Variance Calculator
Calculate the variance of a list of numbers, for either a full population or a sample.
- Free to use
- Accurate results
- No registration required
- Works on all devices
Enter a list of numbers and choose sample or population to calculate the variance and standard deviation.
Enter numbers separated by commas or spaces.
Your result
4.571
Variance
Standard deviation2.138
Mean5
AI explanation
Formula
Population: σ² = Σ(x−mean)² / n. Sample: s² = Σ(x−mean)² / (n−1)Worked example
Population variance of 2, 4, 4, 4, 5, 5, 7, 9
| Field | Value |
|---|---|
| Numbers | 2, 4, 4, 4, 5, 5, 7, 9 |
| Data type | population |
| Variance | 4 |
| Standard deviation | 2 |
| Mean | 5 |
Assumptions
- Sample variance uses Bessel's correction (dividing by n−1 instead of n), the standard adjustment when your data is a sample rather than the entire population.
- A sample calculation requires at least 2 numbers.
Frequently asked questions
What does variance measure?
It measures the average squared deviation of each value from the mean — a larger variance means the data is more spread out.
Why is variance in "squared units"?
Because each deviation from the mean is squared before averaging, the result is in squared units of the original data (e.g., squared rupees) — which is why standard deviation (variance's square root) is usually easier to interpret directly.
Should I use sample or population variance?
Choose "population" if your data represents the entire group. Choose "sample" if your data is a subset used to estimate a larger population's variance.