Question

Calculate mean deviation about Median for the following data :

Class	0-10	10-20	20-30	30-40	40-50	50-60
Frequency	6	7	15	16	4	2

Answer 1

$Class$	$Frequency$ $f_i$	$c.f$	$Class-mark$ $x_i$	$|x_i-M|$ $(x_i-28)$	$f_i|x_i-M|$
$0-10$	$6$	$6$	$5$	$23$	$138$
$10-20$	$7$	$13$	$15$	$13$	$91$
$20-30$	$15$	$28$	$25$	$3$	$45$
$30-40$	$16$	$44$	$35$	$7$	$112$
$40-50$	$4$	$48$	$45$	$17$	$68$
$50-60$	$2$	$50$	$55$	$27$	$54$
	$\sum f_i=50$				$\sum f_i|x_i-M|=508$

$n=50$ then, $\frac{n}{2}=\frac{50}{2}=25$

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

We have, $l=20,c.f=14,f=14$ and $h=10$

$\Rightarrow$ $Median\left(M\right)=l+\frac{\frac{n}{2}-c.f}{f}\times h$

$=20+\frac{25-13}{15}\times 10$

$=20+8$

$=28$

$\Rightarrow$ Mean deviation about median $=\frac{\sum f_i|x_i-M|}{\sum f_i}=\frac{508}{50}=10.16$