Business Statistics - II B.Com.

1. Measure of Dispersion
Dr. Rmkv
SBKC

2. Introduction
• The measure of central tendency serve to locate the center of the
distribution, but they do not reveal how the items are spread out on either
side of the center. This characteristic of a frequency distribution is
commonly referred to as dispersion. In a series all the items are not equal.
There is difference or variation among the values. The degree of variation is
evaluated by various measures of dispersion. Small dispersion indicates
high uniformity of the items, while large dispersion indicates less
uniformity. For example consider the following marks of three students.
• Student A = 68, 75, 65, 67, 70 Total =345 Average = 69
• Student B = 85, 90, 80, 25, 65 Total =345 Average = 69
• Student C= 69, 69, 69 , 69, 69 Total =345 Average = 69

3. Introduction
• The fact is that the second student has failed in one paper. When the
averages alone are considered, the three students are equal. But first
student has less variation than second student. Less variation is a
desirable characteristic.

4. Characteristics of a good measure of
dispersion:
• An ideal measure of dispersion is expected to possess the following
properties
1. It should be rigidly defined
2. It should be based on all the items.
3. It should not be unduly affected by extreme items.
4. It should lend itself for algebraic manipulation.
5. It should be simple to understand and easy to calculate

5. Absolute and Relative Measures
• There are two kinds of measures of dispersion, namely
• Absolute measure of dispersion indicates the amount of variation in a
set of values in terms of units of observations. For example, when
rainfalls on different days are available in mm, any absolute measure
of dispersion gives the variation in rainfall in mm.
• On the other hand relative measures of dispersion are free from the
units of measurements of the observations. They are pure numbers.
They are used to compare the variation in two or more sets, which
are having different units of measurements of observations.

6. Absolute measure
• Range
• Quartile deviation
• Mean deviation
• Standard deviation
Relative measure
• Co-efficient of Range
• Co-efficient of Quartile deviation
• Co-efficient of Mean deviation
• Co-efficient of variation

7. Range
• This is the simplest possible
measure of dispersion and is
defined as the difference
between the largest and
smallest values of the variable
• In symbols, Range = L – S.
• Where L = Largest value.
• S = Smallest value.
Co-efficient of Range
• Co-efficient of Range =
𝐿 −𝑆
𝐿 + 𝑆

8. Illustration
1. Find the value of range and its co-efficient for the following data.
• 7, 9, 6, 8, 11, 10, 4
• Solution:
• L = 11 S = 4
• Range = L – S = 11 – 4 = 7
• Co-efficient of Range =
𝐿 −𝑆
𝐿 + 𝑆
=
11 − 4
11+ 4
=
7
15
= 0.4667
• Range = 7
• Co-efficient of Range = 0.4667

9. 2. Calculate range and its co efficient from the following distribution
X: 20 30 40 50 60 70
F: 8 12 20 10 6 4
• Solution:
• L = 70 S = 20
• Range = L – S = 70 – 20 = 50
• Co-efficient of Range =
𝐿 −𝑆
𝐿 + 𝑆
=
70 − 20
70+20
=
50
90
= 0.556
• Range = 50
• Co-efficient of Range = 0.556

10. Calculate range and its co efficient from the following distribution.
• Size: 60-63 63-66 66-69 69-72 72-75
• Number: 5 18 42 27 8
• Solution:
• L = 75 S = 60
• Range = L – S = 75 – 60 = 15
• Co-efficient of Range =
𝐿 −𝑆
𝐿 + 𝑆
=
75 −60
75 +60
=
15
135
= 0.111
• Range = 15
• Co-efficient of Range = 0.111

11. Exercise
1. Find the range and coefficient of range of the following data.
(i) 63, 89, 98, 125, 79, 108, 117, 68
(ii) 43.5, 13.6, 18.9, 38.4, 61.4, 29.8
2. Calculate the range of the following data.