Question

Q-15 What is the coefficient of range for the following distribution?
Class Interval:
10-19 20-29 30-39 40-49 50_59
Frequency:
11
25
16
7
3
(a) 22
(b) 50
(c) 75.82
(f) 72.46​

Answer 1

GIVEN :

The distribution is

Class Interval:

10-19  20-29  30-39  40-49  50-59

Frequency:

11           25        16           7            3

TO FIND :

The coefficient of range for the following distribution

SOLUTION :

Given distribution table is

Class Interval:              Frequency:

10-19                                    11

20-29                                 25

30-39                                  16

40-49                                   7

50-59                                    3

The formula for coefficient of range is given by :

$coefficient of range=\frac{L-S}{L+S}\times 100$

The given series is in inclusive class. To calculate the coefficient of range we have to convert the inclusive class into exclusive class as below :

Inclusive Class      Exclusive class          Frequency

10-19                         9.5-19.5                       11

20-29                       19.5-29.5                    25

30-39                       29.5-39.5                   16  

40-49                       39.5-49.5                    7

50-59                         49.5-59.5                   3

From the above table L=59.5 and S=9.5

Substitute the values in the formula $coefficient of range=\frac{L-S}{L+S}\times 100$ we get

$coefficient of range=\frac{59.5-9.5}{59.5+9.5}\times 100$

$=\frac{50}{69}\times 100$

$=\frac{5000}{69}$

=72.46

∴ coefficient of range=72.46

⇒ option d) 72.46 is correct.

∴ the coefficient of range for the given distribution is 72.46