Question

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

Marks obtained	No. of students
0-10	5
10-20	8
20-30	15
30-40	16
40-50	6

Answer 1

Class	Frequency $\left(f_i\right)$	Mid point $\left(x_i\right)$	$f_i{x}_i$
$0-10$	5	$\frac{0+10}{2}=5$	$5\times 5=25$
$10-20$	8	$\frac{10+20}{2}=15$	$8\times 15=120$
$20-30$	15	$\frac{20+30}{2}=25$	$15\times 25=375$
$30-40$	16	$\frac{30+40}{2}=35$	$16\times 35=560$
$40-50$	6	$\frac{40+50}{2}=45$	$6\times 45=270$
	$\sum f_i=50$		$\sum f_i{x}_i=1350$

First we calculate mean from table,

Mean $=\frac{\sum f_i{x}_i}{\sum f_i}=\frac{1350}{50}=27$

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

$⟹\frac{5\left(22\right)+8\left(12\right)+15\left(2\right)+16\left(8\right)+6\left(18\right)}{50}=\frac{472}{50}=9.44$