Question

Find out the average deviation from median for the following distribution:

Values	:	6	12	18	24	30	36	42
Frequency	:	4	7	9	18	15	10	5

Answer 1

Value (X)	Frequency (f)	c.f	Deviation from Median |DM|=|X−M| (M = 24)	f|DM|
6	4	4	18	72
12	7	11	12	84
18	9	20	6	54
24	18	38	0	0
30	15	53	6	90
36	10	63	12	120
42	5	68	18	90
	Σf = N = 68			Σf|dm| = 510

$$\begin{gathered} \mathrm{Median}=\mathrm{Size}\mathrm{of}{\left(\frac{N+1}{2}\right)}^{\mathrm{th}}\mathrm{item} \\ =\mathrm{Size}\mathrm{of}{\left(\frac{68+1}{2}\right)}^{\mathrm{th}}\mathrm{item} \\ =34.5^{\mathrm{th}}\mathrm{item} \end{gathered}$$
This corresponds to value 24. Thus, median is 24.
$\therefore \mathrm{Mean}\mathrm{deviation}\mathrm{from}\mathrm{Median}=\frac{\mathrm{\Sigma }f{\displaystyle \left|D_M\right|}}{\Sigma f}=\frac{510}{68}=7.5$