Variance Calculator
Variance measures the average squared deviation from the arithmetic mean and describes dispersion in a data set. The calculator lets you choose population variance for a full defined group or sample variance when estimating a wider population from observations.
How to use this calculator
- Enter the data values and select population or sample variance to match the statistical question.
- Review the worked population example and compare its arithmetic with the inputs you plan to use.
- Change one input at a time when exploring a different scenario, and keep units and assumptions consistent.
Population or sample variance
Population variance = Σ(x − mean)² ÷ n; sample variance = Σ(x − mean)² ÷ (n − 1).
- Variance squares deviations, so its unit is the square of the data unit; standard deviation returns to the original unit scale.
- The page's numerical output is calculated from the values entered; it does not independently verify whether those inputs fit the real-world situation.
Worked examples
Population example
For population values 2, 4, and 6, the mean is 4 and the squared deviations sum to 8.
8 ÷ 3 = 2.6667
Population variance is about 2.667 square units.
Understanding the result
Using n − 1 for sample variance compensates for estimating the mean from a sample under the standard unbiased-estimator setup.
Variance is sensitive to outliers and can be hard to interpret when the squared unit is far from the original measurement scale.
Important notes
State whether sample or population variance was used whenever reporting the value.
Displayed values may be rounded for readability. Keep appropriate precision for intermediate calculations and check the unit labels before using the result.
Frequently asked questions
What does the Variance Calculator result mean?
Using n − 1 for sample variance compensates for estimating the mean from a sample under the standard unbiased-estimator setup.
What should I check before using the variance calculator?
State whether sample or population variance was used whenever reporting the value.
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Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate Standard Deviation — Learn what standard deviation measures, the population and sample formulas, and how to interpret the result.
- How to Calculate a Z-Score — Learn how a z-score shows how far a value is from the mean in standard-deviation units.
- Standard Deviation — Understand standard deviation as a measure of spread and the difference between population and sample standard deviation.
This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.