Find the mean deviation about the median for the following data :
34, 23, 46, 37, 40, 28, 32, 50, 35, 44
Here the number of observations is 10 which is odd.Arranging the data into ascending order,
we have 23, 28, 32, 34, 35, 37, 40, 44, 46, 50
Now, $\quad$ Median $(M)=\left(\frac{5^{\text {th }} \text { observation }+6^{\text {th }} \text { observation }}{2}\right)=\frac{35+37}{2}=36$
The respective absolute values of the deviations from median, i.e., $\left|\mathrm{x}_{\mathrm{i}}-\mathrm{M}\right|$ are
13, 8, 4, 2, 1, 1, 4, 8, 10, 14
Thus, the required mean deviation about the median is
M. D. $(\overline{\mathrm{x}})=\frac{\sum_{\mathrm{i}=1}^{10}\left|\mathrm{x}_{\mathrm{i}}-\mathrm{M}\right|}{10}$
$=\frac{13+8+4+2+1+1+4+8+10+14}{10}=\frac{65}{10}=6.5$
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