Stem-and-Leaf display has been presented:
29 190 29
30 180 25
n =30 𝑋=5130 𝑌=679
SALES(X)
Stem Leaf
9 0
10 0
11
12 0 0 0
13
14 9
15 0 0
16 0 0
17 0 0 4 5 8 9
18 0 0 8
19 0 0 0 0 7
20 0

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5.2 Calculation of Median, Mode and Quartiles of Sales:
The calculation of the median, mode and quartiles are important for the findings and further
analysis of the data. They help to find out the concentration of the data values in the data
sheet.
Sorted values of sales are given bellow:
90 100 120 120 120 149 150 150 160 160
170 170 174 175 178 179 180 180 188 190
190 190 190 197 200 210 210 210 210 220
Median of sales:
The median of the sales help to find out the concentration of the data values in the data set.
Here we can find the following calculation to get the nth
value that is the representative value.
Here,
𝑀𝑒 = 𝐿50 = 𝑛 + 1 ×
50
100
𝑡ℎ 𝑣𝑎𝑙𝑢𝑒
= 30 + 1 ×
50
100
= 15.5𝑡ℎ 𝑣𝑎𝑙𝑢𝑒
= 15𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 + ((16𝑡ℎ − 15𝑡ℎ) × 0.5)
= 178 + ((179 − 178) × 0.5)= TK.178.5
So, we find that the median of the sales is tk. 178.50. So, the shops sell about 178.50 taka
products per day of PRAN Foods Limited.
21 0 0 0 0
22 0
PROFITS (Y)
Stem Leaf
1 3 4 5 7 8 9
2 0 0 0 0 1 1 2 2 3 3 3 3 4 5 6 6 7 7 7 8 8 8 9
3 0

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Mode of the Sales:
The mode of the sales will represent the value that occurs most frequently. That means that
how many shops sell almost same amount of PRAN Foods in taka will be the desired value.
From the survey, we have found:
Mode of sales= 210 (4 times)
So, the shops sell about tk. 210 products of PRAN Foods Limited per day. So, this value is
considered to be the modal value as it appears for 4 times.
1st
and 3rd
Quartiles:
These are some other sorts of statistical calculations the objective of which are also to find
out the concentration of the values.
First Quartile:
The 1st
quartile of the sample sites show about how much data lie within the limitation of
25% of the whole data set. Here, in the calculation, it has been found.
Here,
𝑄1 = 𝐿25 = 𝑛 + 1 ×
25
100
= 30 + 1 ×
25
100
= 7𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 + ((8𝑡ℎ − 7𝑡ℎ) × 0.75)
= 150 + ((150 − 150) × 0.75)= TK.150
So, the 1st
quartile of the sales is tk. 150. It has been found on the basis of the survey of the
30 sample sites of the area of University of Dhaka.
Third Quartile:
The 3rd
Here,
𝑄3 = 𝐿75 = 𝑛 + 1 ×
75
100
= 30 + 1 ×
75
100
= 23𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 + ((24𝑡ℎ − 23𝑡ℎ) × 0.25)

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= 190 + ((197 − 190) × 0.75)= TK.191.75
So, the 3rd
quartile of the sales is tk. 191.75. It has been found on the basis of the survey of
the 30 sample sites of the area of University of Dhaka.
5.3 Calculation of Median, mode and quartiles of profits:
Like the calculation of the variable X that are sales, we now calculate the profits (Y) to reach
our ultimate results appropriately. The calculation of the median, mode and quartiles are
important for the findings and further analysis of the data. They help to find out the
concentration of the data values in the data sheet.
Sorted values of profits are given bellow:
13 14 15 17 18 19 20 20 20 20
21 21 22 22 23 23 23 23 24 25
26 26 27 27 27 28 28 28 29 30
Median of profits:
The median of the sales help to find out the concentration of the data values in the data set. Here we
can find the following calculation to get the nth
Here,
𝑀𝑒 = 𝐿50 = 𝑛 + 1 ×
50
100
= 30 + 1 ×
50
100
= 15𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 + ((16𝑡ℎ − 15𝑡ℎ) × 0.5)
= 23 + ((23 − 23) × 0.5)= TK.23
So, we find that the median of the profit is tk. 23. So, the shops profits about 23 taka per day
on the products of PRAN Foods Limited.
Mode of Profits:
The mode of the profits will represent the value that occurs most frequently. That means that
how many shops make profits almost same amount of PRAN Foods in taka will be the
desired value.

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Mode of profits= 20 & 23 (both 4 times)
Here, this value shows that 20 and 23 are the bimodal values profited by the shops selling
products of PRAN Foods Limited.
1st
and 3rd
Quartiles:
First Quartile:
The 1st
Here,
𝑄1 = 𝐿25 = 𝑛 + 1 ×
25
100
= 30 + 1 ×
25
100
= 7𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 + ((8𝑡ℎ − 7𝑡ℎ) × 0.75)
= 20 + ((20 − 20) × 0.75)= TK.20
So, the 1st
quartile of the sales is tk. 20. It has been found on the basis of the survey of the 30
sample sites of the area of University of Dhaka.
Third Quartile:
The 3rd
Here,
𝑄3 = 𝐿75 = 𝑛 + 1 ×
75
100
= 30 + 1 ×
75
100
= 23𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 + ((24𝑡ℎ − 23𝑡ℎ) × 0.25)
= 27 + ((27 − 27) × 0.75)= TK.27
So, the 3rd

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Mean Deviation and Standard Deviation and Coefficient of Variation of Sales and
Profits:
Here above the table of the whole calculation material to find out Mean Deviation and
Standard Deviation and Coefficient of Variation of Sales and Profits are given.
5.4 Calculating Mean deviation:
The mean deviation of the sample sites show that how much the observations of the sales and
profits differ from the standard and typical value.
The mean deviations of the two variables are given below:
X X- X̅ │X-X̅ │ Y Y-𝑌 │Y-𝑌│ (𝑌 − 𝑌)2
150 -21 21 441 21 -1.63 1.63 2.668
170 -1 1 1 23 0.37 0.37 0.134
210 39 39 1521 28 5.37 5.37 28.801
120 -51 51 2601 14 -8.63 8.63 74.534
200 29 29 841 28 5.37 5.37 28.801
210 39 39 1521 27 4.37 4.37 19.068
100 -71 71 5041 18 -4.63 4.63 21.468
120 -51 51 2601 13 -9.63 9.63 92.801
90 -81 81 6561 15 -7.63 7.63 58.268
160 -11 11 121 19 -3.63 3.63 13.201
190 19 19 361 23 0.37 0.37 0.134
170 -1 1 1 26 3.37 3.37 11.334
210 39 39 1521 28 5.37 5.37 28.801
220 49 49 2401 30 7.37 7.37 54.268
178 7 7 49 20 -2.63 2.63 6.934
190 19 19 361 27 4.37 4.37 19.068
210 39 39 1521 24 1.37 1.37 1.868
188 17 17 289 26 3.37 3.37 11.334
197 26 26 676 22 -0.63 0.63 0.401
120 -51 51 2601 17 -5.63 5.63 31.734
160 -11 11 121 23 0.37 0.37 0.134
174 3 3 9 20 -2.63 2.63 6.934
150 -21 21 441 23 0.37 0.37 0.134
149 -22 22 484 20 -2.63 2.63 6.934
190 19 19 361 27 4.37 4.37 19.068
180 9 9 81 21 -1.63 1.63 2.668
175 4 4 16 22 -0.63 0.63 0.401
179 8 8 64 20 -2.63 2.63 6.934
190 19 19 361 29 6.37 6.37 40.534
180 9 9 81 25 2.37 2.37 5.601
𝑋=
5130
(𝑋 − 𝑋)
=0.00
𝑋 − 𝑋
=786
(X − X̅) 2
=33050
𝑌=
679
(𝑋 − 𝑋)
=0.00
𝑌 − 𝑌
=109.73
(Y − 𝑌) 2
=594.967
(X − X̅) 𝟐

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𝑀𝐷 𝑋 =
│𝑋−𝑋│
𝑛
=
786
30
= TK. 26.2
𝑀𝐷 𝑌 =
│𝑌−𝑌│
𝑛
=
109.73
30
= TK. 3.657778
5.5 Calculating Variance and Standard Deviation of sales and profits:
The calculation of the variance and standard deviation will allow us to count difference of the
tendency of concentration among the two variables.
Here we get from the previously mentioned data tables that:
𝑠 𝑋
2
=
(𝑋−𝑋)2
𝑛−1
=
33050
30−1
= TK. 1139.655
This is the variance of variable X which shows the figure of TK. 1139.655.
𝑠 𝑋 =
(𝑋−𝑋)2
𝑛−1
=
33050
30−1
= 1139.66 = TK. 33.75878
This is the standard deviation of variable X which shows the figure of TK 33.75878
𝑠 𝑌
2
=
(𝑌−𝑌)2
𝑛−1
=
594.967
30−1
= TK. 20.51609
This is the variance of variable Y which shows the figure of TK. 20.51609
𝑠 𝑌 =
(𝑌−𝑌)2
𝑛−1
=
594.967
30−1
= 20.51609 = TK. 4.529469
Here, we can get the comparing figures between the two variables X and Y. Of course there
are some other measures done further in this study to come to the conclusion about the report
on the comparative analysis.
5.6 Calculating Coefficient of variation of sales and profits:
As discussed earlier in the theoretical background about the importance of coefficient of
variation in this study, this statistical measure has been used to satisfy the differing tendency
from the point of concentration when the outputs from the sample sites are different.
𝐶𝑉 𝑋 =
𝑆 𝑋
𝑋
=
33.75878
171
= 0.19742
So, we get the figure here on the Coefficient of Variation (CV) of variable X that is 0.19742.
𝐶𝑉 𝑌 =
𝑆 𝑌
𝑌
=
4.529469
22.63333
= 0.200124
So, we get the figure here on the Coefficient of Variation (CV) of variable Y that is 0.19742.

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When used via computer, we need to know the Software Coefficient of Skewness. So, here
the calculation of the Software Coefficient of Skewness has been given below:
5.7 Software Coefficient of Skewness:
Here, the table in where the calculation has been done is given below:
Sample Sales
(X)
(X- 𝑋)
(
𝑋 − 𝑋
𝑆
)3
Profit (Y) (Y- 𝑌)
(
𝑌 − 𝑌
𝑆
)3
1 150 -21 -0.240711969 21 -1.63 -0.046890247
2 170 -1 -2.5992E-05 23 0.37 0.000530484
3 210 39 1.541819813 28 5.37 1.663305059
4 120 -51 -3.447865608 14 -8.63 -6.924582163
5 200 29 0.633919038 28 5.37 1.663305059
6 210 39 1.541819813 27 4.37 0.896000325
7 100 -71 -9.302824914 18 -4.63 -1.070381714
8 120 -51 -3.447865608 13 -9.63 -9.620282133
9 90 -81 -13.81321774 15 -7.63 -4.786308941
10 160 -11 -0.03459536 19 -3.63 -0.516147436
11 190 19 0.17827917 23 0.37 0.000530484
12 170 -1 -2.5992E-05 26 3.37 0.410637306
13 210 39 1.541819813 28 5.37 1.663305059
14 220 49 3.057933532 30 7.37 4.302006889
15 178 7 0.008915258 20 -2.63 -0.196505882
16 190 19 0.17827917 27 4.37 0.896000325
17 210 39 1.541819813 24 1.37 0.02746919
18 188 17 0.127698726 26 3.37 0.410637306
19 197 26 0.4568355 22 -0.63 -0.002733727
20 120 -51 -3.447865608 17 -5.63 -1.923775521
21 160 -11 -0.03459536 23 0.37 0.000530484
22 174 3 0.000701784 20 -2.63 -0.196505882
23 150 -21 -0.240711969 23 0.37 0.000530484
24 149 -22 -0.276762881 20 -2.63 -0.196505882
25 190 19 0.17827917 27 4.37 0.896000325
26 180 9 0.018948172 21 -1.63 -0.046890247
27 175 4 0.001663488 22 -0.63 -0.002733727
28 179 8 0.013307907 20 -2.63 -0.196505882
29 190 19 0.17827917 29 6.37 2.777118312
30 180 9 0.018948172 25 2.37 0.142649195
n=30 𝑋=
5130
(𝑋 − 𝑋)=
0.00
(
𝑋−𝑋
𝑆
)3
=
-23.06780149
𝒀=
679
(𝑌 − 𝑌)=
0.00
(
𝑌−𝑌
𝑆
)3
=
-9.976193093

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So, the thirty sample table is given upward on the basis of which the major calculation on
Software Coefficient of Skewness has been done.
Here, the skewness of sales is:
𝑠𝑘 𝑜𝑓 𝑠𝑎𝑙𝑒𝑠 =
𝑛
(𝑛 − 1) × (𝑛 − 2)
(
𝑋 − 𝑋
𝑆
)3
=
30
(30−1)×(30−2)
−23.06780149
𝑠𝑘 𝑜𝑓 𝑠𝑎𝑙𝑒𝑠 = −0.852258676
So, we have got that the skewness of sales is -0.852258676.
Now, the skewness of profits is given below:
𝑠𝑘 𝑜𝑓 𝑝𝑟𝑜𝑓𝑖𝑡𝑠 =
𝑛
(𝑛−1)×(𝑛−2)
(
𝑌−𝑌
𝑆
)3
=
30
(30−1)×(30−2)
−9.976193093
= −0.368578563
So, we have got that the skewness of profits to be -0.368578563.
Now the Pearson’s Coefficient of Skewness will be described hereby:
5.8 Pearson’s Coefficient of Skewness:
Pearson’s coefficient of skewness for the sales variable X is given below:
𝑆𝐾 𝑜𝑓 𝑠𝑎𝑙𝑒𝑠 =
3( 𝑋−𝑀𝑒)
𝑠
=
3(171 −178.5)
33.75878
=-0.66649
Here, we can see that the sales variable X has skewness of -0.66649.
Pearson’s coefficient of skewness for the profit variable Y is given below:
𝑆𝐾 𝑜𝑓 𝑝𝑟𝑜𝑓𝑖𝑡 =
3( 𝑌−𝑀𝑒)
𝑠

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=
3(22.63333 −23)
4.529469
=-0.24285406
Here, we can see that the profit variable Y has skewness of -0.24285406.
Now the correlation and regression for the variables X and Y will be expressed further:
5.9 Correlation and Regression Analysis:
The correlation and regression analysis will show the tendency of the data variables and their
effect on each other which means the strength of the linear relationship between the sales
variable X and the profit variable Y and the percentage of dependence of the variables on
each other.
Sample Sales (X) Profit (Y) XY X2
Y2
1 150 21 3150 22500 441
2 170 23 3910 28900 529
3 210 28 5880 44100 784
4 120 14 1680 14400 196
5 200 28 5600 40000 784
6 210 27 5670 44100 729
7 100 18 1800 10000 324
8 120 13 1560 14400 169
9 90 15 1350 8100 225
10 160 19 3040 25600 361
11 190 23 4370 36100 529
12 170 26 4420 28900 676
13 210 28 5880 44100 784
14 220 30 6600 48400 900
15 178 20 3560 31684 400
16 190 27 5130 36100 729
17 210 24 5040 44100 576
18 188 26 4888 35344 676
19 197 22 4334 38809 484
20 120 17 2040 14400 289
21 160 23 3680 25600 529
22 174 20 3480 30276 400
23 150 23 3450 22500 529
24 149 20 2980 22201 400
25 190 27 5130 36100 729
26 180 21 3780 32400 441
27 175 22 3850 30625 484
28 179 20 3580 32041 400
29 190 29 5510 36100 841
30 180 25 4500 32400 625
n= 30 𝑋=
5130
𝑌=
679
𝑋𝑌 =
119842
𝑋2
= 𝑌2
=

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910280 15963
So, the thirty sample table is given upward on the basis of which the major calculations on
correlation and regression have been done
Calculating Correlation:
Calculation of coefficient of correlation between sales and profits are given below where “r”
expresses the coefficient of correlation.
𝑟 =
𝑛 𝑋𝑌 − 𝑋 𝑌
𝑛 𝑋2−( 𝑋)2 ∗( 𝑛 𝑌2− 𝑌 2)
=
30×119842 −(5130×679)
30×910280)− 51302 ∗( (30×15963)− 679 2)
So, 𝑟 = 0.841832989
Here, we have found that the value of “r” is 0.841832989 which refers a strong positive
correlation between the variables. So, the variables are strongly positively correlated to each
other.
Calculation of coefficient of determination:
Coefficient of determination is going to be found by squaring the value of the coefficient of
correlation. So, we get the coefficient of determination:
𝑟2
= (0.841832989)2
Which means, 𝑟2
= 0.708682782
So, we have found the coefficient of determination to be 0.708682782.
For finding out the rate of dependence of the depending variable on the independent variable,
a statistical calculation named regression equation will be discussed further.
Finding of Regression Equation:
The required estimated regression equation is given below:
𝑌 = 𝑎 + 𝑏𝑋
To find out the given equation, we need to find the actual value of its components. The major
components of this equation are “b” and “a”. Now lets discuss on the whole of its
components:

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Here,
“𝑌” stands for the estimated value of the Y variable for X value.
“a” stands for an intercept.
“b” stands for the slope in the line. It measures the change in “𝑌” for each unit change in X.
X is any value that works as independent variable.
Now, to find out the value of “b” the following steps have been used:
𝑏 =
𝑛 𝑋2−( 𝑋)2
=
30×119842 −(5130×679)
(30×910280)− 51302
𝑏 =0.112950076
So, we have found the value of “b” which is 0.112950076.
Now we will find out the value of another major component of the regression equation that is
“a”. Here,
𝑎 = 𝑌 − 𝑏𝑋
S0, 𝑎 =
𝑌−𝑏 𝑋
𝑛
=
679−(0.112950076 × 5130)
30
= 3.318870398
So, we have found the value of “a” to be 3.318870398.
Required regression equation:
So, the required regression equation will be found on the proper substitution of the values that
of “a”, “b”. Here, the regression equation is:
𝑌 = 3.32 + 0.113𝑋
In this equation the desired result can be found on the substitution of the value of the variable
X. So, the independent value of variable X will determine the value of dependent variable Y.
Now, here a regression model has been built to show the effect of varying thirty variables on
the regression analysis. Here, the sales variables (X) are in the horizontal line and Profit
variables (Y) are in the vertical lines. To get a proper analysis, a chart has been provided to
have a proper synthesis.

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Figure 5.2 : Chart of Regression Model
So far the statistical techniques have been used to find out the practical situation of variable Y
on the basis of variable X in the perspective of PRAN Foods Limited. In the analysis section
all the findings will be described to compare between PRAN Foods Limited and Akij Foods
and Beverage Limited to get to the ultimate conclusion to fulfil this study.
y = 0.113x + 3.318
R² = 0.708
0
5
10
15
20
25
30
35
0 50 100 150 200 250
Profit(Y)
Sales (X)
Regression Model

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Chapter 06
Statistical Analysis: Perspective of Akij Foods and
Beverage Limited

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Application of Statistical Techniques on the variables concerning Akij
Foods and Beverage Limited
All the necessary applications of statistical techniques concerning the thirty variables of Akij
Foods and Beverage Limited have been provided step by step in this chapter. The analysis
comparing with PRAN Foods Limited has been provided in the analysis section.
6.1 Arithmetic Mean of Sales and Profits:
In the survey of Akij Foods and Beverage Limited, we have come across with 30 sample sites
and here are the respective sales which have been presented by X, the independent variable
and the respective profits which have been presented by Y, the dependent variable. So, from
here we can find:
Variable X= Independent Variable
Variable Y= Dependent Variable
Sample Sales (X) Profit (Y)
1 100 14
2 130 13
3 155 21
4 140 17
5 170 22
6 190 23
7 80 14
8 150 15
9 120 17
10 180 20
11 140 19
12 130 14
13 250 38
14 100 13
15 120 15
16 110 10
17 120 14
18 168 25
19 145 19
20 111 16
21 160 20
22 109 15
23 100 17
24 132 16
25 160 20
26 190 21
27 120 12
28 130 13

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29 180 20
30 170 18
n =30 𝑋=4260 𝑌=531
The Calculation of Arithmetic Mean: As described previously, here the accumulation of
the values of the independent variable (X) has been divided by the number of the sample sites
to find out the arithmetic mean 𝑋. Simultaneously, the accumulation of the values of the
dependent variable (Y) has been divided by the number of the sample sites to find out the
arithmetic mean 𝑌.
Here,
𝑋 =
𝑋
𝑛
=
4260
30
=142 Tk.
𝑌 =
𝑌
𝑛
=
531
30
= 17.7 Tk
Here, also the Stem-and-Leaf Display of Profits (Y) has been provided for the appropriate
representation of the data. So, the arithmetic mean of the sales is tk. 142 and the arithmetic
mean of the profit is tk. 17.7.
Here below the presentation of sales in the Stem-and-Leaf display has been presented:
SALES(X)
Stem Leaf
8 0
9
10 0,0,0,9
11 0,1
12 0,0,0,0
13 0,0,0,2
14 0,0,5
15 0,5
16 0,0,8
17 0,0
18 0,0
19 0,0
20
21
22
23

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6.2 Calculation of Median, Mode and Quartiles of Sales:
The calculation of the median, mode and quartiles are important for the findings and further
analysis of the data. They help to find out the concentration of the data values in the data
sheet.
Sorted values of sales are given bellow:
80 100 100 100 109 110 111 120 120 120
120 130 130 130 132 140 140 145 150 155
160 160 168 170 170 180 180 190 190 250
Median of sales:
24
25 250
PROFITS (Y)
Stem Leaf
1 0,2,3,3,3,4,4,4,4,5,5,5,6,6,7,7,7,8,9,9
2 0,0,0,0,1,1,2,3,5
3 8

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Here,
𝑀𝑒 = 𝐿50 = 𝑛 + 1 ×
50
100
= 30 + 1 ×
50
100
= 15𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 + ((16𝑡ℎ − 15𝑡ℎ) × 0.5)
= 132 + ((140 − 132) × 0.5)= TK.136
So, we find that the median of the sales is tk. 136. So, the shops sell about 136 taka products
per day Akij Foods and Beverage Limited
Mode of the Sales:
The mode of the sales will represent the value that occurs most frequently. That means that
how many shops sell almost same amount of Akij Foods and Beverage Limited in taka will
be the desired value.
Mode of sales= 120 (4 times)
So, the shops sell about tk. 120 products of Akij Foods and Beverage Limited per day. So,
this value is considered to be the modal value as it appears for 4 times.
6.3 1st
and 3rd
Quartiles
First Quartile:
The 1st
Here,
𝑄1 = 𝐿25 = 𝑛 + 1 ×
25
100

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= 30 + 1 ×
25
100
= 7𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 + ((8𝑡ℎ − 7𝑡ℎ) × 0.75)
= 111 + 120 − 111 × 0.75
= TK.117.75
So, the 1st
quartile of the sales is tk. 117.75. It has been found on the basis of the survey of
the 30 sample sites of the area of University of Dhaka.
Third Quartile:
The 3rd
Here,
𝑄3 = 𝐿75 = 𝑛 + 1 ×
75
100
= 30 + 1 ×
75
100
= 23𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 + ((24𝑡ℎ − 23𝑡ℎ) × 0.25)
= 168 + ((170 − 168) × 0.75)= TK.169.5
So, the 3rd
quartile of the sales is tk. 169.5. It has been found on the basis of the survey of the
30 sample sites of the area of University of Dhaka.
6.4 Calculation of Median, mode and quartiles of profits:
Like the calculation of the variable X that are sales, we now calculate the profits (Y) to reach
our ultimate results appropriately. The calculation of the median, mode and quartiles are
important for the findings and further analysis of the data. They help to find out the
concentration of the data values in the data sheet.
Sorted values of profits are given bellow:
10 12 13 13 13 14 14 14 14 15
15 15 16 16 17 17 17 18 19 19
20 20 20 20 21 21 22 23 25 38

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Median of profits:
Here,
𝑀𝑒 = 𝐿50 = 𝑛 + 1 ×
50
100
= 30 + 1 ×
50
100
= 15𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 + ((16𝑡ℎ − 15𝑡ℎ) × 0.5)
= 17 + ((17 − 17) × 0.5)= TK.17
So, we find that the median of the profit is tk. 17. So, the shops profits about 17 taka per day
on the products of Akij Foods and Beverage Limited .
Mode of Profits:
The mode of the profits will represent the value that occurs most frequently. That means that
how many shops make profits almost same amount of Akij Foods and Beverage Limited in
taka will be the desired value.
Mode of profits= 14 ( 4 times)
Here, this value shows that 14 is the bimodal values profited by the shops selling products
Akij Foods and Beverage Limited
1st
and 3rd
Quartiles:
First Quartile:
The 1st

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Here,
𝑄1 = 𝐿25 = 𝑛 + 1 ×
25
100
= 30 + 1 ×
25
100
= 7𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 + ((8𝑡ℎ − 7𝑡ℎ) × 0.75)
= 14 + ((14 − 14) × 0.75)= TK.14
So, the 1st
Third Quartile:
The 3rd
Here,
𝑄3 = 𝐿75 = 𝑛 + 1 ×
75
100
= 30 + 1 ×
75
100
= 23𝑡ℎ 𝑣𝑎𝑙𝑢𝑒 + ((24𝑡ℎ − 23𝑡ℎ) × 0.25)
= 20 + ((20 − 20) × 0.75)= TK.20
So, the 3rd
6.5 Mean Deviation and Standard Deviation and Coefficient of Variation of Sales
and Profits:
Here,
X (X-X̅ ) |X-X̅ | Y (Y-Y̅ ) |Y-Y̅ |
100 -42 42 1764 14 -3.7 3.7 13.69
130 -12 12 144 13 -4.7 4.7 22.09

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155 13 13 169 21 3.3 3.3 10.89
140 -2 2 4 17 -0.7 0.7 0.49
170 28 28 784 22 4.3 4.3 18.49
190 48 48 2304 23 5.3 5.3 28.09
80 -62 62 3844 14 -3.7 3.7 13.69
150 8 8 64 15 -2.7 2.7 7.29
120 -22 22 484 17 -0.7 0.7 0.49
180 38 38 1444 20 2.3 2.3 5.29
140 -2 2 4 19 1.3 1.3 1.69
130 -12 12 144 14 -3.7 3.7 13.69
250 108 108 11664 38 20.3 20.3 412.09
100 -42 42 1764 13 -4.7 4.7 22.09
120 -22 22 484 15 -2.7 2.7 7.29
110 -32 32 1024 10 -7.7 7.7 59.29
120 -22 22 484 14 -3.7 3.7 13.69
168 26 26 676 25 7.3 7.3 53.29
145 3 3 9 19 1.3 1.3 1.69
111 -31 31 961 16 -1.7 1.7 2.89
160 18 18 324 20 2.3 2.3 5.29
109 -33 33 1089 15 -2.7 2.7 7.29
100 -42 42 1764 17 -0.7 0.7 0.49
132 -10 10 100 16 -1.7 1.7 2.89
160 18 18 324 20 2.3 2.3 5.29
190 48 48 2304 21 3.3 3.3 10.89
120 -22 22 484 12 -5.7 5.7 32.49
130 -12 12 144 13 -4.7 4.7 22.09
180 38 38 1444 20 2.3 2.3 5.29
170 28 28 784 18 0.3 0.3 0.09
4260 0 844 36980 531 0.0 111.8 800.30
Here above the table of the whole calculation material to find out Mean Deviation and
Standard Deviation and Coefficient of Variation of Sales and Profits are given.
Calculating Mean deviation:
The mean deviation of the sample sites show that how much the observations of the sales and
profits differ from the standard and typical value.
The mean deviations of the two variables are given below:
𝑀𝐷 𝑋 =
│𝑋−𝑋│
𝑛
=
844
30
= TK. 28.13333

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𝑀𝐷 𝑌 =
│𝑌−𝑌│
𝑛
=
111.8
30
= TK. 3.73
Calculating Variance and Standard Deviation of sales and profits:
The calculation of the variance and standard deviation will allow us to count difference of the
tendency of concentration among the two variables.
Here we get from the previously mentioned data tables that:
𝑠 𝑋
2
=
(𝑋−𝑋)2
𝑛−1
=
36980
30−1
= TK. 1275.17241
This is the variance of variable X which shows the figure of TK. 1139.655.
𝑠 𝑋 =
(𝑋−𝑋)2
𝑛−1
=
36980
30−1
= 1275.17241 = TK. 35.7095563
𝑠 𝑌
2
=
(𝑌−𝑌)2
𝑛−1
=
800.30
30−1
= TK. 27.5965517
This is the variance of variable Y which shows the figure of TK. 27.5965517
𝑠 𝑌 =
(𝑌−𝑌)2
𝑛−1
=
800.30
30−1
= 27.5965517 = TK. 5.25324202
Here, we can get the comparing figures between the two variables X and Y. Of course there
are some other measures done further in this study to come to the conclusion about the report
on the comparative analysis.
6.6 Calculating Coefficient of variation of sales and profits:
As discussed earlier in the theoretical background about the importance of coefficient of
variation in this study, this statistical measure has been used to satisfy the differing tendency
from the point of concentration when the outputs from the sample sites are different.
𝐶𝑉 𝑋 =
𝑆 𝑋
𝑋
=
35.7095563
142
= 0.2514757486
So, we get the figure here on the Coefficient of Variation (CV) of variable X that is
0.2514757486 .
𝐶𝑉 𝑌 =
𝑆 𝑌
𝑌
=
5.25324202
17.7
= 0.2967933345
So, we get the figure here on the Coefficient of Variation (CV) of variable Y that is
0.2967933345.

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When used via computer, we need to know the Software Coefficient of Skewness. So, here
the calculation of the Software Coefficient of Skewness has been given below:
6.7 Software Coefficient of Skewness:
Here, the table in where the calculation has been done is given below:
Sample Sales (X) 𝑋 − 𝑋 𝑋 − 𝑋
𝑆
^3
Profit
(Y)
(𝑌 − 𝑌) (
𝑌−𝑌
𝑆
)^3
1 100 -42 -
1.627026055
14 -3.70 -
0.349400035
2 130 -12 -0.03794813 13 -4.70 -
0.716162119
3 155 13 0.048247709 21 3.30 0.247890333
4 140 -2 -
0.000175686
17 -0.70 -
0.002365984
5 170 28 0.482081794 22 4.30 0.548432443
6 190 48 2.428680292 23 5.30 1.026940733
7 80 -62 -
5.233855222
14 -3.70 -
0.349400035
8 150 8 0.01124389 15 -2.70 -0.13577164
9 120 -22 -0.23383778 17 -0.70 -
0.002365984
10 180 38 1.2050288 20 2.30 0.083926919
11 140 -2 -
0.000175686
19 1.30 0.015154717
12 130 -12 -0.03794813 14 -3.70 -
0.349400035
13 250 108 27.66418646 38 20.30 57.70399549
14 100 -42 -
1.627026055
13 -4.70 -
0.716162119
15 120 -22 -0.23383778 15 -2.70 -0.13577164
16 110 -32 -
0.719608976
10 -7.70 -
3.149125343
17 120 -22 -0.23383778 14 -3.70 -
0.349400035
18 168 26 0.38598167 25 7.30 2.683405786
19 145 3 0.00059294 19 1.30 0.015154717
20 111 -31 -
0.654231903
16 -1.70 -
0.033889451
21 160 18 0.128074937 20 2.30 0.083926919
22 109 -33 -
0.789202507
15 -2.70 -0.13577164
23 100 -42 -
1.627026055
17 -0.70 -
0.002365984
24 132 -10 -
0.021960723
16 -1.70 -
0.033889451

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25 160 18 0.128074937 20 2.30 0.083926919
26 190 48 2.428680292 21 3.30 0.247890333
27 120 -22 -0.23383778 12 -5.70 -
1.277445376
28 130 -12 -0.03794813 13 -4.70 -
0.716162119
29 180 38 1.2050288 20 2.30 0.083926919
30 170 28 0.482081794 18 0.30 0.000186244
N=30 𝑋 =4260 (𝑋 −
𝑋 )=0
𝑋 − 𝑋
𝑆
3
=
23.24849993
𝒀 =531 (𝑌 −
𝑌)=
0.00
(
𝑌−𝑌
𝑆
)3
=
54.36990948
So, the thirty sample table is given upward on the basis of which the major calculation on
Software Coefficient of Skewness has been done.
Here, the skewness of sales is:
𝑠𝑘 𝑜𝑓 𝑠𝑎𝑙𝑒𝑠 =
𝑛
(𝑛 − 1) × (𝑛 − 2)
(
𝑋 − 𝑋
𝑆
)3
=
30
(30−1)×(30−2)
23.24849993
𝑠𝑘 𝑜𝑓 𝑠𝑎𝑙𝑒𝑠 = 0.8589347265
So, we have got that the skewness of sales is 0.8589347265.
Now, the skewness of profits is given below:
𝑠𝑘 𝑜𝑓 𝑝𝑟𝑜𝑓𝑖𝑡𝑠 =
𝑛
(𝑛−1)×(𝑛−2)
(
𝑌−𝑌
𝑆
)3
=
30
(30−1)×(30−2)
54.36990948
=2.008740498
So, we have got that the skewness of profits to be 2.008740498.
Now the Pearson’s Coefficient of Skewness will be described hereby:
6.8 Pearson’s Coefficient of Skewness:
Pearson’s coefficient of skewness for the sales variable X is given below:

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𝑆𝐾 𝑜𝑓 𝑠𝑎𝑙𝑒𝑠 =
3( 𝑋−𝑀𝑒)
𝑠
=
3(142 −136)
35.7095563
=0.5040667503
Here, we can see that the sales variable X has skewness of 0.5040667503.
Pearson’s coefficient of skewness for the profit variable Y is given below:
𝑆𝐾 𝑜𝑓 𝑝𝑟𝑜𝑓𝑖𝑡 =
3( 𝑌−𝑀𝑒)
𝑠
=
3(17.7 −17)
5.25324202
=0.3997531414
Here, we can see that the profit variable Y has skewness of 0.3997531414.
Now the correlation and regression for the variables X and Y will be expressed further:
6.9 Correlation and Regression Analysis:
The correlation and regression analysis will show the tendency of the data variables and their
effect on each other which means the strength of the linear relationship between the sales
variable X and the profit variable Y and the percentage of dependence of the variables on
each other.
Sample Sales (X) Profit (Y) XY X^2 Y^2
1 100 14 1400 10000 196
2 130 13 1690 16900 169
3 155 21 3255 24025 441
4 140 17 2380 19600 289
5 170 22 3740 28900 484
6 190 23 4370 36100 529
7 80 14 1120 6400 196
8 150 15 2250 22500 225
9 120 17 2040 14400 289
10 180 20 3600 32400 400
11 140 19 2660 19600 361
12 130 14 1820 16900 196
13 250 38 9500 62500 1444
14 100 13 1300 10000 169
15 120 15 1800 14400 225
16 110 10 1100 12100 100
17 120 14 1680 14400 196
18 168 25 4200 28224 625

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19 145 19 2755 21025 361
20 111 16 1776 12321 256
21 160 20 3200 25600 400
22 109 15 1635 11881 225
23 100 17 1700 10000 289
24 132 16 2112 17424 256
25 160 20 3200 25600 400
26 190 21 3990 36100 441
27 120 12 1440 14400 144
28 130 13 1690 16900 169
29 180 20 3600 32400 400
30 170 18 3060 28900 324
n=30
𝑋=
4260
𝑌=
531
𝑋𝑌 =
80063
𝑋2
=
641900
𝑌2
=
10199
So, the thirty sample table is given upward on the basis of which the major calculations on
correlation and regression have been done
Calculating Correlation:
Calculation of coefficient of correlation between sales and profits are given below where “r”
expresses the coefficient of correlation.
𝑟 =
𝑛 𝑋2−( 𝑋)2 ∗( 𝑛 𝑌2− 𝑌 2)
=
30×80063 −(4260×531)
30×641900)− 42602 ∗( (30×10199)− 531 2)
So, 𝑟 = 0.856779844
Here, we have found that the value of “r” is 0.841832989 which refers a strong positive
correlation between the variables. So, the variables are strongly positively correlated to each
other.
6.10 Calculation of coefficient of determination:
Coefficient of determination is going to be found by squaring the value of the coefficient of
correlation. So, we get the coefficient of determination:
𝑟2
= (0.856779844)2

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Which means, 𝑟2
= 0.7340717011
So, we have found the coefficient of determination to be 0.7340717011.
For finding out the rate of dependence of the depending variable on the independent variable,
a statistical calculation named regression equation will be discussed further.
Finding of Regression Equation:
The required estimated regression equation is given below:
𝑌 = 𝑎 + 𝑏𝑋
To find out the given equation, we need to find the actual value of its components. The major
components of this equation are “b” and “a”. Now lets discuss on the whole of its
components:
Here,
“𝑌” stands for the estimated value of the Y variable for X value.
“a” stands for an intercept.
“b” stands for the slope in the line. It measures the change in “𝑌” for each unit change in X.
X is any value that works as independent variable.
Now, to find out the value of “b” the following steps have been used:
𝑏 =
𝑛 𝑋2−( 𝑋)2
=
30×80063 −(4260×531)
(30×641900)− 42602
𝑏 =0.126041103
So, we have found the value of “b” which is 0.126041103.
Now we will find out the value of another major component of the regression equation that is
“a”. Here,
𝑎 = 𝑌 − 𝑏𝑋
S0, 𝑎 =
𝑌−𝑏 𝑋
𝑛
=
531−(0.126041103 × 4260)
30
= -0.197836668
So, we have found the value of “a” to be -0.197836668.

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Required regression equation:
So, the required regression equation will be found on the proper substitution of the values that
of “a”, “b”. Here, the regression equation is:
𝑌 = −0.197836668 + 0.126X
In this equation the desired result can be found on the substitution of the value of the variable
X. So, the independent value of variable X will determine the value of dependent variable Y.
Now, here a regression model has been built to show the effect of varying thirty variables on
the regression analysis. Here, the sales variables (X) are in the horizontal line and Profit
variables (Y) are in the vertical lines. To get a proper analysis, a chart has been provided to
have a proper synthesis
Figure 6.1 : Chart of Regression Model
So far the statistical techniques have been used to find out the practical situation of variable Y
on the basis of variable X in the perspective of Akij Foods and Beverage Limited. In the
analysis section all the findings will be described to compare between PRAN Foods Limited
and Akij Foods and Beverage Limited to get to the ultimate conclusion to fulfill this study.
y = 0.126x - 0.197
R² = 0.734
0
5
10
15
20
25
30
35
40
0 50 100 150 200 250 300
Profit(Y)
Sales (X)

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Chapter 07
Comparative Analysis

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Comparative Analysis on the Basis of the Sales and Profits measurements
through Different Statistical Techniques:
Statistical techniques are being provided in this chapter to measure the information that have
been got through our thirty variable sample collection. In this part a comparative analysis is
going to be performed through which we will be able to make sure whether PRAN Foods
Limited or Akij Foods and Beverage Limited is successful in customer satisfaction in the
Dhaka University area. It is mention worthy that the whole study is going to be held on the
basis of these two companies’ sales and profit performance.
Arithmetic mean Analysis between PRAN Foods Limited and Akij Foods and Beverage
Limited:
Here,
Name of Company AM of Sales/day (TK) AM of Profit/day (TK)
PRAN Foods Limited 171 22.633
Limited
142 17.7
So, we have come to the conclusion that in case of Arithmatic Mean (AM), PRAN Foods
Limited is satisfactory.
Median and mode Analysis between PRAN Foods Limited and Akij Foods and
Beverage Limited:
Here,
Name of Company
Sales/day (TK) Profit/day (TK)
Median Mode Median Mode
PRAN Foods Limited 178.5 210 23 20 & 23
Limited
136 120 17 14
Here, we can easily observe that PRAN Foods Limited is successful in making more median
and mode in sales and profits as well.
1st
Quartile and 3rd
Quartile Analysis between PRAN Foods Limited and Akij Foods
and Beverage Limited:
Name of Company
1st
Quartile 3rd
Quartile 1st
Quartile 3rd
Quartile

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PRAN Foods Limited 150 191.75 20 27
Limited
117.75 169.5 14 20
Here, we found that PRAN Foods limited is more successful than Akij Foods and Beverage
Limited in case of 1st
quartile and 3rd
quartile.
Mean Deviation and Standard deviation Analysis between PRAN Foods Limited and
Akij Foods and Beverage Limited:
Name of Company
Mean
Deviation
Standard
Deviation
Mean
Deviation
Standard
Deviation
PRAN Foods Limited 26.2 33.7588 3.6578 4.53
Limited
28.133 35.709 3.73 5.2324
Here, we can see that the risk level faced by Akij Foods and Beverage Limited is higher than
that of PRAN Foods Limited as the Mean Deviation and Standard Deviation is higher in case
of this analysis.
Coefficient of Variation Analysis between PRAN Foods Limited and Akij Foods and
Beverage Limited:
Name of Company CV of Sales/day (TK) CV of Profit/day (TK)
PRAN Foods Limited 0.91742 0.200124
Limited
0.25148 0.2968
Here, we have used Coefficient of Variation because of varying sales and profits per day.
Here, we find Akij Foods and Beverage Limited to be more risky.
Software Coefficient of Skewness and Pearson’s Coefficient of Skewness Analysis
between PRAN Foods Limited and Akij Foods and Beverage Limited:
Name of Company
Software
Coefficient of
Skewness
Pearson’s
Coefficient of
Skewness
Software
Coefficient of
Skewness
Pearson’s
Coefficient of
Skewness
PRAN Foods Limited -0.85 -0.67 -0.37 -0.24
Limited
0.86 0.504 2.009 0.398

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So, we find the PRAN Foods Limited more successful in case of Software Coefficient of
Skewness and Pearson’s Coefficient of Skewness.
Correlation and Regression Analysis between PRAN Foods Limited and Akij Foods and
Beverage Limited:
Name of Company
Coefficient of
Correlation
Coefficient of
Determination
PRAN Foods Limited 0.841833 0.7086
Limited
0.856779 0.734071
So, we find PRAN Foods Limited more successful in case of Coefficient of Correlation and
Coefficient of Determination.
Analytical Result of Analysis:
As almost all of the measurements support PRAN Foods Limited and the two companies are
positively correlated, we can come to the conclusion that PRAN Foods Limited has become
more successful in achieving more customer satisfaction in the Dhaka University area.

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Chapter 08
Conclusion

Comparative Statistical Analysis between PRAN Foods Limited and Akij Foods and Beverage Limited on Customer Satisfaction in the Dhaka University Area

Comparative Statistical Analysis between PRAN Foods Limited and Akij Foods and Beverage Limited on Customer Satisfaction in the Dhaka University Area

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