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How to use
The coefficient of variation calculator measures spread relative to the dataset mean and reports mean, standard deviation and variance. Choose sample or population mode. CV is useful for comparing relative variability across scales, but becomes unstable when the mean is near zero. You can also enter the mean and standard deviation directly without the dataset.
- Choose Dataset or Mean and standard deviation. In summary mode, use the standard deviation you already calculated.
- Enter values separated by commas, spaces or line breaks.
- Choose sample for a sample standard deviation or population for a complete population.
- Calculate to see CV, mean, standard deviation and variance.
How it is calculated
Example
Example: for 10, 12, 9, 11, 13, 10, the mean is about 10.833. In sample mode, s uses n−1 and CV = s / |mean| × 100%. If you already know mean 50 and standard deviation 5, choose Mean and standard deviation: CV=5/50×100=10% and variance=25. For dataset 8, 10, 12, the mean is 10; population CV is about 16.3299%, while sample CV is 20%. The n versus n−1 divisor explains the difference.
Important notes
Do not rely on CV when the mean is zero or very close to zero. Sample versus population standard deviation also changes the reported CV.
Worked examples and interpreting results
Data 8, 10, 12 have mean 10 and sample standard deviation 2. Sample coefficient of variation is 20%, since the deviation is one fifth of the mean.
| Case | Calculation | Result |
|---|---|---|
| Sample standard deviation | √((4 + 0 + 4) ÷ (3 − 1)) | 2 |
| Coefficient of variation | 2 ÷ 10 × 100 | 20 % |
| CV from mean 50 and standard deviation 5 | 5 ÷ |50| × 100 | 10 % |
| Sample CV for 8, 10, 12 | √(((8−10)² + (10−10)² + (12−10)²) ÷ 2) ÷ 10 × 100 | 20 % |
How to check the result
Select sample; population mode changes the variance divisor. CV comparisons suit a scale with a meaningful zero and positive mean; values become unstable near zero mean.
Frequently asked questions
How is CV different from standard deviation?
Standard deviation keeps the data's units; CV expresses spread relative to the mean as a percentage.
Sample or population?
Use sample when observations are a sample from a broader population; use population when the full population is present.
Why is CV undefined at mean zero?
Because the formula divides by the magnitude of the mean.
How do I calculate CV from mean and standard deviation?
Choose Mean and standard deviation under Available inputs and enter both in the same unit. The calculator returns 100×SD/|mean| without requiring the raw observations.
Is CV appropriate for Celsius temperatures?
Generally no: meaningful CV comparisons require a ratio scale with a meaningful zero. Celsius zero is conventional. Even when a numerical result exists, a near-zero mean or negative values require careful interpretation.