Discussion Forum



1)

 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


A) $\sigma_{A}=3 \sigma_{B}$

B) $3\sigma_{A}=\sigma_{B}$

C) $\sigma_{A}=2 \sigma_{B}$

D) $2 \sigma_{A}= \sigma_{B}$

Answer:

Option A

Explanation:

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

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

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

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

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