Question

Calculate the mean deviation of the following income groups of five and seven members from their medians:

I Income in Rs.	II Income in Rs.
4000 4200 4400 4600 4800	300 4000 4200 4400 4600 4800 5800

Answer 1

Calculate the mean deviation for the first data set.
The data is already arranged in ascending order.
For this data set, n is equal to 5.
Also, median, 

M = 4400

\[MD = \frac{1}{n} \sum^n_{i = 1} \left| d_i \right|, \text{ where } \left| d_i \right| = \left| x_i - M \right|\]

\[x_i\]	\[\left| d_i \right| = \left| x_i - M \right|\]
4000	400
4200	200
4400	0
4600	200
4800	400
Total	1200

\[MD = \frac{1}{5} \times 1200 = 240\]

Therefore, for the income of families in the first group, the mean deviation from the median is Rs 240.
Now, consider the second data set. This is also arranged in ascending order.
Here,

n = 7.

Also, median,

M= 4400

xi	\[\left| d_i \right| = \left| x_i - M \right|\]
300	4100
4000	400
4200	200
4400	0
4600	200
4800	400
5800	1400
Total	6700

\[MD = \frac{1}{7} \times 6700 = 957 . 14\]

Therefore, for the income of families in the second group, the mean deviation from the median is Rs 957.14.