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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 :

 

Solution:

We have,

Therefore, $\overline{\mathrm{X}}=\frac{\sum_{\mathrm{i}=1}^{6} \mathrm{f}_{\mathrm{i}} \mathrm{x}_{\mathrm{i}}}{\sum_{\mathrm{i}=1}^{6} \mathrm{f}_{\mathrm{i}}}=\frac{756}{36}=21$

Now,

Thus, the required mean deviation about the mean is

$\overline{\mathrm{x}}=\frac{\sum_{\mathrm{i}=1}^{6} \mathrm{f}_{\mathrm{i}}\left|\mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}\right|}{\sum_{\mathrm{i}=1}^{6} \mathrm{f}_{\mathrm{i}}}=\frac{288}{36}=8$

 

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