Question

Find the mean deviation about the median for the data.

xi	5	7	9	10	12	15
fi	8	6	2	2	2	6

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.

xi	fi	c.f.
5	8	8
7	6	14
9	2	16
10	2	18
12	2	20
15	6	26

Here, N = 26, which is even.

Median is the mean of 13^th and 14^th observations. Both of these observations lie in the cumulative frequency 14, for which the corresponding observation is 7.

The absolute values of the deviations from median, i.e.are

|xi – M|	2	0	2	3	5	8
fi	8	6	2	2	2	6
fi |xi – M|	16	0	4	6	10	48

and