Question

The sum of the squares deviations for 10 observations taken from their mean 50 is 250. The coefficient of variation is
(a) 10 %
(b) 40 %
(c) 50 %
(d) none of these

Answer 1

(a) 10%

$$\begin{gathered} \mathrm{We}\mathrm{have}: \\ \overline{X}=50,n=10 \\ \sum _{i=1}^{10}{\left(x_i-\overline{X}\right)}^2=250 \\ \therefore \mathrm{SD}=\sqrt{\mathrm{Variance}\mathrm{of}X} \\ =\sqrt{\frac{\sum _{i=1}^{10}{\left(x_i-\overline{X}\right)}^2}{n}} \\ =\sqrt{\frac{250}{10}} \\ =5 \end{gathered}$$

Using $\mathrm{CV}=\frac{\sigma }{\overline{X}}\times 100$

$$\begin{gathered} \Rightarrow \mathrm{CV}=\frac{5}{50}\times 100 \\ =10\% \end{gathered}$$