Question

Find the median of the following frequency distribution

Class	$4-8$	$8-12$	$12-16$	$16-20$	$20-24$	$24-28$
Frequency	$9$	$16$	$12$	$7$	$15$	$1$

Answer 1

Class	Frequency	Cumulative frequency$(c.f.)$
$4-8$	$9$	$9$
$8-12$	$16$	$9+16=25$
$12-16$	$12$	$25+12=37$
$16-20$	$7$	$37+7=44$
$20-24$	$15$	$44+15=59$
$24-28$	$1$	$59+1=60$

Here $n=60\Rightarrow$ $\frac{n}{2}=30$
Cumulative frequency greater than $30$ is $37$ and the class corresponding to it is $12-16$
$\therefore$ Class $12-16$ is the median class
$\therefore$ Lower limit$\left(l\right)=12,\frac{n}{2}=30,c.f.=25,f=12$ and $h=4$
Subtituting the values, we get
$M=l+\frac{(\frac{n}{2}-c.f.)}{f}\times h$
$M=12+\frac{30-25}{12}\times 4=12+\frac{5}{3}$
$=12+1.67$
$=13.67$

Hence, Median is $13.67$