Free · Descriptive statistics

Population and Sample Coefficient of Variation

Compare standard deviation with the mean, with the small-sample correction for normally distributed data.

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

A standard deviation of 20 and mean of 100 give a CV of 20%. For a normally distributed sample of five observations the correction gives 21%.

CV = standard deviation / mean; corrected sample CV = (1 + 1/(4n)) s / mean

Worked example

Enter these known values and leave the other values blank.

Dataset type
Population
Mean (μ)
100
Standard deviation (σ)
20
Coefficient of variation
20 %

Assumptions and limitations

  • Use a ratio scale with a meaningful zero; comparing CVs across interval scales such as Celsius is not meaningful.
  • The sample correction assumes a normally distributed population and at least two observations.
  • The mean must be nonzero. Negative means produce a signed ratio; they do not provide the usual positive relative-dispersion interpretation.
  • The correction is an estimate under the stated model, not a universal removal of bias.

Common questions

Why is the sample result different?

The sample mode multiplies the ratio s/mean by 1 + 1/(4n), using the normally distributed data assumption.

Can I solve for the mean or standard deviation?

Enter a CV and the other known values. Lock known inputs to have incompatible targets reported as a conflict.

References

The sample CV identity directly names visible sample mean and standard deviation so locked inconsistent targets cannot be satisfied solely by hidden population mirrors. The calculation variants and all controls remain captured. A coefficient of variation requires a nonzero mean; the normally distributed sample correction requires at least two observations.

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