Question

Estimate the coefficient of mean deviation from the median from the following data:

Age Group	20−30	30−40	40−50	50−60	60−70
Number of Workers	8	12	20	16	4

Answer 1

Calculation of MD. from Median

Age	Mid value (m)	No. of workers (f)	Cumulative Frequency	|dm| = |m − M| M = 45	f|dm|
20 − 30 30 − 40 40 − 50 50 − 60 60 −70	25 35 45 55 65	8 12 20 16 4	8 8 + 12 = 20 20 + 20 =40 40 + 16 =56 56 + 4 = 60	20 10 0 10 20	160 120 0 160 80
		N=Σf = 60			Σf|dm| = 520

Median = Size of ${\left(\frac{\mathrm{N}}{2}\right)}^{\mathrm{th}}$ item
= Size of ${\left(\frac{60}{2}\right)}^{\mathrm{th}}$ item
= Size of 39^th item

39^th item lies under the 40^th cumulative frequency of the series. So, 40 − 50 will be the median class interval.

Hence, the median value of the series is:

$$\begin{gathered} \mathrm{M}=l_1+\frac{{\displaystyle \frac{N}{2}}-c.f.}{f}\times i \\ \mathrm{or},\mathrm{M}=40+\frac{30-20}{20}\times 10 \\ \mathrm{or},\mathrm{M}=40+\frac{10\times 10}{20} \\ \Rightarrow \mathrm{M}=45 \\ \mathrm{Thus}, \\ \mathrm{Mean}\mathrm{Deviation}\mathrm{from}\mathrm{median}{\mathrm{MD}}_{\mathrm{M}}=\frac{\mathrm{\Sigma }f\left|dm\right|}{\mathrm{\Sigma }f}=\frac{520}{60}=8.67 \\ \mathrm{Coefficient}\mathrm{of}{\mathrm{MD}}_{\mathrm{M}}=\frac{{\mathrm{MD}}_{\mathrm{M}}}{\mathrm{Median}}=\frac{8.67}{45}=0.19 \end{gathered}$$