Instantly find population & sample variance for any data set
Variance Calculator
Separate numbers with commas, spaces, semicolons, or new lines.
Results
Overview
Population (divide by N)
Formula: σ² = Σ(xᵢ − μ)² / N · N = 6
Sample (divide by N−1, Bessel's correction)
Formula: s² = Σ(xᵢ − x̄)² / (N−1) · N−1 = 5
Range Info
Deviation Table
| x | x − mean | (x − mean)² |
|---|---|---|
| 4 | -14 | 196 |
| 8 | -10 | 100 |
| 15 | -3 | 9 |
| 16 | -2 | 4 |
| 23 | +5 | 25 |
| 42 | +24 | 576 |
| Σ | — | 910 |
Each row shows how far a value deviates from the mean and the squared deviation.
The Variance Calculator computes both population variance (σ²) and sample variance (s²) from any list of numbers in seconds. Paste your data set, choose your variance type, and instantly see the mean, squared deviations, and standard deviation — complete with a step-by-step deviation table showing exactly how each value contributes to the result.
Population variance (σ²) divides the sum of squared deviations by N — the total number of values. Sample variance (s²) divides by N−1 (Bessel's correction) to correct for the bias that occurs when estimating variance from a subset of a larger population. Use population variance when you have data for every member of the group; use sample variance when your data is a sample drawn from a larger population.
First, find the mean of the data set. Then subtract the mean from each value and square the result (the squared deviation). Sum all squared deviations together. Finally, divide by N for population variance or by N−1 for sample variance. Standard deviation is simply the square root of the variance.
You can separate numbers with commas, spaces, semicolons, or new lines — any combination works. For example: '4, 8, 15, 16, 23, 42' or one number per line. The calculator accepts integers and decimals, including negative numbers.
Variance measures how spread out values are from the mean. With only one number, there is no spread — every value equals the mean, so the variance is always zero. Sample variance additionally requires at least two values because it divides by N−1, which would be zero for a single-item data set.