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) xx h`

`24 = 20 + (((55 + x)/2 - 30)/x) xx 10`

`24 - 20 = (((55 + x)/2 - 30)/x) xx 10`

`4x = ((55 + x)/2 - 30) xx 10`

4x × 2 = (55 + x – 60) × 10

8x = 550 + 10x – 600

10x – 8x = 600 – 550

2x = 50

x = 25

∴ Missing frequency = 25