Question

Find the mean deviation about the mean for the data
$38,70,48,40,42,55,63,46,54,44$

Answer 1

The given data is $38,70,48,40,42,55,63,46,54,44$
Mean $\overline{x}=\frac{38+70+48+40+42+55+63+46+54+44}{10}$

$=\frac{500}{10}=50$
The deviations of the respective observation from the mean $\overline{x},$ i.e. $x_i=\overline{x}$ are $-12,20,-2,-10,-8,5,13,-4,4,-6$.
The absolute values of the deviations i.e.$\mid x_1-\overline{x}\mid$ are $12,20,2,10,8,5,13,4,4,6$
The required mean deviation about the mean is

$M.D.=\frac{{\sum }_{i=1}^{10}\mid x_i-\overline{x}\mid }{10}$

$=\frac{12+10+2+10+8+5+13+4+4+6}{10}$

$=\frac{84}{10}$

$=8.4$