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Published by odllab, 2019-12-20 02:06:28

BBM203/03 Business Statistics

Course Code: BBM203/03
Course adapted by: Mr. Prakash V. Arumugam School of Business and Administration (SBA)

Professor Dr Zoraini Wati Abas
Content Adapter: Prakash V. Arumugam
Lead Instructional and Visual Designer: Fauziyah Md Aris Instructional and Visual Designers: Norliza Mhd Rodzi and Nurain Mohd Hassan Language Editor: Meilina Puteh
Margin Setting: Magic Khaw Yoke Yee
Cover Page and Content Design: Nurain Mohd Hassan
Prakash V. Arumugam
Online Digital Learning Lab (ODL Lab)
Instructional Design for Engaging Experiences (IDeX) Wawasan Open University
Acknowledgement: This course module has been adapted by the
School of Business and Administration (SBA) from the Online Course Materials for the
Business Statistics (BBM203/05) developed by Wawasan Open University.
First edition, December 2019
This course material was published to support the learning of students registered with Wawasan Open University. Wawasan Open University does not grant any degree, certification or credits based solely on your completion of this course material.
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise,
without prior written permission from Wawasan Open University.
© 2019 Wawasan Open University
Wawasan Open University is Malaysia’s first private not-for-profit tertiary institution dedicated to adult learners.

01 02
04 05
Part 1 |
Part 2 |
About the Course
Course Overview
Course Synopsis
Course Learning Outcomes Course Contents
Study Schedule Assessment Methods
Course Study Guide
Role of Statistics in Business Frequency Distributions and Graphs Data Description
Statistical Hypothesis Testing
Feedback Form
Part 3 |
Unit 1 Unit 2 Unit 3 Unit 4 Unit 5
Part 4 |
Part 5 |

Course Type Credit Hours Learning Hours
Course Title Course Code
: School of Business Administration (SBA) : Core Course
: 3 hours
: 120 hours
: Business Statistics : BBM203/03
Course Coordinator : Mr. Prakash V. Arumugam Email : [email protected]
Core Reading Materials : BBM203/05 Business Statistics
No. Activities
Study Learning Materials, Learning Activities and Self- Tests
8 2
2 Attending 5 Tutorial Classes (2 hours per class)
Participation in Online Forum Discussions
4 Completing the Course Assignments (CA1 & CA2)
5 Exam Revision
6 Examination
BBM203/03 Business Statistics
No. of Hours

Business Statistics undertakes to provide statistics concept to business students. Statistics transforms data into useful information. This information helps you to make decisions in your daily routines. In addition to manual computation, Microsoft Excel is being introduced as a tool in data analysis. This course contains five study units. The first unit introduces the nature of statistics.
This includes introduction to key statistical concepts, therole of statistics in business, data collection, sampling designs and the graphical and numerical presentation of descriptive statistics. Unit 3 discusses data description. Unit 4 focuses on fundamental concepts of probability, discrete and continuous probability distribution. Unit 5 covers hypothesis test for mean with known and unknown standard deviation.
By the end of this course, you should be able to:
1. Discuss and use various data collection methods needed for business decision
2. Evaluate data using standard statistical measures and present such data graphically
for accurate interpretation.
3. Apply basic probability distributions and hypothesis testing in problem solving.
Course topics include:
1. Role of Statistics In Business
2. Frequency Distributions and Graphs
3. Data Description
4. Probability
5. Statistical Hypothesis Testing
BBM203/03 Business Statistics
BBM203/03 Business Statistics

Quiz, Group Work, Presentation, Proposal, Essay, Annotated Bibliography, etc.
TOTAL 100%
Quiz, Group Work, Presentation, Proposal, Essay, Annotated Bibliography, etc.
The student will be assessed through the following methods
Note: The grade for a course is assigned based on the overall score, which combines both the contiuous assignments and the final examination components (please refer to the Student Handbook for details).
BBM203/03 Business Statistics 4
BBM203/03 Business Statistics 3

1.1 Introduction
1.2 Data Collection and Sampling Techniques
2.1 Data Presentation Technique
2.2 Graphical Display of Data
3.1 Measures of Central Tendency
3.2 Measures of Variation
3.3 Measures of Relative Standing
4.1 Basic Concepts
4.2 The Binomial Distribution
4.3 The Poison Distribution
4.4 The Normal Distribution
5.1 Fundamentals of Hypothesis Testing
5.2 Testing of Population Mean with Known Standard Deviation
5.3 Testing of a Population Mean with Unknown Standard Deviation,
Testing of a Population Variance and Testing of Two Independent Populations.
5.4 Hypothesis Testing and Non-Parametric Statistics
BBM203/03 Business Statistics 5 BBM203/03 Business Statistics 4

Unit 1

1.3 1.4
Learning Activity 1.1 Self-Check 1.1
Data Collection and Sampling Techniques
Learning Activity 1.2 Self-Check 1.2
BBM203/03 Business Statistics 6

This unit begins with an introduction to the role of statistics in business. This unit comprises five sections. The first section covers basic statistical concepts including the types of statistics: descriptive and inferential statistics, and also the types of data.
Apart from that, you will learn how to install the Microsoft Excel Add-Ins and use Excel Analysis ToolPack (ATP) to perform some statistical analysis. The next section will introduce various methods of collecting data which will be very useful to conduct sampling. Later in the section, sampling methods and their advantage will be elaborated.
By the end of this Unit 1, you should be able to:
1. Discuss the role of statistics in business.
2. Explain the key concepts in statistics.
3. Discuss various methods of data collection and sampling.
BBM203/03 Business Statistics 7

This section begins with an introduction to statistics and its application in the business world. You will be taught to differentiate between descriptive and inferential statistics; population and sample statistics. We are constantly exposed to some numerical information from newspapers or in our workplace, thus it is important to know whether what they represent is true.
Definition of statistics
The science of collecting, organising, analysing, interpreting and presenting the data for the purpose of decision making.
The role of statistics in business
In today’s business world, numerical evidence plays an important role in convincing clients, investors and decision-makers. Statistics becomes an essential tool to provide the numerical information in a scientific and convincing way. Various statistics processes and ways of presenting them numerically or graphically have become the norm for any business entity. In fact, statistics plays a major part in the success or survival of business entities.
BBM203/03 Business Statistics 8

Key statistical concepts
1 Descriptive and inferential statistics
There are two major branches of statistics: descriptive statistics and inferential statistics:
Descriptive statistics
Involves the data collection, classification, organisation,summarisation and display of data.
Inferential statistics
Utilises findings from a sample (a small segment of population) to generalise about the entire population.
The following example will illustrate the differences between these two types of statistics.
Example 1.1
Example 1
WOU has 300 students. In a recent study done on 30 students in WOU, 24 students stated they prefer to attend night classes rather than day classes. The study concluded that most of the students in WOU prefer to have night classes.
Descriptive statistics
24 of 30 students in WOU stated they prefer to attend night classes than day classes.
Inferential statistics
Most of the students in WOU prefer to attend night classes.
BBM203/03 Business Statistics 9

2 Population and sample
In most surveys or studies, the researcher would like to see the response of the entire population. For example, a survey is conducted to know the preferences for mode of transport in a major city. The researcher would like to know the preferences of each individual in that particular city. However, this exercise will take a lot of time, effort and money. The response of each individual in that city is known as the population of this study. To make a study more manageable, usually the study will be conducted on a small segment of the population in that city which will be picked randomly or according to certain criteria in order to effectively represent the actual population. The response of this segment of population is known as sample.
The following are the definitions of population and sample.
Is the collection of all outcomes, responses, measurements, or counts that are of interest to the researcher.
Is a subset (a small segment) of a population.
Population in general represents a large set. In Example 1 where a survey was conducted on WOU students, the population is the responses of all 300 WOU students while the sample is the responses of the 30 selected students.
3 Statistics and computer
In today’s world, most of the statistical processes are done by software and computer for faster and more accurate results. There are plenty of statistical software available in the market such as SPSS, Minitab and many more. However, in this course, you will be using the statistical application which is incorporated in to Microsoft Excel.
BBM203/03 Business Statistics 10

Types of data
When someone mentions data, the first thing that comes to your mind is numbers. Does data have to be numbers? The age of each of your family members is data and yes, they are in numerical values. The name of each of your family members is a type of data too. They are not in numbers. Data does not necessarily have to be in numerical form. Now, what is data? Data is information derived from observations, counts, measurements or surveys.
Example 1.2
The following variables are types of data.
1. Height of students in your class.
2. Time spent on internet by your classmate in a day.
3. Number of male students in this class.
4. Preference for drink in the morning.
There are two major types of data; qualitative data and quantitative data.
Qualitative data
1 Nominal data
Nominal data is usually represented by names, labels or qualities. You cannot do direct mathematical calculation with nominal data. However, there are cases where these data can be assigned codes in the form of numbers for statistical analysis. You are often required to state your gender, race or religion in most of the survey forms.
The variables in the form of your gender, race, etc. are types of nominal data. In some cases, for example, you need to state code 1 if you are male and 2 if you are female. However, these codes do not carry any weightage. A code 2 is not superior or inferior to code 1. These codes are introduced in nominal data for easier analysis. Instead of rewriting the gender or similar data repeatedly, it is much easier to state the code. For example, the gender of students in a certain class can be represented by the following table:
You can easily count the number of male and female students in this particular class.In the information technology age, the computer can recognise the code faster and compute the needed statistics faster rather than original attribute values.
BBM203/03 Business Statistics 11

2 Ordinal data
Ordinal data is similar to nominal, but comes with added information. The data is given order depending on their values. Ordinal data add order to data but differences between data entries are not meaningful.
Example 1.3
Assign 1 to 4 to the courses below with 1 as the most interesting course and 4 the least interesting course.
Interest Level
You assign, for example, 1 to English and 2 to Science, 3 to Arts and 4 to Mathematics. The interest level between English and Science is not necessarily the same as the interest level between Science and Arts.
BBM203/03 Business Statistics 12

Quantitative data
Quantitative data is also known as interval or numerical data. For this type of data, the value has a meaningful difference. Your age and marks in examination are some of the examples of interval data. If your age is 19 years old and your friend is 28 years old, the numerical value of your age and your friend’s age has a meaningful difference. You two were born 9 years apart.
Example 1.4
The following are the temperatures of five cities in Malaysia on 1 Aug 2011.
Kuala Lumpur
Alor Setar
Quantitative data can be further subcategorised into discrete variables and continuous variables. The data can be obtained through counting and measuring. Discrete variable is usually obtained through counting. The values of discrete variables are always whole numbers, 0, 1, 2, 3... which means it is always a finite or countable value.
Sometimes data can be categorised in a different manner. For example during a survey, the researcher may collect Time Series Data or Cross Section Data.
Times series data are collected at successive points in time. For example, if you are in a slimming programme, you will record your weight before the programme, 1 month after the programme, 2 months after the programme and so on to determine the effectiveness of the programme.
Cross section data are collected simultaneously at the same time or approximately at the same time. For example, you want to know which share counter dropped the most after Euro Debt crisis failed to reach a conclusion in November, 2011. You observed the closing price of top 20 counters on
30 Nov 2011 as reference points for percentage drop calculation.
BBM203/03 Business Statistics 13

Learning Activity 1.1
Please read Unit 1, pages 5 – 12 for further explanation and examples related to this topic.
Self-check 1.1
For each of the following data, categorise them into quantitative data (discrete or continuous data) or qualitative data (nominal or ordinal data).
BBM203/03 Business Statistics 14

We often read articles in newspapers with questionable statistics followed by dubious claims and conclusions. One way to make statistics look credible is in the way samples are collected. In this section, you will learn how to gather relevant data through various means. In statistical study, planning data collection and obtaining the data is an important component of the study. One has to make sure if the data is collected through reliable sources or not.
Data collection
Sources of data
The process of collecting data is often the bottleneck of the whole study. The researcher will have to decide how to gather data whether to gather the data from the actual source or use data gathered by some agencies such as the Census Board of a country, the Statistics Department or data gathered by other researchers.
It is much more economical and faster to use data already collected by other agencies. However, the question that miay arise is how reliable is the collected data for your study? The method used by that particular agency or individual is not known to you. So there are times the researchers prefer to collect the data themselves. If the data is collected by the researcher themselves, then the data is known as primary data. If the study uses data collected by some agencies, it is known as secondary data. There are a few methods that can be used to collect primary data.
BBM203/03 Business Statistics 15

How to collect the data?
Experiments and observation
In gathering data, a researcher needs to distinguish between experiment and observation. If an observational study is done on the subject, observation or measurement is taken directly from the subject without using any influence that change the responses of the subject. For example, you want to determine the number of people who patronise the supermarket in the morning. You collect the data passively and count the number of people going in and out. The data collected through this method has limited information as you only measure passively. In an experimental study, a treatment is deliberately provided to the subjects. Observation and measurement are done on the responses of the subjects before and after treatment.
Census and survey
One important issue that always plagues the researchers is whether to use the entire population or part of the population (sample). If the entire population is measured, the data is known as a census. If the study used sample data, then the measurement is known as a survey.
In a census or a survey, the information or data is collected by asking questions. The simplest form of responses will be ‘Yes’ and ‘No’. In a better measurement scale, the respondents can choose their responses based on their feeling such as follows:
1. Strongly disagree
2. Disagree
3. Neutral
4. Agree
5. Strongly agree
This is known as ‘Likert’ scale. Some choose to ask open-ended questions but the researcher must find ways to convert the responses to numerical value for statistical analysis. The census or survey can be conducted through personal interview or through filling up a survey form (you might have come across some surveyors in supermarkets asking you to fill up simple questionnaires). Some researchers use telephone conversation while some will post or email their questionnaires to the targeted respondents.
BBM203/03 Business Statistics 16

Sampling methods
As discussed earlier, conducting a study on the entire population is time-consuming and also very expensive unless the intended population is small. Most of the studies will use samples. How does one get a sample of the population that represents the population itself? It is not a matter of getting a group of respondents and labelling them as samples. There are a few techniques of sampling.
Simple random sampling
A random sample means there is no bias involved in deciding the proper sample. In other words, each sample group in the population has an equal opportunity to be selected as a sample. In fact, each respondent in the population has an equal chance to be part of the sample. Researchers usually use a computer-based random number generator to pick a sample. A number is assigned to each element in the population. A random number table is generated using Excel. The element carries the same number as the random table number selected as sample. In certain cases, sampling with replacement is used. The selected number will be placed back in to the population to ensure that the chances of being selected among the respondents remain the same.
Stratified random sampling
This technique is used to ensure each segment of the population has an equal chance of being represented in the sample. Each segment of a population with common characteristics is known as strata. In some cases, to ensure fair representation in the sample, each segment is sampled in proportion according to their actual percentage in the population.
For example, if there are 60% males and 40% females in the population, the population will be divided in to two distinct groups, i.e., male and female. For a 50-respondent sample, 30 male and 20 female respondents will be chosen randomly from each group respectively.
One advantage of stratified sampling is that besides obtaining information on the entire population, you get to compare statistics among the strata.
BBM203/03 Business Statistics 17

Systematic sampling
This is another technique of sampling. This is much easier to obtain compared with other techniques.
The respondents are arranged in a sequential order and every kth respondent is chosen as sample.
You have 1,000 bags of sugar. Each is 1 kg in weight. The study asked you to check the accuracy of the weight of the bags. The researcher needs 50 samples, so he chooses every 20th sugar bag in the production line. However, this technique has weaknesses. If the packaging equipment has a flaw in weighing the 8th package in every cycle, the problem cannot be detected at all.
Cluster sampling
This technique is popular for a large population. The researcher will choose a few segments of the population and then take all the respondents in the segment as sample. This type of sampling is different from stratified sampling.
For example, if a study is conducted on the behaviour of students in a particular school, the researcher randomly picks a few classes in the school and use all the students in the chosen classes as samples.
Quota sampling
This technique is faster and cheaper. The researcher predetermines the number of samples according to certain criteria. The selection of the sample is usually not random.
For example, the study involves the spending habits of the population in Kuala Lumpur. The researcher might plan to have 5 males each in 4 age groups and 5 females each in the same 4 age groups. He or she might also decide to have 2 from the upper income, 2 from the middle income and 1 lower income person for every group.
The first respondent who fits the criteria for each category will be taken as sample. The results from this kind of sampling are not so accurate. Generalisation made based on this result must be done with extra caution.
population size sample size
BBM203/03 Business Statistics 18

Convenience sampling
This is the simplest technique of sampling. The researcher will get the required samples by taking the first available respondent. For instance, to gauge people’s opinion on the annual national budget, the researcher will get the opinions of the first 50 people he comes across. The result can be biased.
Sampling and non-sampling error
In any study, the risk of error is always there. There are two categories of errors: one is contributed by the sampling technique and the other is contributed by the sampling process. Sampling error is caused by poor representation of the population in a sample. The difference in measurement between the sample and population will usually be obvious. Non-sampling error is mainly caused by sample design, sloppy data collection, and inaccurate measurement tools such as the questionnaires, statistical tools and so on.
BBM203/03 Business Statistics 19

Learning Activity 1.2
Please read Unit 1, pages 5 – 12 for further explanation and examples related to this topic.
Self-check 1.2
Categorise the sampling techniques used below as either simple random sample, stratified sampling, systematic sampling, cluster sampling or convenience sampling.
1. A local municipal council plans to conduct a survey to gauge the level of services provided such as rubbish collection, drain cleaning, etc. The suggested sampling techniques are:
a. Assign each household a number and use computer-generated random numbers to select the sample.
b. Divide the municipality into 20 zones. Randomly choose 4 zones and take entire households in the chosen zone as samples.
c. Number the entire household in the municipality according to alphabetical order of the name of the household head. Pick every 100th household in the list as sample.
d. Group the household into upper class, upper-middle class, lower-middle class and lower class. Then choose randomly 50 households from each group.
e. Send 20 research assistants to different areas and instruct them to interview the first 5 households that they come across.
BBM203/03 Business Statistics 20

Now that you have completed Unit 1, you should be able to:
1. Discuss the role of statistics in business.
2. Explain the key concepts in statistics.
3. Discuss various methods of data collection and sampling designs.
Anderson, D. R., Sweeney, D. J., &Williams, T. A. (2014). Statistics for business and Economics (12th ed.). South-Western: Cengage Learning.
Keller, G. (2018). Statistics for management and economics (11th ed.). South Western: Cengage Learning.
Wawasan Open University(2013). Unit 1, BBM203/05 Business Statistics (pp.21-36). Penang: Wawasan Open University.
BBM203/03 Business Statistics 21

Unit 2

2.3 2.4
Data Presentation Technique
Learning Activity 2.1 Self-Check 2.1
Graphical Display of Data
Learning Activity 2.2 Self-Check 2.2
BBM203/03 Business Statistics 24

Raw data is the data obtained from data collection methods such as experiments, observations, census, survey and counting. It is not easy to analyse the data if they are presented as raw data. To be meaningful, they should be organised in a systematic way such as in table form or graphical display such as in a bar chart, pie chart and histogram.
In this unit , various methods of organising and presenting data will be delivered. It is important to organise and present your data in a meaningful form so that the message can get across to the intended target.
By the end of this Unit 2, you should be able to:
1. Compute the distribution frequency.
2. Represent data graphically.
BBM203/03 Business Statistics 25

For example, if you want to know the trend or the performance of students in certain subjects, you may collect their test marks.
The data below show marks (in percentage) obtained by 30 students in a Calculus test.
78, 39, 48, 90, 85, 68, 74, 93, 57, 59, 42, 60, 72, 49, 50 65, 32, 64, 80, 75, 88, 72, 61, 36, 49, 56, 70, 85, 58, 95
By looking at the given data, you cannot say much about the performance of the students. You need to organise the data in a way where the audience can see the trend and the performance of the students without much analysis.
The simplest way to organise raw data is the array. The array is an arrangement of data in either ascending order (from the lowest value to the highest value) or descending order (from the highest value to the lowest value). The array can be done manually or by using software such as Excel.
Let us look at the following example on how to arrange data in an array.
Example 2.1
The following data is the height (in cm) of 12 selected male students in class Z. 167, 155, 169, 172, 148, 160, 151, 163, 170, 168, 165, 144
1. Arrange the data in ascending order.
2. Arrange the data in descending order.
Please refer to the course material Unit 1, pg. 22 for the solution
BBM203/03 Business Statistics 26

Frequency distribution
If you are dealing with large sets of data, it is useful to consolidate them in a table. You can group the data into classes. All the data are listed along with the frequency with which each data class occurs.
The frequency table is a way of presenting data in an easier form for analysis. You can deduce the pattern of the data by observing the frequency table.
Example 2.2
The grades of 20 students in a Mathematics examination are shown below. A, B, D, B, C, A, B, D, B, B, C, C, D, B, A, C, B, B, B, A
Construct a frequency table for the above data. Solution:
BBM203/03 Business Statistics 27

Grouped frequency distribution
For a larger set of data, it will be more practical to condense the data into a grouped frequency table. This frequency table groups data into classes and count the total number of appearance of the data in each class.
You need to decide on a few factors before constructing the frequency table.
1 Number of classes
The more classes you use, the narrower the class interval width will be. A smaller number of classes increase the width of class interval. In this aspect, you might lose important details and it might defeat the purpose of the frequency table.
2 Class interval width
The formula is as follows. Round up the number after calculation:
Class interval width
Range Number-of-classes
Example 2.3
The following are the marks obtained by 24 students in question 1 of a Calculus test.
Calculate the class size in a frequency table with 5 classes.
Refer to Unit 1, pg. 26 for the answers.
BBM203/03 Business Statistics 28

Relative frequency distribution
The relative frequency table computes the frequency of each class in relative to total frequency. You can observe the proportion of data in each class. The relative frequency of each class is obtained by dividing the class frequency with total frequency. The total relative frequency is always 1. Look at the following example on how to construct a relative frequency table.
Example 2.4
Given the frequency table consists of marks obtained in Example 2.3 construct a relative frequency table.
Refer to Unit 1, pg. 27 for the answers.
BBM203/03 Business Statistics 29

Learning Activity 2.1
Please read Unit 1 pg. 21-29 for a full description of the distributions as well as the solutions to some of the examples given.
Please watch this video as it provides a deeper understanding of the characteristics of frequency distribution.
Duration : 5.19 minutes
BBM203/03 Business Statistics

Self-check 2.1
A survey is conducted on the number of children in 60 households in Alor Setar. Construct a frequency table for the following data.
Please check the solution in Unit 1, pg. 52.
BBM203/03 Business Statistics 31

Data can be presented in various ways as you have seen in the early part of this section. Graphical method is one way to display data in an attractive way. Data presented in graphical ways are more eye-catching and easy to examine. In this section, you will look at four types of graphical display: ogive, pie chart, bar chart and histogram.
1 Ogive
An ogive is a graphical method for displaying a cumulative frequency table. You can approximate proportion of the collected data by using ogive. Constructing an ogive is easy; just plot the cumulative frequency to the upper boundary of the respective classes.
Example 2.5
Given the frequency table consisting of marks obtained in Example 3 construct an ogive and then find the marks obtained by half of the students.
Source: Once you have done so, please check the solution in Unit 1 pg. 30-31.
Watch this video, before you try constructing the ogive. Duration: 5.08 minutes.
BBM203/03 Business Statistics 32

2 Histogram
Histogram is a graphical method of displaying frequency table. A bar is used to represent each class and the height of each bar is the class frequency. In histogram, horizontal axis represents classes and vertical axis represents frequency of each class.
Example 2.6
Given the frequency table consisting of marks obtained in Example 3 construct a histogram based on the given table.
Please check the solution in Unit 1, pg. 32.
3 Pie chart
A pie chart is a circular chart in which the circle is divided into sectors. Each sector represents an item in a data set which matches the amount of the item as a percentage or fraction of the total data set. Pie charts are useful for comparing different parts of a whole amount. To construct a pie chart, first you need to calculate the percentage representing each item.
Example 2.7
Given the frequency table consists of marks obtained in Example 3 compute the following numbers for each class that is required in a pie chart.
1. the angle
2. the percentage
Construct a pie chart based on your calculation above.
Please check the solution in Unit 1, pg. 33 & 34.
BBM203/03 Business Statistics 33

4 Bar chart
Bar charts are drawn with parallel bars placed vertically (or horizontally).The width of each bar and the spacing between the bars are kept the same to avoid misleading representations. The height of the bar represents the frequency of the class.
Example 2.8
Given the frequency table consisting of marks obtained in Example 3 construct a bar chart based on the frequency table.
Once you have done so, you may compare your answers with the suggested solution in Unit 1, pg. 35.
Watch this video on how to draw a bar chart. Using what you have learnt, draw the bar chart. Duration: 5.13 minutes.
BBM203/03 Business Statistics 34

Learning Activity 2.2
Please read Unit 1, pg. 35-36 for a description on the many shapes of data distribution.
Please watch this video which gives a broad description of the graphical presentation of data distribution. Duration : 3.17 minutes
Source: Once you have done that, please try out Self-Check 2.2.
BBM203/03 Business Statistics 35

Self-check 2.2
1. The following data are the temperature readings from 40 healthy adults in a company.
a. Construct a frequency table with 11 classes.
b. Construct a relative frequency table.
c. Construct a cumulative frequency table.
2. Use the frequency table created in (1) to construct
a. Ogive
b. Histogram
c. Pie Chart
d. Bar Chart
Suggested answers to Self-Check 2.2 can be found in Unit 1, pg. 67 - 70.
BBM203/03 Business Statistics 36

Now that you have completed Unit 2, you should be able to:
1. Compute the distribution frequency
2. Represent data graphically.
Anderson, D. R., Sweeney, D. J., &Williams, T. A. (2014). Statistics for business and Economics (12th ed.). South-Western: Cengage Learning.
Keller, G. (2018). Statistics for management and economics (11th ed.). South Western: Cengage Learning.
Mays, S. (2011, Sep 6). Ogives [Video file]. Retrieved from
Quantitative Specialists. (2018, Jan 22). How to calculate a frequency distribution table: frequency table [Video file]. Retrieved from
Stevens, S. (2014, Oct 27). Making a simple bar graph in excel [Video file]. Retrieved from
Tutorials Point (India) Pvt.Ltd. (2018, Jan 22). Statistics: introduction on graphical representation of data [Video file]. Retrieved from ttps://
Wawasan Open University(2013). Unit 1, BBM203/05 Business Statistics (pp.21-36). Penang: Wawasan Open University
BBM203/03 Business Statistics 37

Unit 3

3.4 3.5
Measures of Central Tendency
Learning Activity 3.1 Self-Check 3.1
Measures of Variation
Learning Activity 3.2 Self-Check 3.2
Measures of Relative Standing
Learning Activity 3.3 Self-Check 3.3
BBM203/03 Business Statistics 40

When you are given a set of data, how do you make sense of it. The data alone is meaningless without some form of measurement that would add meaning to all the numbers in the data.
In this Unit, you will learn how to compute measurement of central tendency and variability. These measurements are simple and a good way to explain the distribution of your data. In the last section, you will learn the measures of relative standing. This measurement is important to see the relative distribution of a set of data.
By the end of this Unit 3, you should be able to:
1. Compute the measures of central tendency.
2. Compute the measures of variation.
3. Compute the measures of relative standing.
BBM203/03 Business Statistics 41

Central tendency measure is one way to describe a set of data. For example, there are more than 5000 private colleges in Malaysia which charge different rates of tuition fees. On average, the tuition fee to study a business undergraduate course in a local college is about RM10,000 per semester. Does this mean each college charges the same amount? Of course not. The amount RM10,000 is derived through some statistical process. One of the processes is measurement of central tendency. The three types of measures of central tendency are mean, median and mode.
1 Mean of ungrouped data
Mean is the total sum of the data divided by the number of data.
Table 3.1 Differences between population mean and sample mean
In most cases, it is not possible to compute the mean of a population as discussed in the earlier session. The following example shows how to compute the mean of a sample.
Example 3.1
Kader spent RM212 in June, RM265 in July, RM200 in August and RM241 in September for food. Compute the monthly mean Kader spent on food.
BBM203/03 Business Statistics 42

On average, Kader spent RM229.50 per month on food. However, this cannot represent the monthly amount Kader spent on food throughout his life. Why?
Find the mean of the following data.
32, 35, 49, 12, 25, 34, 25, 30, 38, 32
2 Mean of grouped data
In grouped data, there is another element to be considered, the frequency, f of each data.
The formula for mean of grouped data:
BBM203/03 Business Statistics
Table 3.2 Mean of grouped data

The following table shows the age of students. Find the mean age of the students.
Please check Unit 1, pg. 40 for the answers.
In a grouped data with interval classes, you need to find the midpoint of each class and denote it as x. Look at the following example:
The following frequency table shows the marks obtained by 24 students in Example 2.3.
Calculate the mean marks.
Please check Unit 1, pg. 41 for the answers.
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Median is another measure of central tendency and is obtained by taking the middle data after rearranging the data in ascending or descending order. In the case of even data, we take the average of two middle data.
1 Median of ungrouped data
Find the median of the following data.
(a) 4, 7, 2, 6, 3
(b) 32, 35, 49, 12, 25, 34, 25, 30, 38, 34
Arrange data according to descending order first.
(a) 2, 3, 4, 6, 7
The middle number is 4, then the median is 4.
(b) 12, 25, 25, 30, 32, 34, 34, 35, 38, 49
There are two middle data, 32 and 34. The average of these data is 35 and the median is 33.
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2 Median of grouped data
In a grouped data, the data is arranged in ascending order. The median data depend on whether the number of data is odd or even. In the case of frequency table with interval classes, you use the mid- point of the class.
Table 3.3 Differences between odd data and even data
Example 3.6
Find the median of the following data: (a)
Please check your answers with the suggested solutions in Unit 1, pg. 44.
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