Question

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

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

Answer 1

Frequency distribution table :

$ci$	$f_i$	$cf$
$0-10$	$5$	$5$
$10-20$	$25$	$5+25=30$
$20-30$	$f$	$30+f$
$30-40$	$18$	$48+f$
$40-50$	$7$	$55+f$

Median $=l+\frac{(\frac{N}{2}-cf)}{f_m}\times c$

Here,

Class Interval $c=10$

$N=\Sigma f_i=55+f$

Median $=24$

$\Rightarrow$ Median class $=20-30$

$\Rightarrow$Frequency of median class$f_m=f$

Lower boundary of median class $l=20$

previous cumulative frequency of median class $cf=30$

$\therefore 24$ $=20+\frac{(\frac{55+f}{2}-30)}{f}\times 10$

$\therefore 24$ $=20+\frac{(f-5)}{2f}\times 10$

$\therefore 24$ $=\frac{40f+10f-50}{2f}$

$\therefore 50f-48f=50$

$\therefore f=25$