Frequency Distribution.pdf

vA frequency distribution is the
organization of raw data in table
form, using classes and
frequencies.
vThe division of counts
(frequencies) of number of
scores that fall into each class
(category) is called frequency
distribution.
3
FREQUENCY DISTRIBUTION

vFrequency distribution is a most
convenient way of organizing
raw data.
vThe reasons for constructing a
frequency distribution are as
follows:
§ To organize the data in a
meaningful, intelligible way.
§ To enable the reader to make
comparisons among different data
sets.
4

vThe original form of data is
called raw data.
vLittle meaningful information
can be obtained from raw data
5
RAW DATA

vEach raw data value is placed
into a quantitative or qualitative
category called a class.
6
CLASS

vThe frequency of a class is the
number of data values contained
in a specific class.
vFrequency is the number of
times that a repeated
observation occurs.
7
FREQUENCY

v‘Message Portal’ is a software
project that comprises of 30
different modules. On first
deployment to client, several
bugs were identified in each
module of project in Staging
environment. No. of bugs of
each module varies with respect
to each other.
8
CASE STUDY # 1 (OPEN BUGS)

vNumber of bugs in each module
is enlisted below:
v23, 55, 13, 67, 43, 32, 15, 9,
27, 26, 34, 39, 42, 55, 61, 31,
68, 56, 35, 48, 57, 26, 64, 8,
11, 38, 23, 71, 13, 68.
9

vRaw Data
§ In previous Slide, the data in its
original form is raw data.
§ No useful information about bugs
can be obtained from this form of
data.
10

11
Class Limits Tally Frequency
8-17 |||| | 6
18-27 |||| 5
28-37 |||| 4
38-47 |||| 4
48-57 |||| 5
58-67 ||| 3
68-77 ||| 3
Total: 30

vClasses
§ The classes in this distribution are 8–17,
18–27, etc.
§ The data values 8, 9, 10, 11, 12, 13, 14,
15, 16, 17 can be tallied in the first class;
18, 19, 20, 21, 22, 23, 24, 25, 26, 27 in
the second class; and so on.
12

vInterpretations
§ Frequency distribution table shows that 8-
17 number of bugs were reported in each
of 6 modules of ‘Message Portal’.
However, having small number of open
bugs, these 6 modules are more stable in
this project.
§ 3 modules are very critical with respect to
quality, because these modules have 68-
77 number of open bugs.
13

vThe cumulative frequency for a
class is the sum of the
frequencies of that class and all
the previous classes.
14
CUMULATIVE FREQUENCY

15
Class Limits Frequency
Cumulative
Frequency
8-17 6 6
18-27 5 11
28-37 4 15
38-47 4 19
48-57 5 24
58-67 3 27
68-77 3 30

vThe relative frequency for any class is
obtained by dividing the frequency for
that class by the total number of
observations.
vFormula:
Relative Frequency= Frequency of class / Total no. of observation
16
RELATIVE FREQUENCY

17
Class
Limits
Frequency
Relative
Frequency
Cumulative
Frequency
8-17 6 6/30 = 0.2 6
18-27 5 0.167 11
28-37 4 0.133 15
38-47 4 0.133 19
48-57 5 0.167 24
58-67 3 0.1 27
68-77 3 0.1 30

vThe cumulative relative
frequency for a class is the sum
of the relative frequencies of
that class and all the previous
classes.
18
CUMULATIVE RELATIVE FREQUENCY

19
Class
Limits
Frequency
Relative
Frequency
Cumulative
relative
Frequency
8-17 6 6/30 = 0.2 0.2
18-27 5 0.167 0.367
28-37 4 0.133 0.5
38-47 4 0.133 0.633
48-57 5 0.167 0.8
58-67 3 0.1 0.9
68-77 3 0.1 1

vThe values or numbers
specifying a class are called
class limits.
vThe smallest value specifying a
class is called lower class limit
while the largest value
specifying a class is called upper
class limit.
20
CLASS LIMITS

v8-17, 18-27 etc. values are
called class limits.
v8 is lower class limit and 17 is
upper class limit of class 8-17
21
CLASS LIMITS

vClass boundaries are the numbers used
to separate classes, but without the
gaps created by class limits.
vThey are obtained by increasing the
upper class limits and decreasing the
lower class limits by the same amount
so that there are no gaps between
consecutive classes.
vThese boundaries are also called
precise limits or true limits.
22
CLASS BOUNDARIES

vClass limits should have the same
decimal place value as the data, but
the class boundaries should have one
additional place value and end in a 5.
vFormulas:
§ Lower Boundary = Lower Limit - 0.5
§ Upper Boundary = Upper Boundary + 0.5
23
CLASS BOUNDARIES

24
Class Limits Class Boundaries Frequency
8-17 7.5-17.5 6
18-27 17.5-27.5 5
28-37 27.5-37.5 4
38-47 37.5-47.5 4
48-57 47.5-57.5 5
58-67 57.5-67.5 3
68-77 67.5-77.5 3

vA frequency distribution with an open-
ended class is called an open-ended
distribution.
vOpen-ended distribution is used to
include outliers into class limits.
25
OPEN-ENDED DISTRIBUTION

26
Class Limits Frequency
Below 17 6
18-27 5
28-37 4
38-47 4
48-57 5
58-67 3
68 and above 3

vClass marks or midpoints of the
classes are obtained by adding
lower class limits to the
corresponding upper class limits
and dividing by 2.
vFormula:
Xm = (Lower Limit +Upper Limit) / 2
27
CLASS MARK (MIDPOINTS)

vClass marks can also be obtained by
adding lower class boundary to the
corresponding upper class boundary
and dividing by 2.
vFormula:
Xm = Lower boundary +Upper boundary / 2
28
CLASS MARK (MIDPOINTS)

29
Class Limits Class Mark Frequency
8-17 8+17/2 = 12.5 6
18-27 22.5 5
28-37 32.5 4
38-47 42.5 4
48-57 52.5 5
58-67 62.5 3
68-77 72.5 3

vClass Interval or class width is the
difference between two
consecutive lower class limits or
two consecutive lower class
boundaries.
§ Class Width = 18-8 = 10
30
CLASS INTERVAL (WIDTH)

vFind the highest value and lowest
value from raw data:
§ L : 8 and H: 71
vFind the Range (R)
§ R = H - L
§ R = 71 – 8
§ R = 63
vSelect the desired number of
classes. Suppose 7 in this case
31
CALCULATION OF CLASS WIDTH

vFind Width by dividing the Number of
classes:
§ Width = Range / No. of classes
§ Width = 63 / 7
§ Width = 9
vIf answer is a Fraction no., then
Round up to nearest whole number,
otherwise add one into the computed
width. i.e.
§ Width = 9 + 1 = 10
32
CALCULATION OF CLASS WIDTH

vIn ‘Message Portal’ software
project, the number of Change
Requests in each module is
enlisted below:
§ 32, 55, 31, 76, 34, 23, 51, 90, 72,
62, 43, 93, 24, 55, 16, 13, 86, 65,
53, 84, 75, 62, 46, 80, 11, 83, 32,
17, 31, 86.
33
ASSIGNMENT # 1 (CHANGE REQUESTS)

vFrom Raw data of previous slide
compute the Class Width (Suppose No.
of Classes = 8), Draw the Frequency
Distribution Table by computing
following:
§ Class Limits, Class Boundaries Tallies,
Frequency, Cumulative Frequency,
Relative Frequency, Cumulative Relative
Frequency, Class Mark (Midpoint)
34
ASSIGNMENT # 1 (CHANGE REQUESTS)

vAlthough there is no hard-and-fast
rule for the number of classes
contained in a frequency distribution,
but, it is recommended that there
should be 5-20 classes in a frequency
distribution.
vThe classes must be exhaustive.
There should be enough classes to
accommodate all the data.
35
IMPORTANT POINTS FOR CLASSES

vThe classes must be mutually
exclusive. Mutually exclusive classes
have non-overlapping class limits so
that data cannot be placed into two
classes. E.g.
§ 10-20
§ 20-30 à Incorrect
§ 10-20
§ 21-30 à Correct
36

vThe classes must be continuous.
Even if there are no values in a class,
the class must be included in the
frequency distribution.
vThe classes must be equal in width.
37

vThere are two types of frequency
distribution:
§ 1. Grouped Frequency Distribution
§ 2. Categorical Frequency Distribution
38
TYPES OF FREQUENCY DISTRIBUTION

vThe grouping of quantitative data
is called grouped frequency
Distribution.
vExample à Case Study # 1
39
1. GROUPED FREQUENCY DISTRIBUTION

vThe categorical frequency
distribution is used for data that can
be placed in specific categories, such
as nominal- or ordinal-level data.
vDiscrete Classes are used for
categorical frequency distribution
vNo class limits, class boundaries,
class Midpoints and Class width are
computed for categorical frequency
distribution.
40
2. CATEGORICAL FREQUENCY DISTRIBUTION

vHowever, Tallies and all types of
Frequencies are computed in
similar way as those of Grouped
Frequency distribution.
41
2. CATEGORICAL FREQUENCY DISTRIBUTION

vQuality Management Department has
reviewed the Use Case Document of
‘Message Portal’ software project. They
found document issues with different
severities.
vRaw data of Bugs Severity is as follows:
§ Low, Medium, Medium, Low, High,
Medium, Very High, Low, High, High,
Medium, Very High, High, Medium, Low,
Medium, Very High, High, Medium, Low,
Medium, High
42
CASE STUDY # 2 (SEVERITY OF ISSUES)

vThere are four types of Severities of
Document issues: Low, Medium, High
and Very High.
vThese types will be used as the Classes
for the distribution.
43

44
Classes Frequency
Low 5
Medium 8
High 6
Very High 3

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