Question

Find the mean deviation about the mean for the data
$4,7,8,9,10,12,13,17$

Answer 1

The given data is $4,7,8,9,10,12,13,17$
Mean of the data $\overline{x}=\frac{4+7+8+9+10+12+13+17}{8}=\frac{80}{8}=10$
The deviations of the respective observations from the mean $\overline{x}i.e.x_i-\overline{x},$ are $-6,-3,-2,-1,0,2,3,7$.
The absolute values of the deviations i.e. $\mid x_i-\overline{x}\mid$, are $6,3,2,1,0,2,3,7$.
The required mean deviation about the mean is
$M.D.=\frac{{\sum }_{i=1}^8\mid x_i-\overline{x}\mid }{8}$
$M.D.=\frac{6+3+2+1+0+2+3+7}{8}=\frac{24}{8}=3$