Coefficient of Variation Calculator
This coefficient of variation calculator turns a list of numbers into mean, standard deviation and relative spread in percent. Example: the values 12, 15, 11, 18, 14, 16, 13 and 17 give a CV of about 16.89 %.
Source: Wikipedia – Variationskoeffizient. Updated: .
How it is calculated
The coefficient of variation divides the standard deviation by the mean, which makes spread comparable across different scales. A standard deviation of 5 is huge next to a mean of 10 but tiny next to a mean of 1,000; the coefficient of variation shows exactly that.
Formula
CV = s / |x̄|, usually quoted as a percentage. For a sample use the standard deviation with denominator n − 1, for a complete population the one with denominator n. The calculator lists the mean, the squared deviations and both intermediate steps.
Example
For 12, 15, 11, 18, 14, 16, 13, 17 the mean is 14.5 and the squared deviations add up to 42. As a sample, s = √(42 / 7) ≈ 2.449, so CV ≈ 16.89 %. Treating the same numbers as a population gives σ = √(42 / 8) ≈ 2.291 and CV ≈ 15.80 %.
- The smaller the CV, the more uniform the values; above roughly 30 % a series is often called highly variable.
- With a mean close to 0 the CV explodes and says little.
- It is not meaningful for temperatures in degrees Celsius, where zero is arbitrary.
Frequently asked questions
When is the coefficient of variation better than the standard deviation?
When you compare series at different levels or in different units, such as the weights of mice and elephants. The standard deviation depends on the magnitude, the coefficient of variation does not.
What is a good coefficient of variation?
It depends on the field. Measurement technology often expects a few percent, while incomes or share prices vary much more. What matters is the comparison with similar series.
Should I choose sample or population?
If the values are a sample, choose n − 1. If you really have every element, such as all employees of one firm, n is correct. With large data sets the difference is small.
Sources and legal basis
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