## Definition The ==Coefficient of Variation== (CV) is the ratio of the standard deviation to the mean, expressing variability as a proportion of the average. It is a dimensionless measure that allows comparison of dispersion across distributions with different units or scales: $ \text{CV} = \frac{\sigma}{\mu} $ > [!example]- Loss distribution $A$ has mean 1000 and standard deviation 200. Loss distribution $B$ has mean 5000 and standard deviation 600. Which is relatively more variable? > $ \text{CV}_A = \frac{200}{1000} = 0.20, \quad \text{CV}_B = \frac{600}{5000} = 0.12 $ > Distribution $A$ is relatively more variable (CV = 20% vs. 12%), even though $B$ has a larger standard deviation in absolute terms.