Question

Find the value of standard deviation and coefficient of variation from the following:

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

Answer 1

Size (X)	Frequency (f)	fX	$\mathit{x}\mathbf{=}\left(\mathbf{X}\mathbf{-}\overline{\mathbf{X}}\right)$	x2	fx2
10	6	60	−34	1156	6936
20	8	160	−24	576	4608
30	16	480	−14	196	3136
40	15	600	−4	16	240
50	32	1600	+6	36	1152
60	11	660	16	256	2816
70	12	840	26	676	8112
	Σf=100	ΣfX=4400			Σfx2=27000

$$\begin{gathered} Mean,\overline{X}=\frac{\Sigma fX}{\Sigma f}=\frac{4400}{100}=44 \\ \mathrm{Standard}\mathrm{deviation},\left(\sigma \right)=\sqrt{\frac{\Sigma f{x}^2}{\Sigma f}} \\ or,\left(\sigma \right)=\sqrt{\frac{27000}{100}} \\ or,\left(\sigma \right)=\sqrt{270} \\ \Rightarrow \left(\sigma \right)=16.43 \\ \mathrm{Coefficient}\mathrm{of}\mathrm{S}.\mathrm{D}.=\frac{\left(\sigma \right)}{\overline{X}}\times 100=\frac{16.43}{44}\times 100=37.34 \end{gathered}$$