# Coefficient of Variation

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## coefficient of variation

[¦kō·ə′fish·ənt əv ‚ver·ē′ā·shən] (statistics)

The ratio of the standard deviation of a distribution to its arithmetic mean.

## Coefficient of Variation

the ratio of the quadratic deviation to the average value. In variational statistics the difference of any set of positive numbers x_{1,... ,}x_{n} from their arithmetic average x¯ = (x_{1} +... x_{n})/n is characterized by the standard deviation

A relative characteristic of such “scatter” is the coefficient of variation *s/x¯*. In probability theory and mathematical statistics the coefficient of variation of a positive random quantity *X* is defined as the ratio *σ/a*, where *a = EX* is the mathematical expectation, and σ^{2} = DX = E(X -a)^{2} is the dispersion. If *X* is the result of the measurement of some unknown positive constant *a* = *EX*, then the coefficient of variation is a natural characteristic of the relative error of measurement.

## coefficient of variation

The

**standard deviation**expressed as a percentage of the average.