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Find the mean deviation about the mean for the following data

Question:

Find the mean deviation about the mean for the following data

7, 8, 4, 13, 9, 5, 16, 18

 

Solution:

We have, 7, 8, 4, 13, 9, 5, 16, 18

Mean of the given data is

$\overline{\mathrm{x}}=\frac{7+8+4+13+9+5+16+18}{8}=\frac{80}{8}=10$

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

3, 2, 6, 3, 1, 5, 6, 8

Thus, the required mean deviation about the mean is

M. D. $(\overline{\mathrm{x}})=\frac{\sum_{\mathrm{i}=1}^{8}\left|\mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}\right|}{8}$

$=\frac{3+2+6+3+1+5+6+8}{8}=\frac{34}{8}=4.25$

 

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