About this calculator
Choose sample to divide by n − 1 or population to divide by N.
How to use it
- Enter the numbers.
- Choose sample or population.
- Read the variance.
The formula
s² = Σ(x − x̄)² ÷ (n − 1); σ² = Σ(x − μ)² ÷ N
- Σ(x − x̄)²
- sum of squared deviations
Worked example
12, 15, 9, 20, 14
- Mean 14; squared deviations 4, 1, 25, 36, 0 add to 66.
- Sample variance = 66 ÷ 4 = 16.5; population variance = 66 ÷ 5 = 13.2.
What the result means
Variance is in squared units (marks², ₹²), so the standard deviation is easier to interpret. Variances are useful because they add up for independent quantities.
Assumptions
- Real numbers, at least two of them.
Limitations
- Results are rounded to 10 significant figures.
Frequently asked questions
Should I use sample or population?
Use sample (n − 1) when your data are a sample from a bigger group, which is most of the time. Use population (N) only when you have every member of the group.
Why divide by n − 1?
A sample’s values sit closer to the sample mean than to the true mean, so dividing by n slightly underestimates the spread. Dividing by n − 1 (Bessel’s correction) fixes that on average.
How are variance and standard deviation related?
Standard deviation is the square root of variance.
Last reviewed on 6 October 2026. Found a mistake? Tell us.