Question

Find the Mean Deviation about median for the following data :

Class	0 - 10	10 - 20	20 - 30	30 - 40	40 - 50	50 - 60	60 - 70	70 - 80
frequency	5	8	7	12	28	20	10	10

Answer 1

$Class$	$Frequency$	$cf$	$x_i$	$|x_i-M|$ $(|x_i-56.43|)$	$f_i|x_i-M|$
$0-10$	$5$	$5$	$5$	$51.43$	$257.15$
$10-20$	$8$	$13$	$15$	$41.43$	$331.44$
$20-30$	$7$	$20$	$25$	$31.43$	$220.01$
$30-40$	$12$	$32$	$35$	$21.43$	$257.16$
$40-50$	$28$	$60$	$45$	$11.43$	$320.04$
$50-60$	$20$	$80$	$55$	$1.43$	$28.6$
$60-70$	$10$	$90$	$65$	$8.57$	$85.7$
$70-80$	$10$	$100$	$75$	$18.57$	$185.7$
	$\sum f_i=100$				$\sum f_i|x_i-M|=1685.8$

Here, $n=100$ then, $\frac{n}{2}=\frac{100}{2}=50$

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

$l=50,cf=32,f=28,h=10$

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

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

$=50+6.43$

$=56.43$

$\Rightarrow$ Mean deviation about median $=\frac{\sum f_i|x_i-M|}{\sum f_i}=\frac{1685.8}{100}=16.858$