Question

Calculate mean deviation from the median of the following data:

Class interval:	0-6	6-12	12-18	18-24	24-30
Frequency:	4	5	3	6	2

Answer 1

$Class-interval$	$Class-mark$ $x_i$	$Frequency$ $f_i$	$c.f$	$|x_i-14|$	$f_i|x_i-M|$
$0-6$	$3$	$4$	$4$	$11$	$44$
$6-12$	$9$	$5$	$9$	$5$	$45$
$12-18$	$15$	$3$	$12$	$1$	$3$
$18-24$	$21$	$6$	$18$	$7$	$42$
$24-30$	$27$	$2$	$20$	$13$	$26$
		$\sum f_i=20$			$\sum f_i|x_i-M|=160$

$N=20$ then, $\frac{N}{2}=\frac{20}{2}=10$

$\therefore$ Median class $=12-18$

$l=12,c.f=9,f=3,h=6$

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

$=12+\frac{10-9}{3}\times 6$

$=12+2$

$\therefore$ $Median\left(M\right)=14$

Mean deviation from median $=\frac{\sum f_i|x_i-M|}{\sum f_i}=\frac{160}{20}=8$