Question

Coefficient of variation of two distributions are $60\text{and}70$, and their standard deviations are $21\text{and}16$, respectively. What are their arithmetic means?

Answer 1

Standard deviation of $1^{st}$ distribution $\left({\sigma }_1\right)=21$

$C.V.\left(1st\text{distribution}\right)=\frac{{\sigma }_1}{{\overline{x}}_1}\times 100$

$\Rightarrow \frac{21}{{\overline{x}}_1}\times 100=60$

$\Rightarrow \frac{21}{60}\times 100={\overline{x}}_1$

$\Rightarrow {\overline{x}}_1=\frac{21}{60}\times 100$

$\Rightarrow {\overline{x}}_1=0.35\times 100=35$

$\Rightarrow {\overline{x}}_1=35$

Standard deviation of $2^{nd}$ distribution $\left({\sigma }_2\right)=16$

$C.V.\left(2nd\text{distribution}\right)=\frac{{\sigma }_2}{{\overline{x}}_2}\times 100$

$\Rightarrow \frac{16}{{\overline{x}}_2}\times 100=70$

$\Rightarrow \frac{16}{70}\times 100={\overline{x}}_2$

$\Rightarrow {\overline{x}}_2=\frac{16}{70}\times 100$

$\Rightarrow {\overline{x}}_2=0.2285\times 100=22.85$

Thus, the arithmetic means ${\overline{x}}_1\text{and}{\overline{x}}_2$ are $35\text{and}22.85$ respectively.