Coefficient of variation

In probability theory and statistics, the coefficient of variation (CV) is a measure of dispersion of a probability distribution. It is defined as the ratio of the standard deviation $$\ \sigma $$ to the mean  $$\ \mu $$:


 * $$c_{v} = {\sigma \over \mu }$$

The coefficient of variation is a dimensionless number. For distributions of positive-valued random variables, it allows comparison of the variation of populations that have significantly different mean values. It is often reported as a percentage (%) by multiplying the above calculation by 100.

When the mean value is near zero, the coefficient of variation is sensitive to change in the standard deviation, limiting its usefulness.

The coefficient of variation is also common in applied probability fields such as renewal theory, queueing theory, and reliability theory. In these fields, the exponential distribution is often more important than the normal distribution. The standard deviation of an exponential distribution is equal to its mean, so its coefficient of variation is equal to 1. Distributions with CV < 1 (such as an Erlang distribution) are considered low-variance, while those with CV > 1 (such as a hyper-exponential distribution) are considered high-variance. Some formulas in these fields are expressed using the squared coefficient of variation, often abbreviated SCV.

The absolute value of the coefficient of variation expressed as a percentage is often referred to as the relative standard deviation (RSD or %RSD).