Question

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

Class	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequency	$5$	$25$	$?$	$18$	$7$

Answer 1

$CI$	$Frequency$	$c.f$
$0-10$	$5$	$5$
$10-20$	$25$	$30$
$20-30$	$x$	$30+x$
$30-40$	$18$	$48+x$
$40-50$	$7$	$55+x$
	$N=55+x$

Median $=24$

Median class $=20-30$

Here, $l=20,h=10,f=x,cf=30,\frac{N}{2}=\frac{55+x}{2}$

$\Rightarrow$ $Median=l+\frac{\frac{N}{2}-cf}{f}\times h$

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

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

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

$\Rightarrow$ $4x\times 2=(55+x-60)\times 10$

$\Rightarrow$ $8x=550+10x-600$

$\Rightarrow$ $10x-8x=600-550$

$\Rightarrow$ $2x=50$

$\therefore$ $x=25$