Question

An incomplete distribution is given as follows:

Variable:	0-10	10-20	20-30	30-40	40-50	50-60	60-70
Frequency:	$10$	$20$	?	$40$	?	$25$	$15$

You are given that the median value is $35$ and the sum of all the frequencies is $170$. Using the median formula, fill up the missing frequencies.

Answer 1

Class interval	Frequency	Cumulative Frequency
$0-10$	$10$	$10$
$10-20$	$20$	$30$
$20-30$	$f_1$	$30+f_1$
$30-40$	$40$	$70+f_1$
$40-50$	$f_2$	$70+f_1+f_2$
$50-60$	$25$	$95+f_1+f_2$
$60-70$	$15$	$110+f_1+f_2$

Here, $Median=35$.

$\therefore$ median class is $30-40,N=170,then\frac{N}{2}=\frac{170}{2}=85$

$L=30,f=40,F=30+f_1,h=10$

$\Rightarrow$ Now, $Median=L+\frac{\frac{N}{2}-F}{f}\times h$

$\Rightarrow$ $35=30+\frac{85-(30+f_1)}{40}\times 10$

$\Rightarrow$ $35\times 4=120+(55-f_1)$

$\Rightarrow$ $f_1=35$

$\Rightarrow$ Also, $110+f_1+f_2=170$

$\Rightarrow$ $110+35+f_2=170$

$\therefore$ $f_2=170-145=25$

Hence, the missing frequencies are,

Class $20-30\Rightarrow 35$

Class $40-50\Rightarrow 25$