Variance Calculator
Calculate population or sample variance from a dataset with step-by-step squared deviations.
About Variance Calculator
Variance measures how far a set of numbers are spread out from their mean. Sample variance divides by n−1 (Bessel's correction) to give an unbiased estimate; population variance divides by n.
Formulas
Sample Variance
s² = Σ(xᵢ − x̄)² / (n − 1)
- xᵢ
- Data point
- x̄
- Sample mean
- n
- Sample size
Population Variance
σ² = Σ(xᵢ − μ)² / n
- xᵢ
- Data point
- μ
- Population mean
- n
- Population size
Worked example
With the default values below, Variance Calculator returns Variance of 3.700000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Data (comma separated)
- 4, 8, 6, 5, 3
- Typeone of Sample (n−1), Population (n)
- Sample (n−1)
Results
- Variance
- 3.700000
- Standard Deviation
- 1.923538
- Mean
- 5.2000
- Count
- 5
Step by step
- 1Values used
- 2Sample Variance
- 3Population Variance
- 4Variance= 3.700000
- 5Standard Deviation= 1.923538
- 6Mean= 5.2000
- 7Count= 5
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
When should I use sample vs population variance?
Use sample variance (divides by n−1) when your data is a subset of a larger population. Use population variance (divides by n) only when you have data for every member of the population.
What is the relationship between variance and standard deviation?
Standard deviation is the square root of variance. It is often preferred because it has the same units as the original data.