Question

The index number of prices of cotton and coal shares in 1998 were as under:
Index Number of Prices:

Cotton	:	188	178	173	164	172	183	184	185	211	217	232	240
Coal	:	131	130	130	129	129	129	127	127	130	137	140	142

Which of these two shares do you consider more variable in prices:

Answer 1

For Cotton

S. No.	Price X	Deviation from mean $$\begin{gathered} \left(x=X-\overline{\mathit{X}}\right) \\ \overline{\mathit{X}}=193.9 \end{gathered}$$	x2
1 2 3 4 5 6 7 8 9 10 11 12	188 178 173 164 172 183 184 185 211 217 232 240	5.9 15.9 20.9 29.9 21.9 10.9 9.9 8.9 17.1 23.1 38.1 46.1	34.81 252.81 436.81 894.01 479.61 118.81 98.01 79.21 292.41 533.61 1451.61 2125.61
	ΣX = 2327		Σx2 = 6796.92

$$\begin{gathered} \overline{\mathit{X}}=\frac{\mathit{\Sigma }\mathit{X}}{\mathit{N}}=\frac{2327}{12}=193.9 \\ SD=\sqrt{\frac{\mathrm{\Sigma }{x}_{}^2}{N}}=\sqrt{\frac{6796.92}{12}}=\sqrt{566.41}=23.80 \\ \mathrm{Coefficient}\mathrm{of}\mathrm{Variation}=\frac{SD}{\overline{\mathit{X}}}\times 100=\frac{23.8}{193.9}\times 100=12.27\% \end{gathered}$$

For Coal

S. No.	Price X	Deviation from mean $x=X\mathit{-}\overline{\mathit{X}}$	x2
1 2 3 4 5 6 7 8 9 10 11 12	131 130 130 129 129 129 127 127 130 137 140 142	−.75 −1.75 −1.75 −2.75 −2.75 −2.75 −4.75 −4.75 −1.75 5.25 8.25 10.25	.56 3.06 3.06 7.56 7.56 7.56 22.56 22.56 3.06 27.56 68.06 105.06
	ΣX = 1581		Σx2= 278.22

$$\begin{gathered} \overline{\mathit{X}}=\frac{\mathit{\Sigma }\mathit{X}}{\mathit{N}}=\frac{1581}{12}=131.75 \\ SD\left(\sigma \right)=\sqrt{\frac{\mathrm{\Sigma }{x}_{}^2}{N}}=\sqrt{\frac{278.22}{12}}=4.815 \\ \mathrm{Coefficient}\mathrm{of}\mathrm{Variation}=\frac{\sigma }{\overline{\mathit{X}}}\times 100=\frac{4.815}{131.75}\times 100=3.65\% \end{gathered}$$
Since coefficient of variance is more of cotton than that of coal. So, prices of cotton shares are more variable.