Variance Calculator
Variance Calculator
Enter a list of numbers and choose whether it's a sample or the full population. This calculates the variance — the average of the squared differences from the mean, and the basis for the standard deviation.
Variance and standard deviation measure exactly the same underlying spread, but standard deviation (variance's square root) is usually easier to interpret because it's back in the same units as the original data — variance itself is in squared units, which is why it's often used as an intermediate step in statistical formulas rather than reported on its own. As with standard deviation, the sample formula (dividing by n−1) applies to data sampled from a larger population, while the population formula (dividing by n) applies only when your dataset is the entire population being studied.
- Sample formula: Variance = Σ(x − mean)² ÷ (n − 1) — divides by n−1 (Bessel's correction), used when your data is a sample drawn from a larger population.
- Population formula: Variance = Σ(x − mean)² ÷ n — divides by n, used only when your dataset IS the entire population you care about.
- Relationship to standard deviation: variance is standard deviation squared — standard deviation is usually easier to interpret since it's back in the original units, while variance is in squared units.
Why is variance in squared units?
Because it's built from squared deviations from the mean — this makes the raw number harder to interpret directly, which is why standard deviation (its square root) is more commonly reported.
Should I use sample or population variance?
Use sample (n−1) almost always in practice — it's the correct choice whenever your data represents a subset of a larger group you're trying to describe.
Variance Calculator
Enter a list of numbers and choose whether it's a sample or the full population. This calculates the variance — the average of the squared differences from the mean, and the basis for the standard deviation.
Variance and standard deviation measure exactly the same underlying spread, but standard deviation (variance's square root) is usually easier to interpret because it's back in the same units as the original data — variance itself is in squared units, which is why it's often used as an intermediate step in statistical formulas rather than reported on its own. As with standard deviation, the sample formula (dividing by n−1) applies to data sampled from a larger population, while the population formula (dividing by n) applies only when your dataset is the entire population being studied.
- Sample formula: Variance = Σ(x − mean)² ÷ (n − 1) — divides by n−1 (Bessel's correction), used when your data is a sample drawn from a larger population.
- Population formula: Variance = Σ(x − mean)² ÷ n — divides by n, used only when your dataset IS the entire population you care about.
- Relationship to standard deviation: variance is standard deviation squared — standard deviation is usually easier to interpret since it's back in the original units, while variance is in squared units.
Why is variance in squared units?
Because it's built from squared deviations from the mean — this makes the raw number harder to interpret directly, which is why standard deviation (its square root) is more commonly reported.
Should I use sample or population variance?
Use sample (n−1) almost always in practice — it's the correct choice whenever your data represents a subset of a larger group you're trying to describe.