Two chapter 2 statistics

18 | P a g e C h a p t e r 2 : F r e q u e n c y T a b l e
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CHAPTER
2
[Frequency Distribution Table]
Subtopics:-
[2.1] [Introduction Of Frequency Table]
[2.2] [Organizing Qualitative Data]
[2.3] [Organizing Quantitative Data]
[2.4] [Frequency Distribution]
[2.5] [Constructing A Frequency Table]
[2.6] [Single Value Groups]
[2.7] [Relative Frequency]
[Synopsis]
Recognizing the application of business research statistics into frequency
distribution analysis.
[Learning Objectives]
[To Understand Sources Of Raw Data Into a frequency
distribution]
[To Construct Tables and Graph Application
[To Recognize How Business Research Statistics develop
Frequency Tables for qualitative and quantitative data
variables]

[2.1] [Introduction Of Frequency Table]
[The frequency distribution table is provided to analyze data which is needed to divide
the data into groups called classes and count how many times each class is represented.]
Respondent Sampling
1,2,3,4,5,6,7,8, 9,10,11,12,13,14,15,16,17,18,
19,20,21, 22,23,24,25,26,27,28, 29, 30
Example
Respondent 10 answer A Scaling 5 For -
Question 1
Respondent 2 answer B Question 2
[2.1.1] [How To Establish The Frequency Table]
Figure 2.1: Ways to Organize Data Into categories To Establish The Frequency Table
MAJOR (CATEGORY)
Tally Frequency
Business //// / 6
Economics /// 3
MIS //// / 6
Marketing // 2
Other //// /// 8
Sum= 25

[2.1.2] [Definition Of Qualitative & Comparison Data Versus Quantitative]
[According to Cambridge Dictionary in UK English, it defines the word of qualitative
research as a type of market research that aims to find out people’s opinions and feelings
rather than information which easily can be shown in numbers. Also, generally it is defined
as robustness analysis of mathematical statistics [(“The Oxford Dictionary Statistical Terms
Mathematics”, (Yadolah Dodge (2006); (Hanson, DL, Koopmans, C.H (1964) (1887 – 1896)].
The role of frequency distribution table is for organizing the qualitative data by creating
one that mutually exclusive. This means that two classes must be developed not
overlapping to the other class’s distribution.]
2.1.2a [Table Elements Of Qualitative & Comparison Data Versus Quantitative]
Table 2.1: Quantitative Versus Qualitative Data Analysis
Qualitative Quantitative

[2.2] [Organizing Qualitative Data]
[2.3] [Organizing Quantitative Data]
[Qualitative is famously used as the grounded field research based that may be
applied by the business statisticians as well for social research. This definition has been
discussed by the scholar expertise called Paivi Eriksson and Anne Kovalainen,
“Quantitative Methods Business Research : A Practical Guide”, SAGE Publication (2011),
[Statistics supplies the techniques that help to condense
large data sets by using tables, graphs and summary
measures. We see such tables, graphs and summary
measures in newspapers and magazines every day. At a
glance, these tabular and graphical displays present
information on every aspect of life. Consequently,
statistics is of immense importance because it provides
efficient and effective methods for summarizing and
analysing information.]
[When data are collected, the information obtained from
each member of a population or sample is recorded in the
sequence in which it becomes available. This sequence of
data recording is random and unranked.]
[Classify Study Area
Interest]
[Categorize the mark tally with symbol]
[Read, Hear, Write
The Sample
Population’s
Perception Rating]
[Total all frequencies entries]

(2012), (2013), (2014), (2016), Cited 2297. According to Cambridge English dictionary, it
defines the quantitative which relating to numbers or amounts. Whereas, the
www.businessdictionary.com.my, the quantitative data analysis is associated with an
objective, quantify a thing which is phenomenon that is measurable and verifiable such
as lightness or heaviness. However, the Oxford dictionary defines the quantitative relating
to measurement by the quality rather than its quantity [“Quality rather Than Quantity.
Assessing Individual Research Performance”, J A Sahel (2011), Cited by 46, Hence, with
the integration of quantitative and qualitative data information it may produce mix
methods [Integrating Quantitative and Qualitative Research. How is it done?; A Bryman
(2006), Cited by 2517] from the organizing qualitative and quantitative data, this will lead
to a better way to handle as well as to satisfy the lowest value which fits into the first class
width classification.]
[2.4] [Frequency Distribution]
In the frequency distribution table for the 32 test scores must be compared within the
class range of five and size class within 1 to 10 comparisons that may justify as a fair
range estimation. Below is the information on the number of TV sets per household for 50
randomly selected households. Use classes based on a single value to construct a
grouped-data table for these data.
.
[2.4.1 Upper Class Boundary]
[The upper class boundary is given by the midpoint of the upper limit of one class and the
lower limit of the next class.]
[Example: Class of 301 – 400]
301 – 400 400 + 401 = 400.5
2
401 – 500
Lower Limit
Upper
Limit
Number of TVs Frequency
0 1
1 16
2 14
3 12
4 3
5 2
6 2
Total 50
Because each class is based on a single value, the
midpoint of each class is the
same as the class.

[2.4.2 Lower Class Boundary]
[The class boundary is given by the midpoint of the upper limit of one class and the
lower limit of the previous class. Example Class of 301 – 400]
300
301 – 400
301 + 300 = 300.5
2
[2.4.3 Mid Point]
[The midpoint is obtained by dividing the sum of the two limits for the two
boundaries of a class by 2. Example: Class of 301 – 400]
301 - 400
301 + 400 = 300.5
2
401 - 500
Lower
Limit
Salary(RM) f Lower boundary
301-400 9 301+300 = 300.5
2
401-500 16 401+400 = 400.5
2
501-600 33 501+500 =500.5
2
601-700 20 601+600 = 600.5
2
Lower
limit
Upper
Limit
Lower limit + Upper
Limit
2

[2.4.4 Class Width]
[The class width is the difference between two limits of a class and add by 1 depends to
the data or number in the table.]
Class of 10 - 20 Class of 2 – 0.5 Class Of 0.05 – 0.10
Class Width
20 – 10 + 1
Class Width
0.5 – 0.2 + 0.1 = 0.4
Class Width
0.10 – 0.05 + 0.01 = 0.06
[Example:]
[The following table gives the frequency distribution of the duration ( in minutes ) of 100
long-distance phone calls made by persons using long distance service:]
Find:-
1. The number of classes in the table is _______
2. The class width is ___________
3. The midpoint of the third class ____________
4. The lower boundary of the second class is __________
5. The upper limit of the second class is_________________
6. The sample size is _____________
4-0+1=5
5
(10+14)/2=12
(5+4)/2=4.5
9
100

[2.5] [Constructing Frequency Table]
[In constructing a frequency distribution, attention must be given to selecting the
appropriate number of class grouping for the table, obtaining a suitable class interval, or
width of each class grouping, and establishing the boundaries of each class grouping to
avoid overlapping.]
[2.5.1] [ Steps Of Constructing Frequency Table]
2.5.2 Selection On The Number Of Classes]
CALCULATION OF NUMBER OF CLASSES (Stages Flow)
Number of classes = 1 + 3.3 Log n
Class Mark = lower class + upper class limit
2
= (40 +50) / 2 = 45
The other class marks are 55, 65, 75, 85, and 95.
Figure 2.4: Grade Scores Frequency Table
Score Frequency
40 – 50 3
50 – 60 2
60 – 70 4
70 – 80 9
80 – 90 7
90 – 100 7
We use the Stages Flow to get the
number of classes.

[2.5.3] [Calculation Of Class Width]
Class width = Largest Value – Smallest Value
Number of classes
[2.5.4 Set The Lower Limit Of The First Class Or Starting Point]

[2.6] [Single Value Groups]
[Example]
[The following data give the heights (in inches) or a random sample of 30 National
Basketball Association players selected from that data set. Construct a frequency
distribution table.]
[2.6] [Relative Frequency]
81 84 79 76 73 74 77 82 75 81
76 76 80 82 78 72 80 83 80 77
78 78 79 84 73 86 83 79 83 79
Steps
Step 1:Number of classes =1 + 3.3 log n
= 1 + 3.3 log 30
= 5.87
≈6 Classes
Step 2: Class width
In these data, the minimum value is 70 and the maximum value is 86.
Suppose the number of classes is 5, so
Class width = (86-70) /6 = 2.66 ≈ 3
Step 3: Lower limit of the 1st class
Suppose we round this approximate width to 3 (depends to the data). The lower limit of
the first class can be taken as 70 (smallest number in the data).
First class = 70-72 inch
Step 4: Form Frequency Distribution Table
We read each value from the given data and make a tally mark. After the tally column
is completed, we account the tally marks for each class and write those numbers in the
third column. This gives the column of frequency.

Relative frequency = Frequency of each class
Sum of all frequencies
[2.7] [Relative Frequency Table]
[2.7.1 Set The Relative Frequency On Percentage]
Percentage Relative frequency x 100
6/15 =0.4
3/15 =0.2
6/15 =0.4
TOTAL = 0.4 +0.2+0.4=1.00

[2.7.2] [Cumulative Frequency Distribution]
Score Frequency Relative Frequency
%
Cumulative
40 – 50 3 9.4
[((3/32) x 100)]
32
[32 (total f)]
50 – 60 2 6.3
[((2/32) x 100)]
29
[32-3]
60 – 70 4 12.5
[((4/32) x 100)]
27
[29-2]
70 – 80 9 28.1
[((9/32) x 100)]
23
[27-4]
80 – 90 7 21.9
[((7/32) x 100)]
14
[23-9]
90 – 100 7 21.9
[((7/32) x 100)]
7
[14-7]
32
Figure 2.5: Score Grade Assessment Performance Cumulative Frequency Table
[One variation on a frequency distribution it can be made a relative frequency
table. The frequencies are converted into percentage of the total into different sizes. On
the top (right) is an example relationships frequency distribution for the 32 test scores and
relative frequencies do not total to 100% due to rounding.]
[The percentage of scores from 60 to 90 is higher for the pre-calculus exam than the
statistics exam, whereas the percentage of scores from 40 to 60 and 90 to 100 is lower.
Another variation of the frequency distribution is the cumulative frequency distribution. In
such a distribution we list how many values are in that class or lower. To obtain cumulative
frequencies, we add our way down the frequency column. We also can create
cumulative greater than frequency distribution values are in the class labeled 70 – 80
there are 27 cumulative frequency distributions in the last four classes in a greater than
frequency distribution for the at least 60.]
Total Frequency (f)

[References]
1. Fundamentals of Business Statistics, 6th
Edition, Dennis J. Sweeney, Thomas A. William, David R.
Anderson, Thomson South Western, 2013.
2. Statistics, 3rd
Edition, Lau Too Kya, Phang Yook Ngor & Zainudin Awang, Oxford Fajar, 2015
Supplementary References Materials:
1. Basic Statistics for Business & Economics, 8th
Edition, Douglas A. Lind, William G. Marchall,
Samuel A. Wetern, Mc Graw Hill, 2012.
2. Introductory Statistics, Neil A. Weiss, 8th
Edition, Pearson, 2011.

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