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Two distributions $A$ and $B$ have the same mean. If their coefficients of variation are 6 and 2 respectively and $\sigma_{A^{\prime}} \sigma_B$ are their standard deviations, then
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Verified Answer
The correct answer is:
$\sigma_A=3 \sigma_B$
Let $\bar{x}_A=\bar{x}_B=x$
$$
\begin{aligned}
& \frac{\sigma_A}{\bar{x}_A} \times 100=6, \frac{\sigma_B}{\bar{x}_B} \times 100=2 \\
& \frac{\sigma_A}{x} \times 100=6, \frac{\sigma_B}{x} \times 100=2 \\
& \frac{\sigma_A \times 100}{6}=x, \frac{\sigma_B \times 100}{2}=x \\
\Rightarrow \quad & \frac{\sigma_A \times 100}{6}=\frac{\sigma_B \times 100}{2} \Rightarrow \sigma_A=3 \sigma_B
\end{aligned}
$$
$$
\begin{aligned}
& \frac{\sigma_A}{\bar{x}_A} \times 100=6, \frac{\sigma_B}{\bar{x}_B} \times 100=2 \\
& \frac{\sigma_A}{x} \times 100=6, \frac{\sigma_B}{x} \times 100=2 \\
& \frac{\sigma_A \times 100}{6}=x, \frac{\sigma_B \times 100}{2}=x \\
\Rightarrow \quad & \frac{\sigma_A \times 100}{6}=\frac{\sigma_B \times 100}{2} \Rightarrow \sigma_A=3 \sigma_B
\end{aligned}
$$
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