The coefficient of variation (CV) expresses the standard deviation as a percentage of the mean. That simple ratio makes variability comparable across data sets measured in different units or at very different sizes: the precision of a lab assay at two concentrations, the consistency of two production lines, or the risk of two investments. Paste one or two data sets, or type a mean and standard deviation, to get the CV and a direct comparison.
How to use the coefficient of variation calculator
- Choose Raw data to paste values, or Mean and SD if you already have those summaries.
- For raw data, choose a sample (n − 1) or population (N) standard deviation. Sample is the usual choice.
- Optionally paste a second data set to compare relative variability.
- Read the CV on the tape. With two data sets, the comparison line says which is relatively more variable and by how much.
Coefficient of variation formula
where s is the standard deviation and x̄ the mean (use σ and μ for a population). The absolute value keeps the CV positive. Its reciprocal, x̄ ÷ s, is sometimes called the signal-to-noise ratio.
Worked example
Two filling machines are checked with ten packages each.
- Machine A fills 100-gram bags: 98, 102, 101, 97, 103, 99, 100, 104, 96, 100 g. The mean is 100 g and the sample SD is 2.582 g.
- Machine B fills 10-gram sample packets: 9.1, 10.4, 8.7, 11.2, 9.8, 10.9, 8.5, 11.6, 9.3, 10.5 g. The mean is 10 g and the SD is 1.080 g.
Machine A has the larger standard deviation, but relative to what it fills:
- CVA = 2.582 ÷ 100 × 100% = 2.58%.
- CVB = 1.080 ÷ 10 × 100% = 10.80%.
- Machine B is about 4.2 times as variable relative to its target, so it is the one that needs attention.
From a mean and SD alone: a mean of 250 with an SD of 18 gives CV = 18 ÷ 250 = 7.2%.
Interpreting the coefficient of variation
Typical uses
- Laboratory precision. Clinical and analytical labs report intra-assay and inter-assay CVs (often called %RSD); acceptance limits are set by the method and regulator.
- Manufacturing. Comparing consistency across products of different sizes, as in the example.
- Finance. The CV of returns, the SD divided by the mean return, measures risk per unit of reward; lower is better when comparing investments.
- Biology and agriculture. Comparing variability of traits measured on different scales, like seed weight and plant height.
Cautions
The CV is only meaningful on a ratio scale, where zero means “none of the quantity.” Weight, length, time, counts and money qualify; temperature in °F or °C, pH, and test scores with an arbitrary zero do not. When the mean is near zero, small changes in the mean make the CV explode, so it becomes unstable and misleading.
The sample CV is also slightly biased low for small samples. For normally distributed data, a common correction multiplies it by (1 + 1/(4n)), which matters little once n exceeds about 20.
Related measures
For the standard deviation alone, use the standard deviation calculator. For a complete profile that includes the CV alongside skewness, quartiles and more, use the descriptive statistics calculator. If you want the precision of the mean rather than the spread of the values, the standard error calculator reports the relative standard error.
Frequently asked questions
What is a good coefficient of variation?
It depends entirely on the context. Lab assays often aim for a CV under 10% between runs and under 5% within a run; machined parts may need well under 1%; monthly sales or crop yields routinely vary by 20% or more. Compare a CV with others measuring the same kind of thing.
Is the coefficient of variation the same as relative standard deviation?
Yes. Relative standard deviation (RSD), common in chemistry and quality control, is the same quantity: the standard deviation divided by the absolute value of the mean, usually expressed as a percentage.
When should I not use the coefficient of variation?
Avoid it when the mean is close to zero, when values can be negative, or when the scale has no true zero, such as temperature in Fahrenheit or Celsius. A temperature series would have a different CV in Fahrenheit and Celsius, which shows the number has no physical meaning there.
Why compare CVs instead of standard deviations?
Standard deviations carry the units and size of the data. A 1-gram variation is negligible in a 1-kilogram bag but huge in a 2-gram vitamin tablet. Dividing by the mean puts both on the same relative footing.