Question

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

$x_i$	$1$	$4$	$9$	$12$	$13$	$14$	$21$	$22$
$f_i$	$3$	$4$	$5$	$2$	$4$	$5$	$4$	$3$

• A. $5.33$
• B. $4.33$
• C. $6.33$
• D. $8$

Answer 1

Answer: (A)

$x_i$	$f_i$	$f_i{x}_i$	$|x_i-\bar{x}|$	$f_i|x_i-\bar{x}|$
1	3	3	11	33
4	4	16	8	32
9	5	45	3	15
12	2	24	0	0
13	4	52	1	4
14	5	70	2	10
21	4	84	9	36
22	3	66	10	30
Total	30	360		160

Mean $\left(\bar{x}\right)=\frac{\Sigma f_i{x}_i}{\Sigma f_i}$
$=\frac{360}{30}=12$
$M.D.\left(\bar{x}\right)=\frac{\Sigma f_i|x_i-\bar{x}|}{\Sigma f_i}$
$=\frac{160}{30}=5.33$.