Use this Variance Calculator to calculate sample or population variance from a numeric dataset. Variance measures how spread out values are around their mean.

Calculation Method

Population variance:

σ² = Σ(x − μ)² ÷ N

Sample variance:

s² = Σ(x − x̄)² ÷ (n − 1)

Example

For:

2, 4, 6, 8

The mean is:

(2 + 4 + 6 + 8) ÷ 4 = 5

The sum of squared deviations is:

9 + 1 + 1 + 9 = 20

Population variance = 20 ÷ 4 = 5

Sample variance = 20 ÷ 3 ≈ 6.67

Important Note

Use population variance when the entered values represent the entire population being described. Use sample variance when the data are a sample used to estimate variability in a larger population.

Source

• OpenStax Introductory Statistics 2e — Measures of the Spread of the Data