Find the mean deviation about the mean for the data

4, 7, 8, 9, 10, 12, 13, 17

The given data is

4, 7, 8, 9, 10, 12, 13, 17

Mean of the data, $\overline{\mathrm{x}} = \frac{4+7+8+9+10+12+13+17}{8} = \frac{80}{8} = 10$

The deviations of the respective observations from the mean $\overline{\mathrm{x}} \mathrm{i}.\mathrm{e}. {\mathrm{x}}_{\mathrm{i}} - \overline{\mathrm{x}}$ are

–6, – 3, –2, –1, 0, 2, 3, 7

The absolute values of the deviations, i.e. $\left|x_i - \overline{x}\right|$, are

6, 3, 2, 1, 0, 2, 3, 7

The required mean deviation about the mean is

$\mathrm{MD} \left(\overline{\mathrm{x}}\right) = \frac{{\displaystyle \sum _{\mathrm{i}=1}^8} \left|{\mathrm{x}}_{\mathrm{i}} - \overline{\mathrm{x}}\right|}{8} = \frac{6+3+2+1+0+2+3+7}{8} = \frac{24}{8} = 3$