Variance Calculator
Calculate population or sample variance from a dataset with step-by-step squared deviations.
Inputs
Variance
3.700000
Standard Deviation
1.923538
Mean
5.2000
Count
5
Step by step
Values used
Data (comma separated) = 4, 8, 6, 5, 3; Type = Sample (n−1)
Sample Variance
s² = Σ(xᵢ − x̄)² / (n − 1)
Population Variance
σ² = Σ(xᵢ − μ)² / n
Variance
= 3.700000
Standard Deviation
= 1.923538
Mean
= 5.2000
Count
= 5
How it works
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
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.