Question

Find the mean deviation about the mean for the following data:

Marks obtained	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Number of students	$5$	$8$	$15$	$16$	$6$

Answer 1

Marks	Average Marks	Number of Students
$0-10$	$5$	$5$
$10-20$	$15$	$8$
$20-30$	$25$	$15$
$30-40$	$53$	$16$
$40-50$	$45$	$6$

Mean $=\frac{5\times 5+15\times 8+28\times 15+35\times 16+45\times 6}{5+8+15+16+6}$

$=\frac{1350}{50}$

$=27$

So mean deviation about mean $=\frac{5\times |5-27|+8\times |15-27|+15\times |25-27|+16\times |35-27|+6\times |45-27|}{5+8+15+16+6}$

$=\frac{472}{50}$

$=9.44$