Variance Calculator
Calculate the variance (s² or σ²) of numerical datasets. Variance measures the expectation of squared deviations from the mean, serving as the foundational parameter in ANOVA and regression analysis.
Enter dataset values separated by commas or spaces
Select sample for surveys/subsets; population for whole groups
Average of squared differences from the mean
How to Use This Calculator
- Enter your data values separated by spaces or commas.
- Select whether your data represents a sample or an entire population.
- Review the variance, standard deviation, and sum of squares.
Formula & Calculation Methodology
Variance aggregates squared differences from the mean, eliminating negative signs and penalizing distant deviations. Sample variance uses n-1 degrees of freedom.
Worked Example
Sample variance of 4, 8, 15, 16, 23, 42
Population variance of 10, 20, 30
Frequently Asked Questions
Why are deviations squared in variance?↓
Squaring turns negative deviations into positive values and assigns disproportionate weight to large outliers, reflecting true risk and volatility.
What units does variance have?↓
Variance is expressed in squared units (e.g. dollars squared, meters squared), which is why standard deviation is often preferred for human interpretation.
What does a variance of zero mean?↓
A variance of zero means all values in the dataset are identical, with zero dispersion.
What is a limitation of variance?↓
Because units are squared, variance cannot be directly added to or compared against the original raw mean.
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Source Citation & Disclaimer
Informational tool only; not licensed tax, legal, or financial advice.