Question

Calculate coefficient of variation from the following data:

Variables	10	20	30	40	50	60	70
Frequencies	6	8	16	15	32	11	12

Answer 1

X	f	fX	$\mathit{x}\mathit{=}\mathit{X}\mathit{-}\mathit{}\overline{\mathit{X}}$	x2	fx2
10 20 30 40 50 60 70	6 8 16 15 32 11 12	60 160 480 600 1600 660 840	−34 −24 −14 −4 6 16 26	1156 576 196 16 36 256 676	6936 4608 3136 240 1152 2816 8112
	∑f = 100	∑fX = 4400			∑f x2 = 27000

$$\begin{gathered} \overline{X}=\frac{{\sum }_{}^{}fX}{{\sum }_{}^{}f}=\frac{4400}{100}=44 \\ \mathrm{Standard}\mathrm{Deviation}\left(\sigma \right)=\sqrt{\frac{{\sum }_{}^{}f{x}^2}{{\sum }_{}^{}f}}=\sqrt{\frac{27000}{100}}=16.43 \\ \mathrm{Coefficient}\mathrm{of}\mathrm{Variation}=\frac{\mathit{\sigma }}{\overline{\mathit{X}}}\times 100=\frac{27000}{100}\times 100=37.34 \end{gathered}$$