Question

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

Age (in years)	No. of persons
0 - 10	5
10 - 20	25
20 - 30	x
30 - 40	18
40 - 50	7

• A. 15
• B. 25
• C. 10
• D. 19

Answer 1

The correct option is B 25

Age (in years)	NO. OF PERSONS	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
TOTAL	55 + x

Median = 24
Median lies in median class
∴ Median class is “20 – 30”

$l=20,\frac{N}{2}=\frac{55+x}{2},C.f:30,f=x,h=10$

MEDIAN $=l+\left(\frac{\frac{N}{2}-c.f.}{f}\right)\times h$

$\Rightarrow 24=20+\left(\frac{\frac{55+x}{2}-30}{x}\right)\times 10$

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

$\Rightarrow 4=\frac{(x-5)}{2x}\times 10$

$\Rightarrow 4x=5x-25$

$\Rightarrow 4x-5x=-25$

$\Rightarrow -x=-25$

$\therefore x=25$