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

Question:

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

Solution:

The given observations are in ascending order. Adding a row corresponding to cumulative frequencies to the given data, we get,

Now, $N=29$ which is odd.

Since, $15^{\text {th }}$ observation lie in the cumulative frequency 21 , for which the corresponding observation is 30 .

$\operatorname{Median}(\mathrm{M})=\left(\frac{29+1}{2}\right)^{\text {th }}$ or $15^{\text {th }}$ observation $=30$

Now, absolute values of the deviations from the median,

We have $\sum_{\mathrm{i}=1}^{5} \mathrm{f}_{\mathrm{i}}=29$ and $\sum_{\mathrm{i}=1}^{5} \mathrm{f}_{\mathrm{i}}\left|\mathrm{x}_{\mathrm{i}}-\mathrm{M}\right|=148$

$\therefore \mathrm{M} . \mathrm{D}(\mathrm{M})=\frac{\sum_{\mathrm{i}=1}^{5} \mathrm{f}_{\mathrm{i}}\left|\mathrm{x}_{\mathrm{i}}-\mathrm{M}\right|}{\sum_{\mathrm{i}=1}^{5} \mathrm{f}_{\mathrm{i}}}$

$=\frac{148}{29}=5.10$