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

Question:

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

 

Solution:

we make the following table from the given data:

The class interval containing $\frac{N^{t h}}{2}$ 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, l = 20, C = 13, f = 15, h = 10 and N = 50

Therefore, Median $=20+\frac{\frac{50}{2}-13}{15} \times 10=20+8=28$

Now,

We have, $\sum_{\mathrm{i}=1}^{6} \mathrm{f}_{\mathrm{i}}=50$ and $\sum_{\mathrm{i}=1}^{6} \mathrm{f}_{\mathrm{i}}\left|\mathrm{x}_{\mathrm{i}}-\mathrm{M}\right|=508$

$\therefore M . D(M)=\frac{\sum_{i=1}^{6} f_{i}\left|x_{i}-M\right|}{\sum_{i=1}^{6} f_{i}}$

$=\frac{508}{50}=10.16$

 

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