Variance Calculator
Calculate Population Variance (σ²) and Sample Variance (s²) for large datasets. Features high-precision statistical logic and Bessel correction support.
About
Statistical variance quantifies how spread out a data set is relative to its mean. Financial analysts use this metric to assess asset volatility and risk. Quality control engineers rely on it to measure manufacturing consistency. A low variance indicates data points are clustered closely around the average. A high variance suggests scattered data and less predictability. Distinguishing between population and sample data is critical for accuracy. Using population formulas on sample data underestimates the true spread. This tool applies the Bessel correction automatically when sample mode is selected.
Formulas
The calculation differs based on the data scope.
Population Variance:
σ2 = N∑i=1 xi − μ2NSample Variance (Bessel's Correction):
s2 = n∑i=1 xi − 2n − 1Reference Data
| Sample Size (n) | Correction Factor (nn − 1) | Bias Impact (%) |
|---|---|---|
| 2 | 2.000 | 50.0% |
| 5 | 1.250 | 20.0% |
| 10 | 1.111 | 10.0% |
| 20 | 1.053 | 5.0% |
| 30 | 1.034 | 3.3% |
| 50 | 1.020 | 2.0% |
| 100 | 1.010 | 1.0% |
| 500 | 1.002 | 0.2% |
| 1000 | 1.001 | 0.1% |