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
20 - 30	x	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 = 30 and f = x

Median `=l+{(N/2-F)/f}xxh`

`24=20+((55+x)/2-30)/x xx10`

`24 - 20=((55+x)/2-30)/x xx10`

`4x=((55+x)/2-30)xx10`

`4x xx2=(55 + x -60)xx10`

8x = 550 + 10x - 600

10x - 8x = 600 - 550

2x = 50

x = 25

∴ Missing frequency = 25