Question:
Find the mean deviation about the mean for the data
4, 7, 8, 9, 10, 12, 13, 17
Solution:
The given data is
4, 7, 8, 9, 10, 12, 13, 17
Mean of the data, $\bar{x}=\frac{4+7+8+9+10+12+13+17}{8}=\frac{80}{8}=10$
The deviations of the respective observations from the mean $\bar{x}$, i.e. $x_{i}-\bar{x}$, are
$-6,-3,-2,-1,0,2,3,7$
The absolute values of the deviations, i.e. $\left|x_{i}-\bar{x}\right|$, are
6, 3, 2, 1, 0, 2, 3, 7
The required mean deviation about the mean is
M.D. $(\bar{x})=\frac{\sum_{i=1}^{8}\left|x_{i}-\bar{x}\right|}{8}=\frac{6+3+2+1+0+2+3+7}{8}=\frac{24}{8}=3$