Discussion Forum

 Two distributions A and B have the same mean. If their  coefficients of variation are 6 and 2 respectively  and $\sigma _{A}, \sigma_{B}$ are their standard deviations, then

Answer:

Explanation:

Let   $\overline{x}_{A}=\overline{x}_{B}=x$

$\frac{\sigma_{A}}{\overline{x}_{A}}\times100=6,\frac{\sigma_{B}}{\overline{x}_{B}}\times100=2$

$\frac{\sigma_{A}}{x}\times100=6,\frac{\sigma_{B}}{x}\times100=2$

$\frac{\sigma_{A}\times100}{6}=x,\frac{\sigma_{B}\times100}{2}=x$

$\Rightarrow$     $\frac{\sigma_{A}\times100}{6}=\frac{\sigma_{B}\times100}{2}\Rightarrow \sigma_{A}=3\sigma_{B}$