Question

Find the frequency of the median class if the following information is known for a grouped data whose median is = 45:

Lower limit of median class = 25
Sum of frequencies = 100
Cumulative frequency of the class preceding the median class = 30
And, class size = 10.

• A. 15
• B. 25
• C. 10
• D. 20

Answer 1

The correct option is C 10

The formula for median of a grouped data is given by,

$M=L+\left[\frac{\frac{n}{2}-cf}{f}\right]\times h$
where,
M = median of the grouped data
L = Lower limit of median class
n = Sum of frequencies
cf = Cumulative frequency of the class preceding the median class
f = frequency of the median class
and, h = class size

Substituting the given values, we get:

$45=25+\left[\frac{\frac{100}{2}-30}{f}\right]\times 10\Rightarrow 45=25+[\frac{20}{f}\times 10]\Rightarrow 45=25+\frac{200}{f}\Rightarrow \frac{200}{f}=20\Rightarrow f=\frac{200}{20}=10$

Or, the frequency of the median class = 10.