Question

Find the mean deviation about the mean for the data

$X_i$	10	30	50	70	90
$f_i$	4	24	28	16	8

Answer 1

$X_i$	$f_i$	$f_i\times X_i$	$\mid X_i-\overline{X}\mid$	$f_1\mid X_i-\overline{X}\mid$
10	4	40	40	160
30	24	720	20	480
50	28	1400	0	0
70	16	1120	20	320
90	8	720	40	320
	80	4000		1280

$N=\sum _{i=1}^5{f}_1=80,$ $\sum _{i=1}^5{f}_1{x}_i=4000$
$\therefore \overline{X}=\frac{1}{N}\sum _{i=1}^5{f}_1{X}_1=\frac{1}{80}\times 4000=50$
$\therefore MD\left(\overline{x}\right)=\frac{1}{N}\sum _{i=1}^1{f}_1\mid x_i-\overline{x}\mid =\frac{1}{80}\times 1280=16$