Two distributions A and B have the same mean. | vedclass

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(A) Let the common mean of both distributions be $\bar{x}$.Given that the coefficients of variation $(CV)$ for $A$ and $B$ are $6$ and $2$ respectivel

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$\sigma_A = 3 \sigma_B$

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(A) Let the common mean of both distributions be $\bar{x}$.Given that the coefficients of variation $(CV)$ for $A$ and $B$ are $6$ and $2$ respectively.The formula for the coefficient of variation is $CV = \frac{\sigma}{\bar{x}} 	imes 100$.For distribution $A$: $\frac{\sigma_A}{\bar{x}} 	imes 100 = 6 \implies \bar{x} = \frac{100 \sigma_A}{6}$.For distribution $B$: $\frac{\sigma_B}{\bar{x}} 	imes 100 = 2 \implies \bar{x} = \frac{100 \sigma_B}{2}$.Equating the two expressions for $\bar{x}$:$\frac{100 \sigma_A}{6} = \frac{100 \sigma_B}{2}$.$\frac{\sigma_A}{6} = \frac{\sigma_B}{2}$.$\sigma_A = \frac{6}{2} \sigma_B$.$\sigma_A = 3 \sigma_B$.

Two distributions $A$ and $B$ have the same mean. If their coefficients of variation are $6$ and $2$ respectively and $\sigma_A$ and $\sigma_B$ are their standard deviations,then:

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