Question

Calculate the Coefficient of Variation for the following distribution of the wages of 200 workers in a factory:

Wages ( in ₹)	:	40-49	50-59	60-69	70-79	80-89	90-99	100-109	110-119
No. of workers	:	11	23	40	60	35	16	9	6

Answer 1

In order to calculate coefficient of variation, first we will convert the given inclusive series into exclusive series as follows:

Wages	Mid Point (m)	Frequency (f)	fm	Deviation from $$\begin{gathered} x=\left(m-\overline{\mathrm{X}}\right) \\ \overline{\mathrm{X}}=74.45 \end{gathered}$$	x2	fx2
39.5 − 49.5 49.5 − 59.5 59.5 − 69.5 69.5 − 79.5 79.5 − 89.5 89.5 − 99.5 99.5 − 109.5 109.5 − 119.5	44.5 54.5 64.5 74.5 84.5 94.5 104.5 114.5	11 23 40 60 35 16 9 6	489.5 1253.5 2580 4470 2957.5 1512 940.5 687	29.95 19.95 9.95 .05 10.05 20.05 30.05 40.05	897 398 99 .002 101 402 903 1604	9867 9154 3960 0.12 3535 6432 8127 9624
		Σf = 200	Σfm = 14890			Σfx2 = 50699.12

$$\begin{gathered} \overline{\mathit{X}}=\frac{\mathrm{\Sigma }fm}{\mathrm{\Sigma }f}=\frac{14890}{200}=74.45 \\ SD\mathit{}\left(\mathrm{\sigma }\right)=\sqrt{\frac{\mathrm{\Sigma }f{x}^2}{\mathrm{\Sigma }f}}=\sqrt{\frac{50699.12}{200}}=\sqrt{253.4956}=15.921 \\ \mathrm{Coefficient}\mathrm{of}\mathrm{variation}=\frac{\sigma }{\overline{\mathit{X}}}\times 100 \\ =\frac{15.921}{74.45}\times 100=\frac{1592.1}{74.45} \\ =21.38\% \end{gathered}$$