Variance Calculator
Calculate population variance (σ²) or sample variance (s²) for any data set. Also shows standard deviation, mean, and sum of squared differences.
Variance
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Standard Deviation —
Mean —
Count (n) —
Sum of Squared Differences —
How to Use This Calculator
Enter your data set as comma-separated numbers (e.g. 10, 20, 30, 40, 50). Choose Population or Sample type. The calculator returns variance, standard deviation, mean, count, and sum of squared differences.
Formula
σ² = Σ(xᵢ−μ)²/N (Population) • s² = Σ(xᵢ−x̄)²/(n−1) (Sample)
Example
10,20,30,40,50 → Mean=30, SSD=1000, σ²=200, σ≈14.14
Frequently Asked Questions
- Variance measures how far numbers are spread from the mean. It is the average of the squared differences from the mean.
- Population variance divides by N (all data points). Sample variance divides by n−1 (Bessel's correction) to give an unbiased estimate.
- Squaring eliminates negative signs and emphasizes larger deviations. Taking the square root of variance gives the standard deviation in the original units.
- Variance is used in statistical calculations like ANOVA and linear regression. Standard deviation is easier to interpret as it is in the same units as the data.
- High variance means data is widely spread from the mean. Low variance means data points are close together.