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

Solution

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 $=30\%$

Re‑arrange the formula to solve for SD:

$$\text{SD}=\frac{\text{CV}\times \text{Mean}}{100}$$

Substitute the known values:

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

$$\boxed{\text{Standard Deviation}=6}$$