How this calculator works
Population variance divides squared deviations by n. Sample variance divides by n − 1 to estimate variance from a sample; it is undefined for one value. The calculation uses a stable incremental method. Enter up to 1,000 finite values with magnitudes at most 10¹².
The formula
Population variance = Σ(x − mean)² / n
Sample variance = Σ(x − mean)² / (n − 1)A quick example
For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5, population variance is 4 and population standard deviation is 2.
How to use this calculator
- Enter the labeled values, using a decimal point for fractions.
- Check the units and assumptions.
- Calculate, review the result and copy it if needed.
A few common questions
How is this result calculated?
Population variance = Σ(x − mean)² / n
Sample variance = Σ(x − mean)² / (n − 1)
What assumptions should I check?
Population variance divides squared deviations by n. Sample variance divides by n − 1 to estimate variance from a sample; it is undefined for one value. The calculation uses a stable incremental method. Enter up to 1,000 finite values with magnitudes at most 10¹².
Can I see a worked example?
For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5, population variance is 4 and population standard deviation is 2.