Variance measures how far values are spread around the mean by averaging squared deviations.

When should I use sample variance?

Use sample variance when your data is a sample from a larger population. It divides by n - 1 to reduce bias in the estimate.

Why review standard deviation too?

Standard deviation is the square root of variance, so it expresses spread in the original units and is often easier to interpret.

Can I calculate sample variance from one value?

No. Sample variance divides by n - 1, so it needs at least two values. Population variance for one value is valid and equals zero.

Variance Calculator

Paste a dataset, choose population or sample, and see the variance with every step needed to check the math.

Sample or population

Your dataset

Enter the values you want to compare

Use Population when you have every value. Choose Sample when these values represent a larger group.

Dataset values · comma, space, or line break

Decimal, negative, and scientific-notation values are supported.

Variance type

Calculation steps

Each value, its deviation from the mean, and the squared deviation.

Value	Mean	Deviation	Squared deviation
4	8.0000	-4.0000	16.0000
6	8.0000	-2.0000	4.0000
8	8.0000	0.0000	0.0000
10	8.0000	2.0000	4.0000
12	8.0000	4.0000	16.0000
Sum of squared deviations			40.0000

Formula

Choose the denominator by intent

Population: σ² = Σ(xᵢ − μ)² / N

Sample: s² = Σ(xᵢ − x̄)² / (n − 1)

Variance uses squared units. Standard deviation takes the square root so the spread returns to the original units.

Method reference: NIST Measures of Scale →

Interpret the result

Lower variance means values stay closer to the mean. Higher variance means the dataset is more spread out. Compare variance only when the datasets use compatible units and definitions.

Worked example

For 4, 6, 8, 10, 12, the mean is 8. The squared deviations are 16, 4, 0, 4, and 16, for a total of 40. Population variance is 40 ÷ 5 = 8. Sample variance is 40 ÷ 4 = 10.