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

The class interval containing $\frac{\mathrm{N}}{2}^{\mathrm{th}}$ or 25th item is 20-30. Therefore, 20–30 is the median class. We know that

Median $=1+\frac{\frac{\mathrm{N}}{2}-\mathrm{C}}{\mathrm{f}} \times \mathrm{h}$

Here, $I=20, C=14, f=11, h=10$ and $N=50$

Therefore,

Median $=20+\frac{\frac{50}{2}-14}{11} \times 10=20+10=30$

Now

We have, $\sum_{\mathrm{i}=1}^{6} \mathrm{f}_{\mathrm{i}}=50$ and $\sum_{\mathrm{i}=1}^{6} \mathrm{f}_{\mathrm{i}}\left|\mathrm{x}_{\mathrm{i}}-\mathrm{M}\right|=540$

$\therefore \mathrm{M} . \mathrm{D}(\mathrm{M})=\frac{\sum_{\mathrm{i}=1}^{6} \mathrm{f}_{\mathrm{i}}\left|\mathrm{x}_{\mathrm{i}}-\mathrm{M}\right|}{\sum_{\mathrm{i}=1}^{6} \mathrm{f}_{\mathrm{i}}}$

$=\frac{540}{50}=10.8$