$CV = \frac{\sigma}{\mu} = \frac{\sqrt{\text{Var}(X)}}{E[X]}$
The Coefficient of Variation ($CV$) is the ratio of the standard deviation to the mean, expressing dispersion as a dimensionless proportion of the mean.
$CV$ is used to compare the relative variability of distributions with different units or scales. A larger $CV$ indicates greater dispersion relative to the mean; it is meaningful only when $E[X] > 0$.
> [!example]- Comparing Variability of Two Loss Distributions {💡 Example}
> Distribution A has mean \$500 and standard deviation \$100. Distribution B has mean \$2{,}000 and standard deviation \$300. Which has greater relative variability?
>
> > [!answer]- Answer
> > Compute each $CV$:
> > $CV_A = \frac{100}{500} = 0.20, \qquad CV_B = \frac{300}{2{,}000} = 0.15$
> > Distribution A has greater relative variability, even though its absolute standard deviation is smaller.