Question

The mean deviation about the mean for the following frequency distribution is

Class interval	0-4	4-8	8-12	12-16	16-20
Frequency	4	6	8	5	2

• A. $2.84$
• B. $4.84$
• C. $3.84$
• D. $1.84$

Answer 1

Answer: (C)

Class interval	$f_i$	$x_i$	$f_i{x}_i$	$|d_i|=|x_i-\bar{x}|=|x_i-9.2|$	$f_i|d_i|$
0 - 4	4	2	8	7.2	28.8
4-8	6	6	36	3.2	19.2
8-12	8	10	80	0.8	6.4
12-16	5	14	70	4.8	24.0
16-20	2	18	36	8.8	17.6
	$\Sigma f_i=25$		$\Sigma f_i{x}_i=230$		96.0

Mean $(\bar{x})=\frac{\Sigma f_i{x}_i}{\Sigma f_i}=\frac{230}{25}=9.2$
Mean deviation$=\frac{\Sigma f_i|d_{ij}|}{\Sigma f_i}=\frac{96}{25}=3.84$
Hence, the mean deviation about the mean is $3.84$.