Question

Calculate mean deviation from median for the following:

Marks (less than)	80	70	60	50	40	30	20	10
No. of Students	100	90	80	60	32	20	13	5

Answer 1

$CI$	$cf$	$f$	$x_i$	$|x_i-M|$	$f_i|x_i-M|$
$0-10$	$5$	$5$	$5$	$41.43$	$207.15$
$10-20$	$13$	$13-5=8$	$15$	$31.43$	$251.44$
$20-30$	$20$	$20-13=7$	$25$	$21.43$	$150.01$
$30-40$	$32$	$32-20=12$	$35$	$11.43$	$137.16$
$40-50$	$60$	$60-32=28$	$45$	$1.43$	$40.04$
$50-60$	$80$	$80-60=20$	$55$	$8.57$	$171.4$
$60-70$	$90$	$90-80=10$	$65$	$18.57$	$185.7$
$70-80$	$100$	$100-90=10$	$75$	$28.57$	$285.7$
		$\sum f_i=100$			$\sum f_i|x_i-M|=1428.6$

$N=100$, then, $\frac{N}{2}=\frac{100}{2}=50$

$\therefore$ Median class $=40-50$

Then we have, $l=40,cf=32,f=28,h=10$

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

$=40+\frac{50-32}{28}\times 10$

$=40+6.43$

$=46.43$

Mean deviation from median $=\frac{\sum f_i|x_i-M|}{\sum f_i}=\frac{1428.6}{100}=14.286$