Question

Estimate coefficient of variation of the following data:

Weight (kg)	0−20	20−40	40−60	60−80	80−100
Number of Persons	81	40	66	49	14

Answer 1

Class Interval	Mid Value (m)	f	fm	$\mathit{x}\mathit{=}\mathit{X}\mathit{-}\mathit{}\overline{\mathit{X}}$	x2	fx2
0 − 20 20 − 40 40 − 60 60 − 80 80 − 100	10 30 50 70 90	81 40 66 49 14	810 1200 3300 3430 1260	−30 −10 10 30 50	900 100 100 900 2500	72900 4000 6600 44100 35000
		∑f = 250	∑fm = 10000			∑fx2 = 162600

$$\begin{gathered} \overline{X}=\frac{{\sum }_{}^{}fm}{{\sum }_{}^{}f}=\frac{10000}{250}=40 \\ \mathrm{Standard}\mathrm{Deviation}\left(\sigma \right)=\sqrt{\frac{{\sum }_{}^{}f{x}^2}{{\sum }_{}^{}f}}=\sqrt{\frac{162600}{250}}=25.50 \\ \mathrm{Coefficient}\mathrm{of}\mathrm{Variation}=\frac{\sigma }{\overline{X}}\times 100=\frac{25.50}{40}\times 100=63.75 \end{gathered}$$