Question

The approximate value of the mean deviation about the mean for the following data is

Class	0-2	2-4	4-6	6-8	8-10
Frequency	1	2	3	2	1

• A. 3.56
• B. 4.61
• C. 2.19
• D. 1.78

Answer 1

Answer: (D)

Classinterval	mid-value $(x_i)$	frequency $(f_i)$	$x_i{f}_i$	$\left(x_i-\bar{x}\right)=d_i$	$f_i{d}_i$
0-2	1	1	1	4	4
2-4	3	2	6	2	4
4-6	5	3	15	0	0
6-8	7	2	14	2	4
8-10	9	1	9	4	4
		$\Sigma f_i=9$	$\Sigma f_i{X}_i=45$		$\Sigma f_i{d}_i=16$

$\bar{x}=\frac{\Sigma f_i{x}_i}{\Sigma f_i}=\frac{45}{9}=5$
Mean deviation = $\frac{\Sigma f_i{d}_i}{\Sigma f_i}$
$=\frac{16}{9}=1.78$