The mean and coefficient of variation of a certain data are 20 and 30% respectively. Calculate standard deviation.

The coefficient of variation (CV) is defined as

$$\text{CV}=\frac{\text{Standard Deviation (SD)}}{\text{Mean}}\times 100\%$$

Given

• Mean $\bar{x}=20$
• CV $=30\%$

Solve for SD:

$$\text{SD}=\frac{\text{CV}\times \text{Mean}}{100}=\frac{30\times 20}{100}=\frac{600}{100}=6$$

Hence the standard deviation of the data set is 6.