Coefficient of variation
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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 to the mean:
- <math>c_{v} = {\sigma \over \mu }.</math>
The coefficient of variation is a dimensionless number that allows comparison of the variation of populations that have significantly different mean values. It is often reported as on a scale of 0 to 100% by multiplying the above calculation by 100%.
The coefficient of variation is often used when discussing the normal distribution for positive mean values with the standard deviation significantly less than the mean. This application may be reasonable for many models, but breaks down theoretically if the distribution is known to be positive valued, since there is a nonzero probability that the distribution will assume a negative value.
When the mean value is near zero, the coefficient of variation is sensitive to change in the standard deviation, limiting its usefulness.
