Question

Coefficient of variation of two distributions are 60% and 75%, and their standard deviations are 18 and 15 respectively. Find their arithmetic means.

Answer 1

Given: $C{V}_1=60,C{V}_2=75,{\sigma }_1=18$ and ${\sigma }_2=15$

Let ${\overline{x}}_1$ and ${\overline{x}}_2$ be the means of 1st and 2nd distribution respectively.

Then,

$C{V}_1=\frac{{\sigma }_1}{{\overline{x}}_1}\times 100\Rightarrow {\overline{x}}_1=\frac{{\sigma }_1\times 100}{C{V}_1}$

$\Rightarrow {\overline{x}}_1=\frac{18\times 100}{60}=30$

$C{V}_2=\frac{{\sigma }_2}{x_2}\times 100\Rightarrow {\overline{x}}_2=\frac{{\sigma }_2\times 100}{C{V}_2}$

$\Rightarrow {\overline{x}}_2=\frac{15\times 100}{75}=20$

Hence, ${\overline{x}}_1=30$ and ${\overline{x}}_2=20$