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

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. $(\overline{\mathrm{x}})=\frac{\sum_{\mathrm{i}=1}^{10}\left|\mathrm{x}_{\mathrm{i}}-\mathrm{M}\right|}{10}$

$=\frac{13+8+4+2+1+1+4+8+10+14}{10}=\frac{65}{10}=6.5$