If the coefficient of variation of a distribution is $60\%$ and the standard deviation is $12,$ then the arithmetic mean of the distribution is:

Solution

1. The formula for the coefficient of variation is $CV=\left(\frac{\sigma }{\bar{x}}\right)\times 100$, where $\sigma$ is the standard deviation and $\bar{x}$ is the mean.
2. Substitute the given values into the formula: $60=\left(\frac{12}{\bar{x}}\right)\times 100$.
3. Solve for $\bar{x}$ by rearranging the equation: $\bar{x}=\frac{12\times 100}{60}$.
4. Calculate the final value: $$\begin{array}{rl}\bar{x}& =\frac{1200}{60}\\ & =20\end{array}$$.
5. Hence the answer is (C).