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

Question:

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

4, 15, 9, 7, 19, 13, 6, 21, 8, 25, 11

 

Solution:

Here the number of observations is 11 which is odd.

Arranging the data into ascending order, we have 4, 6, 7, 8, 9, 11, 13, 15, 19, 21, 25

Now, Median $(M)=\left(\frac{11+1}{2}\right)^{\text {th }}$ or $6^{\text {th }}$ observation $=11$

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

7, 5, 4, 3, 2, 0, 2, 4, 8, 10, 14

Thus, the required mean deviation about the median is

M.D. $(\overline{\mathrm{x}})=\frac{\sum_{\mathrm{i}=1}^{11}\left|\mathrm{x}_{\mathrm{i}}-\mathrm{M}\right|}{11}$

$=\frac{7+5+4+3+2+0+2+4+8+10+14}{11}=\frac{59}{11}=5.3$

 

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