Variance Calculator
Calculate population and sample variance with step-by-step calculations. Perfect for statistics, data analysis, research, and understanding data spread and variability.
Calculate Variance
Common Variance Calculations
Click on these links to see instant calculations with sample datasets:
Variance Calculations
Variance is a statistical measure that describes how spread out data points are from the mean (average). It quantifies the degree of variation in a dataset.
Variance Formulas
Sample Variance: s² = Σ(xi - x̄)² / (N-1)
Where: xi = data points, μ = population mean, x̄ = sample mean, N = count
Variance Examples
| Dataset | Mean | Population Variance | Sample Variance |
|---|---|---|---|
| 1, 2, 3, 4, 5 | 3.0 | 2.0 | 2.5 |
| 10, 20, 30 | 20.0 | 66.67 | 100.0 |
| 85, 90, 95 | 90.0 | 16.67 | 25.0 |
| 2, 4, 6, 8 | 5.0 | 5.0 | 6.67 |
| 100, 100, 100 | 100.0 | 0.0 | 0.0 |
- Statistics: Measure data spread and variability in research and analysis
- Quality Control: Monitor process variation and consistency in manufacturing
- Finance: Assess investment risk and portfolio volatility
- Research: Analyze experimental data and survey results
- Education: Evaluate test score distributions and performance metrics
Frequently Asked Questions
What is variance in statistics?
Variance is a measure of how spread out data points are from the mean. It's calculated as the average of the squared differences from the mean. A higher variance indicates more spread in the data.
What is the difference between population and sample variance?
Population variance divides by N (total count), while sample variance divides by N-1 (degrees of freedom). Use sample variance when working with a subset of data to estimate the population variance.
How is variance related to standard deviation?
Standard deviation is the square root of variance. While variance is in squared units, standard deviation is in the same units as the original data, making it easier to interpret.