Coefficient of Variation

A standard deviation of 5 kg means something very different for newborn birth weights than for adult body weights, so the coefficient of variation divides the spread by the mean to get a unit-free ratio. Enter it with the % display unit and s = 15 against x̄ = 60 reads as 25% relative variability. Analytical chemists live by this number: a method whose CV (they call it relative standard deviation) exceeds a few percent on replicate injections is considered out of control, regardless of whether the analyte is measured in parts per million or grams per litre.

Two traps. First, CV is meaningless when the mean sits near zero or the scale has an arbitrary origin — the CV of a set of Celsius temperatures changes completely if you re-express them in Fahrenheit, because 0 °C is not "no temperature". Use it only on ratio scales with a true zero. Second, it is not a measure of error; a rainfall record can honestly have a CV of 80% simply because rainfall is genuinely erratic. Worked backwards: if a process reports CV = 20% around a mean of 45 units, its standard deviation is 0.20 × 45 = 9 units.