Question

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

Answer 1

Class interval	Frequency	Cumulative frequency
0 – 10	5	5
10 – 20	25	30 (F)
20 – 30	x (f)	30 + x
30 – 40	18	48 + x
40 – 50	7	55 + x
	N = 55 + x

Given

Median = 24

Then, median class = 20 – 30

L = 20, h = 30 -20 = 10, f = x, F = 30

$Median=L+\frac{\frac{N}{2}-F}{f}\times h$

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

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

$4x=(\frac{55+x}{2}-30)\times 10$

$4x=275+5x-300$

$4x-5x=275-300$

$-x=-25$

$x=25$

Missing frequency = 25