Question

If n = 10, $\overline{X}=12$ and $\Sigma x_i^2\mathit{=}1530$, then the coefficient of variation is
(a) 36%
(b) 41%
(c) 25%
(d) none of these

Answer 1

(c) 25%

Standard deviation is expressed in the following manner:
$$\begin{gathered} \sigma =\sqrt{\frac{1}{n}\sum _i{x_i}^2-{\left(\overline{X}\right)}^2} \\ =\sqrt{\frac{1530}{10}-{\left(12\right)}^2} \\ =\sqrt{9} \\ =3 \end{gathered}$$

$$\begin{gathered} CV=\frac{\sigma }{\overline{X}}\times 100 \\ =\frac{3}{12}\times 100 \\ =25\% \end{gathered}$$