Question

Using Mean Deviation from median of the income group of 5 and 7 members given below, compare which of the group has more variability?

Group A	:	4000	4200	4400	4600	4800
Group B	:	3000	4000	4200	4400	4600	4800	5800

Answer 1

For Group A

Income (X)	Deviation from median DM=|X−M| (M=4400)
4000	400
4200	200
4400	0
4600	200
4800	400
	Σ|DM|=1200

$$\begin{gathered} \mathrm{Mean}\mathrm{deviation}\mathrm{from}\mathrm{Median}=\frac{\mathrm{\Sigma }\left|D_M\right|}{N}=\frac{1200}{5}=240 \\ \mathrm{Coefficient}\mathrm{of}MD\mathrm{from}\mathrm{median}=\frac{MD\mathrm{from}\mathrm{Median}}{\mathrm{Median}}=\frac{240}{4400}=.054 \end{gathered}$$

For Group B

Income	Deviation from median DM=|X−M| (M=4400)
3000	1400
4000	400
4200	200
4400	0
4600	200
4800	400
5800	1400
	Σ|DM|=4000

$$\begin{gathered} \mathrm{Mean}\mathrm{deviation}\mathrm{from}\mathrm{Median}=\frac{\mathrm{\Sigma }{\displaystyle \left|D_M\right|}}{N}=\frac{4000}{7}=571.4 \\ \mathrm{Coefficient}\mathrm{of}MD\mathrm{from}\mathrm{median}=\frac{MD\mathrm{from}\mathrm{Median}}{\mathrm{Median}}=\frac{571.4}{4400}=0.13 \end{gathered}$$

In case of group B, as the coefficient of MD is more, so group B has greater variation.