Page 139 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes 7.5 Range

The range of a distribution is the difference between its two extreme observations, i.e., the
difference between the largest and smallest observations. Symbolically, R = L – S where R
denotes range, L and S denote largest and smallest observations, respectively. R is the absolute
measure of range. A relative measure of range, also termed as the coefficient of range, is
defined as:
L S
Coefficient of Range
L S

Example: Find range and coefficient of range for each of the following data:
1. Weekly wages of 10 workers of a factory are:

310, 350, 420, 105, 115, 290, 245, 450, 300, 375.
2. The distribution of marks obtained by 100 students:
Marks : - 0 10 10 -20 20 -30 30 -40 40 -50
.
No of Students : 6 14 21 20 18
Marks : 50 -60 60 -70 70 -80 80 -90 90 -100
No of Students : 10 5 3 2 1
.
3. The age distribution of 60 school going children:

Age (in years) : 5 -7 8 -10 11 -13 14 -16 17 -19
Frequency : 20 18 10 8 4
Solution:

1. Range = 450 – 105 = 345
450 105
.
Coefficient of Range = 0 62.
450 105
2. Range = 100 – 0 = 100 marks
100 0
Coefficient of Range = 1.
100 0
3. Range = 19 – 5 = 12 Years
19 5
.
Coefficient of Range = 0 583
19 5
7.5.1 Merits and Demerits of Range

Merits

1. It is easy to understand and easy to calculate.
2. It gives a quick measure of variability.

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