Variance Calculator
Calculate population and sample variance, mean, and standard deviation from a list of numbers.
Numbers (comma, space, or line separated)
Mean
18
8 values
Population Variance σ²
24
σ = 4.899Sample Variance s²
27.4286
s = 5.2372How to Calculate Variance
Variance quantifies how far a set of numbers is spread from their mean. It is calculated by: (1) finding the mean, (2) subtracting the mean from each value and squaring the result, and (3) averaging those squared differences.
Population variance (σ²) divides by n and is used when your data is the entire population. Sample variance (s²) divides by n−1 to correct for bias when your data is a sample of a larger population. Enter comma-separated numbers below to see both.
Example
For 10, 12, 23, 23, 16, 23, 21, 16: the mean is 18. The squared differences from the mean are 64, 36, 25, 25, 4, 25, 9, 4 — totaling 192. Population variance = 192/8 = 24. Sample variance = 192/7 ≈ 27.4286.
Common Use Cases
- Measuring the spread or dispersion of data in statistics.
- Comparing the consistency between two datasets (lower variance = more consistent).
- Foundation for calculating standard deviation, confidence intervals, and more.
- Quality control and process capability analysis.
FAQs
What is the difference between variance and standard deviation?
Variance is the average of squared deviations from the mean, while standard deviation is the square root of variance. Standard deviation is in the same units as the original data, making it more intuitive to interpret. Both measure spread, but standard deviation is more commonly reported.
Why are there two formulas for variance?
Population variance divides by n, suitable when you have data for every member of the group. Sample variance divides by n−1 (Bessel's correction) to produce an unbiased estimate when working with a subset of the population.
Can variance be negative?
No — variance is always zero or positive, since it is based on squared differences. A variance of zero means all values are identical.