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

Question:

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

$17,20,12,13,15,16,12,18,15,19,12,11$

Solution:

We have, 17, 20, 12, 13, 15, 16, 12, 18, 15, 19, 12, 11

Mean of the given data is

$\overline{\mathrm{x}}=\frac{17+20+12+13+15+16+12+18+15+19+12+11}{12}$

$\overline{\mathrm{x}}=\frac{180}{12}=15$

The respective absolute values of the deviations from the mean, i.e.' $\left|\mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}\right|$ are

2, 5, 3, 2, 0, 1, 3, 3, 0, 4, 3, 4

Thus, the required mean deviation about the mean is

M. D. $(\overline{\mathrm{x}})=\frac{\sum_{\mathrm{i}=1}^{12}\left|\mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}\right|}{12}$

$=\frac{2+5+3+2+0+1+3+3+0+4+3+4}{12}=\frac{30}{12}=2.5$