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

Question:

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

70, 34, 42, 78, 65, 45, 54, 48, 67, 50, 56, 63

 

Solution:

Here the number of observations is 12 which is odd.

Arranging the data into ascending order, we have 34, 42, 45, 48, 50, 54, 56, 63, 65, 67, 70, 78

Now, Median $(M)=\left(\frac{6^{\text {th }} \text { observation }+7^{\text {th }} \text { observation }}{2}\right)=\frac{54+56}{2}=55$

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

21, 13, 10, 7, 5, 1, 1, 8, 10, 12, 15, 23

Thus, the required mean deviation about the median is

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

$=\frac{21+13+10+7+5+1+1+8+10+12+15+23}{12}=\frac{126}{12}=10.5$

 

 

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