Question

Find the mean deviation about the median for the data

xi	15	21	27	30	35
fi	3	5	6	7	8

Answer 1

The given observations are already in ascending order. 

Adding a column corresponding to cumulative frequencies of the given data, we obtain the following table.

\(x_i\)	\(f_i\)	\(c.f\)
15	3	3
21	5	8
27	6	14
30	7	21
35	8	29

Here, N = 29, which is odd.

∴ Median= \((\frac{29+1}{2})^{th}\)  observation = 15^th observation.

This observation lies in the cumulative frequency 21, for which the corresponding observation is 30. 

∴ Median = 30

The absolute values of the deviations from median, i.e \(|x_i-M|,\) are 

\(|x_i,M|\)	15	9	3	0	5
\(f_i\)	3	5	6	7	8
\(f_i|x-M|\)	45	45	18	0	40

\(\sum_{I=1}^{5}f_i=29\) ,  \(\sum_{I=1}^{5}f_i|x_i-M|=148\)

\(=M.D.(M)=\frac{1}{N}\sum_{i=1}^{5}f_i|x_i-M|=\frac{1}{29}×148=5.1\)