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

Question:

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

12, 5, 14, 6, 11, 13, 17, 8, 10

 

Solution:

Here the number of observations is 9 which is odd.

Arranging the data into ascending order, we have 5, 6, 8, 10, 11, 12, 13, 14, 17

Now, Median $(M)=\left(\frac{9+1}{2}\right)^{\text {th }}$ or $5^{\text {th }}$ observation $=11$

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

6, 5, 3, 1, 0, 1, 2, 3, 6

Thus, the required mean deviation about the median is

M. D. $(\overline{\mathrm{x}})=\frac{\sum_{\mathrm{i}=1}^{9}\left|\mathrm{x}_{\mathrm{i}}-\mathrm{M}\right|}{9}$

$=\frac{6+5+3+1+0+1+2+3+6}{9}=\frac{27}{9}=3$

 

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