Coefficient of Variation

Coefficient of variation (CV)

The coefficient of variation takes the standard deviation and expresses it as a fraction of the mean: CV = σ / μ · 100%. Because it carries no units (it's just a percentage), you can compare how spread out two populations are even when their scales or units differ. Adult human height comes in around CV ~5%, which is very uniform; salary, by contrast, runs CV > 50% and is all over the place. A sample with μ = 15 and σ = 3 gives you CV = 20%. As a quick guide, CV < 10% means low variability and anything past 30% is high. One caveat: skip the CV when μ sits near zero or the variable can go negative. In those cases the number gets unstable, or stops meaning anything at all.

Applications

Quality control leans on it (Six Sigma chases a low CV). So does finance, where the Sharpe ratio is essentially a normalized risk/return figure. Biologists use it to track variability among individuals or populations. In analytical method validation, the laboratory CV of repeated measurements usually stays under 5%. And engineers reach for it when comparing the precision of instruments that measure on very different scales.

FAQ

CV vs standard deviation, when to use which? Reach for σ when you want absolute dispersion in the same unit as the data. Switch to CV when you're comparing variability across datasets that use different units, or whose means are far apart.

Can CV be greater than 100%? It can. That just tells you σ is bigger than μ, which happens often in skewed distributions like income or species counts.

Sample CV or population CV? If you're working with a sample, use the sample standard deviation (n − 1); if you have the entire population, use the population σ (divided by N). For small n that decision actually moves the result.