Question

Find the mean deviation about median for the following data.

$CI$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$	$70-80$
$f$	$9$	$18$	$7$	$21$	$11$	$4$

Answer 1

$CI$	$f_i$	$cf$	$Midpoint$ $x_i$	$|x_i-M|$	$f_i|x_i-M|$
$20-30$	$9$	$9$	$25$	$26.4$	$237.6$
$30-40$	$18$	$27$	$35$	$16.4$	$295.2$
$40-50$	$7$	$34$	$45$	$6.4$	$44.8$
$50-60$	$21$	$55$	$55$	$3.6$	$75.6$
$60-70$	$11$	$66$	$65$	$13.6$	$149.6$
$70-80$	$4$	$70$	$75$	$23.6$	$94.4$
	$\sum f_i=70$				$\sum f_i|x_i-M|=897.2$

$\Rightarrow$ $\frac{N}{2}=\frac{70}{2}=35$

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

$\Rightarrow$ $L=40,cf=27,f=7$ and $h=50-40=10$

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

$=40+\frac{35-27}{7}\times 10$

$=40+11.4$

$=51.4$

$\therefore$ $Median\left(M\right)=51.4$

$\Rightarrow$ Mean deviation about the mean $=\frac{\sum f_i|x_i-M|}{\sum f_i}$

$=\frac{897.2}{70}$

$=12.82$