Coefficient Of Variation CalculatorFree online math calculator — instant results, no sign-up
Calculate population standard deviation relative to a positive mean.
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About the Coefficient Of Variation Calculator
The Coefficient Of Variation Calculator measures population standard deviation relative to a positive mean and expresses the result as a percentage. Enter a set of values to assess its spread relative to its average, using the population formula rather than the sample formula. For the default values 2, 4, 6, 8, 10, the coefficient of variation is 47.1404520791%.
- Values
- Enter the numeric observations, separated by commas, with every observation expressed in the same measurement unit; the default is 2, 4, 6, 8, 10.
Formula and method
μ = (Σᵢ₌₁ᴺ xᵢ) / N; σ = √[(Σᵢ₌₁ᴺ (xᵢ − μ)²) / N]; CV (%) = (σ / μ) × 100, for μ > 0.
- xᵢThe observation at position i in the entered values.
- iThe observation index, running from 1 through N.
- NThe total number of observations.
- ΣSummation over all entered observations.
- μThe arithmetic mean of the entered values, which must be positive.
- σThe population standard deviation, calculated by dividing the sum of squared deviations by N.
- CV (%)The coefficient of variation expressed as a percentage; the measurement units cancel in the ratio σ / μ.
The calculator finds the arithmetic mean, calculates each value's squared deviation from that mean, and divides their sum by the number of values to obtain population variance. It takes the square root to obtain population standard deviation, then divides by the positive mean and multiplies by 100. For 2, 4, 6, 8, 10, N = 5 and μ = 6. The squared deviations are 16, 4, 0, 4, 16, totaling 40, so population variance is 40 / 5 = 8 and σ = √8. Thus CV = (√8 / 6) × 100 = 47.1404520791% when rounded to ten decimal places.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Values2, 4, 6, 8, 10
Results
- Coefficient of variation (%)47.1404520791
How to use the Coefficient Of Variation Calculator
- 1Enter your observations in Values, separated by commas, or retain the default values 2, 4, 6, 8, 10.
- 2Check that all observations use the same measurement unit and that the list includes the population you intend to summarize.
- 3Confirm that the arithmetic mean is positive and that a relative-spread measure is meaningful for your measurement scale.
- 4Run the calculation to obtain the coefficient of variation as a percentage.
- 5Read the result as population standard deviation relative to the mean; the default values produce 47.1404520791%.
Reading your result
The Coefficient of variation (%) output reports population standard deviation as a percentage of the mean. The default result, 47.1404520791%, means that the population standard deviation is approximately 47.14% of the mean. A smaller CV indicates less spread relative to the mean, while a larger CV indicates more relative spread. A CV of zero means all entered values are identical, provided their mean is positive; there is no universal cutoff for an acceptable CV.
Limitations
This tool treats the entered observations as a population and divides by N, not N − 1. It requires a positive mean: a zero mean makes the ratio undefined, and negative means are outside its stated scope. Means close to zero can produce very large, unstable percentages. CV is generally meaningful for ratio-scale measurements with a genuine zero, not scales such as Celsius or Fahrenheit. Negative observations can also make relative-spread interpretations unsuitable even if the mean is positive. Outliers can strongly affect both the mean and standard deviation, and the displayed decimal precision does not imply equivalent measurement accuracy.
Common questions
Why do the default values produce 47.1404520791%?+
For 2, 4, 6, 8, 10, the mean is 6 and the sum of squared deviations is 40. Dividing by the population count of 5 gives variance 8, so the CV is (√8 / 6) × 100 = 47.1404520791%.
Does this calculator use population or sample standard deviation?+
It uses population standard deviation, dividing the sum of squared deviations by N. A calculation using sample standard deviation divides by N − 1 and will give a larger CV for the same nonconstant data.
Can the coefficient of variation exceed 100%?+
Yes. With a positive mean, a CV above 100% means the population standard deviation exceeds the mean. CV has no fixed upper limit.
Will converting measurement units change the coefficient of variation?+
Multiplying every observation by the same positive conversion factor leaves CV unchanged because both the mean and standard deviation scale equally. Adding an offset changes the mean without changing standard deviation, so CV generally changes and is unsuitable for comparisons across offset-based scales.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.