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Coefficient of variation of two distributions are 50 and 60 and their arithmetic means are 30 and 25 , respectively. Then, difference of their standard deviations is
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We know that,
$$
\begin{aligned}
&\text { Coefficient of variation }=\frac{\sigma}{\overline{\mathrm{x}}} \times 100 \\
&\therefore \mathrm{CV} \text { of } 1 \text { st distribution }=\frac{\sigma_1}{30} \times 100 \\
&\Rightarrow \quad 50=\frac{\sigma_1}{30} \times 100 \Rightarrow \sigma_1=15 \\
&\qquad[\mathrm{CV} \text { of } 1 \text { st distribution }=50 \text { (given) }] \\
&\text { Also, } \mathrm{CV} \text { of } 2 \text { nd distribution }=\frac{\sigma_2}{25} \times 100 \\
&\Rightarrow 60=\frac{\sigma_2}{25} \times 100 \\
&\Rightarrow \sigma_2=\frac{60 \times 25}{100} \Rightarrow \sigma_2=15 \\
&\text { Thus, } \sigma_1-\sigma_2=15-15=0
\end{aligned}
$$
$$
\begin{aligned}
&\text { Coefficient of variation }=\frac{\sigma}{\overline{\mathrm{x}}} \times 100 \\
&\therefore \mathrm{CV} \text { of } 1 \text { st distribution }=\frac{\sigma_1}{30} \times 100 \\
&\Rightarrow \quad 50=\frac{\sigma_1}{30} \times 100 \Rightarrow \sigma_1=15 \\
&\qquad[\mathrm{CV} \text { of } 1 \text { st distribution }=50 \text { (given) }] \\
&\text { Also, } \mathrm{CV} \text { of } 2 \text { nd distribution }=\frac{\sigma_2}{25} \times 100 \\
&\Rightarrow 60=\frac{\sigma_2}{25} \times 100 \\
&\Rightarrow \sigma_2=\frac{60 \times 25}{100} \Rightarrow \sigma_2=15 \\
&\text { Thus, } \sigma_1-\sigma_2=15-15=0
\end{aligned}
$$
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