StatisticsdrillCoefficient of variation
The coefficient of variation is the standard deviation divided by the mean, usually expressed as a percent: CV = sd / mean * 100%. It measures relative spread, so you can compare the variability of data sets with different units or very different averages.
Syntax
CV = sd / mean * 100%| Part | What it is |
|---|---|
sd | the standard deviation (sample or population, stated consistently) |
mean | the mean of the same data; must be positive for the CV to make sense |
Examples
mean = 50, sd = 5
CV = 5 / 50 * 100%Result: 10%
Excel: =STDEV.S(A1:A10) / AVERAGE(A1:A10)
Product A: mean 100, sd 10 -> CV = 10%
Product B: mean 20, sd 4 -> CV = 20%Result: B is relatively more variable even though its sd is smaller
Portfolio returns: mean 8%, sd 12%
CV = 12 / 8Result: 1.5 (150%), i.e. 1.5 units of risk per unit of return
Common mistakes
- Using the CV when the mean is zero or negative (temperatures in Celsius, returns that average below zero); the ratio is meaningless there.
- Comparing a sample CV with a population CV; compute both the same way.
- Forgetting the CV is unitless; a CV of 10% is 10% whether the data is in dollars or kilograms, which is exactly why it is useful.
Practice Coefficient of variation
These drills check your answer on live data, free, no account needed.
- Coefficient of variationA sample of 6 minutes to resolve a support ticket (minutes): 46, 35, 28, 23, 26, 17. What is the coefficient of variation, using the sample standard deviation? Give it as a percent. Give the percent rounded to 2 decimal places.
Questions
What is a good coefficient of variation?
It depends on the field. In lab assays a CV under 10% is often acceptable; in finance a lower CV means less risk per unit of return. Compare CVs within the same context rather than against a fixed cutoff.
Is the coefficient of variation the same as relative standard deviation?
Yes. Relative standard deviation (RSD) is the same ratio, usually quoted as a percent, and the term is common in chemistry and lab work.
Related
- Standard deviationThe standard deviation formula, sample versus population versions, a worked example with exact numbers and the Excel functions STDEV.S and STDEV.P.
- VarianceHow to calculate variance step by step, why the sample version divides by n - 1, how it relates to standard deviation, and Excel VAR.S and VAR.P.
- Mean, median and modeHow to calculate the mean, median and mode of a data set by hand and in Excel, when each average is the right one, and the mistakes that give a wrong answer.
- z-scoreThe z-score formula z = (x - mean) / sd, worked examples, how to read a z-score as a percentile with the normal table, and the Excel function STANDARDIZE.