Calculate the missing frequency from the following distribution, it being given that the median of the distribution is 24.

Age in years:	0-10	10-20	20-30	30-40	40-50
No. of persons:	5	25	?	18	7

Given:

The median of the given distribution is 24.

To do:

We have to find the missing frequency.

Solution:

Let the missing frequency be $p$.

Here,

Median$ = 24$ which lies in class 20-30.

Therefore,

$l = 20, f = p, F = 30, h = (30 - 20) = 10$ and $N=55+p$

Medain $=\mathrm{l}+\frac{\frac{\mathrm{N}}{2}-\mathrm{F}}{\mathrm{f}} \times \mathrm{h}$

$24=20+\frac{\frac{55+p}{2}-30}{p} \times 10$

$24-20=\frac{55+p-60}{2p} \times 10$

$4=\frac{5(p-5)}{p}$

$4p= 5p - 25$

$5p-4p= 25$

$p=25$

The missing frequency is 25.   

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Updated on: 10-Oct-2022

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