Coefficient of variation

The coefficient of variation is the standard deviation divided by the mean — spread relative to size, without units.

\text{CV} = \frac{s}{\xbar} \quad (\times 100\% \text{ to express as a percentage})

Sample coefficient of variation.

$s$: Sample standard deviation ( $n - 1$ ).
$\xbar$: Sample mean (must be positive).

When to use

Comparing variability of quantities with very different means or units (price volatility of a cheap vs an expensive item, precision of two lab methods).
Only for ratio-scale data with a true zero and positive values.

How to interpret

A CV of 0.03 (3%) means the SD is 3% of the mean. A larger CV means more relative variability. The CV has no units.

Common mistakes

Using it for interval data such as °C, where the zero is arbitrary (the CV changes if you switch to °F).
Using it when the mean is near zero — the CV explodes and becomes meaningless.
Comparing CVs computed with different SD conventions.

Example

Machine A fills 48, 50, 52, 50 g: $s = 1.633$ , $\xbar = 50$ , CV = 3.3%. Machine B fills 4, 6, 5, 5 g: $s = 0.816$ , $\xbar = 5$ , CV = 16.3%. B has the smaller SD but is five times more variable relative to its target.