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.

xi	fi	c.f.
15	3	3
21	5	8
27	6	14
30	7	21
35	8	29

Here, N = 29, which is odd.

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.are

|xi – M|	15	9	3	0	5
fi	3	5	6	7	8
fi |xi – M|	45	45	18	0	40

∴