Question

Calculate Mean and Mean Deviation and coefficient of M.D. for the following distribution:

Weekly wages	:	20-40	40-60	60-80	80-100
Workers	:	20	40	30	10

Answer 1

Weekly wages (X)	Mid value m	f	fm	$$\begin{gathered} \left|{\mathit{D}}_{\overline{\mathbf{X}}}\right|\mathbf{=}\left|\mathit{m}\mathit{-}\overline{X}\right| \\ \overline{X}\mathbf{=}\mathbf{56} \end{gathered}$$	$\mathit{f}\left|{\mathit{D}}_{\overline{\mathbf{X}}}\right|$
20−40	30	20	600	26	520
40−60	50	40	2000	6	240
60−80	70	30	2100	14	420
80−100	90	10	900	34	340
		Σf = 100	Σfm = 5600		$\mathrm{\Sigma }\mathit{f}\left|{\mathit{D}}_{\overline{\mathbf{X}}}\right|=1520$

$$\begin{gathered} \overline{X}=\frac{\mathrm{\Sigma }fm}{\mathrm{\Sigma }f}=\frac{5600}{100}=56 \\ \mathrm{Mean}\mathrm{deviation}\mathrm{from}\mathrm{Mean}=\frac{\mathrm{\Sigma }\mathit{f}\left|{\mathit{D}}_{\overline{\mathbf{X}}}\right|}{\mathrm{\Sigma }f}=\frac{1520}{100}=15.2 \\ \mathrm{Coefficient}\mathrm{of}\mathit{}MD=\frac{MD\mathrm{from}\mathrm{Mean}}{\mathrm{Mean}} \\ =\frac{15.2}{56} \\ =0.27 \end{gathered}$$