Variance Calculator
Find the population or sample variance of a list of numbers, with the standard deviation and steps.
Change the values and press Calculate to work out your own figures.
Enter numbers and say whether they are a whole population or a sample.
Show the working
- Mean = 178 ÷ 8 = 22.25
- Sum of squared deviations = Σ(x − mean)² = 1,059.5
- σ² = 1,059.5 ÷ (N) = 132.4375
- σ = √132.4375 = 11.5081492865
How to use it
Enter numbers and say whether they are a whole population or a sample.
Paste or type the numbers separated by commas, spaces or new lines. Results are worked out exactly and shown to 12 significant figures; Show the working lists each step.
Key facts
σ² = Σ(x − μ)² ÷ N; s² = Σ(x − x̄)² ÷ (n − 1)
Variance and standard deviation
Variance is the standard deviation squared. It is in squared units (square dollars, say), which is why the standard deviation is usually easier to interpret.
Questions
How do I calculate variance?
Find the mean, square each value's distance from it, add the squares and divide by N (population) or n − 1 (sample).
Why square the deviations?
So negative and positive deviations don't cancel out.
Formulas
σ² = Σ(x − μ)² ÷ N; s² = Σ(x − x̄)² ÷ (n − 1)
Sources
Limitations
- Up to 5,000 values. Values are separated by commas, spaces or new lines, so write 1250 rather than 1,250.