Find the mean deviation about the mean for the following data: 

6,7, 10, 12, 13,4,8, 12 

Mean of the given data is $\overline{x}=\frac{6+7+10+12+13+4+8+12}{8}=\frac{72}{8}=9$

The deviations of the respective observations from the mean 

$\begin{array}{l}\overline{x},\text{ i.e., }{x}_i-\overline{x}\text{ are: }\\ 6-9,7-9,10-9,12-9,13-9,4-9,8-9,12-9\\ \text{ or }-3,-2,1,3,4,-5,-1,3\end{array}$

$\begin{array}{r}\text{ The absolute values of the deviations, i.e., }⌊x_i-\overline{x}\mid \text{ are: }3,2,1\text{ , }3,4,5,1,3\\ \end{array}$

The required mean deviation about the mean is:
$\text{ M.D. }\left(\overline{x}\right)=\frac{\sum _{i=1}^8 \left|x_i-\overline{x}\right|}{8}$

$\begin{array}{r}=\frac{3+2+1+3+4+5+1+3}{8}=\frac{22}{8}\\ =2.75\end{array}$