Question

Find the mean deviation about the mean for the data.

$x_i$	5	10	15	20	25
$f_i$	7	4	6	3	5

Answer 1

$X_i$	$f_i$	$f_i\times X_i$	$\mid X_i-\overline{X}\mid$	$f_1\mid X_i-\overline{X}\mid$
5	7	35	9	63
10	4	40	4	16
15	6	90	1	6
20	3	60	6	18
25	5	125	11	55
	25	350		158

$N=\sum _{i=1}^5{f}_1=25,$
$\sum _{i=1}^5{f}_1{x}_i=350$
$\therefore \overline{X}=\frac{1}{N}\sum _{i=1}^5{f}_1{X}_1=\frac{1}{25}\times 350=14$
$\therefore MD\left(\overline{x}\right)=\frac{1}{N}\sum _{i=1}^1{f}_1\mid x_i-\overline{x}\mid =\frac{1}{25}\times 158=6.32$