Coefficient of Variation

Study guide: Exam P-1

The Coefficient of Variation CV is the ratio of the standard deviation to the mean, measuring dispersion as a proportion of the mean.

CV = \frac{\sigma}{\mu}

= \frac{\sqrt{\text{Var}(X)}}{E[X]}

• CV is dimensionless, so it can compare the relative variability of distributions with different units or scales
• A larger CV indicates greater dispersion relative to the mean
• It requires E[X] \neq 0; it is used to compare the variability of positive distributions, such as losses, with different expected values

Comparing Variability of Two Loss Distributions 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 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.