Question

For a distribution, the coefficient of variation is 22.5% and mean is 7.5. Calculate standard deviation.

Answer 1

Given,

Coefficient of variation= 22.5%
Mean, $\overline{\mathit{X}}$= 7.5

$$\begin{gathered} \mathrm{Coefficient}\mathrm{of}\mathrm{Variation}=\frac{\sigma }{\overline{X}}\times 100 \\ 22.5=\frac{\sigma }{7.5}\times 100 \\ \frac{22.5\times 7.5}{100}=\mathrm{\sigma } \\ \mathrm{\sigma }=\frac{168.75}{100} \\ \Rightarrow \mathrm{\sigma }=1.687=1.69approx \end{gathered}$$

Hence, standard deviation is 1.69