Variance Calculator
Enter a list of numbers and calculate the variance instantly. Toggle between population (σ²) and sample (s²) variance. Also shows standard deviation, mean, and count.
Variance Formula Comparison
| Type | Symbol | Formula | Divisor |
|---|---|---|---|
| Population | σ² | Σ(xi − μ)² ÷ N | N |
| Sample | s² | Σ(xi − x̄)² ÷ (n−1) | n − 1 |
Understanding Variance
- Variance = 0 — all values are identical (no spread)
- Small variance — values are clustered close to the mean
- Large variance — values are widely spread from the mean
- Units — variance is in squared units (cm², $²), which is why standard deviation is often preferred
Related Statistics Calculators
- Standard Deviation Calculator — square root of variance with step-by-step
- Mean / Average Calculator
- Range Calculator — simplest measure of spread
- Five Number Summary Calculator
- All Statistics Calculators
Frequently Asked Questions
What is variance?
Variance measures how far each number in a data set is from the mean. It is the average of the squared differences from the mean. The unit of variance is the square of the original data’s unit (e.g., if data is in meters, variance is in meters²).
Variance vs standard deviation?
Variance = average of squared deviations. Standard deviation = square root of variance. Standard deviation is in the same units as the data, making it easier to interpret. Variance is preferred in mathematical formulas and statistical tests.
Population vs sample variance?
Population variance divides by n (total count). Sample variance divides by n−1 (Bessel’s correction) for an unbiased estimate. Use population when you have all data; use sample for a subset.
Can variance be negative?
No. Variance can never be negative because it is the sum of squared values divided by a positive number. A variance of 0 means all values are identical. The larger the variance, the more spread out the data.
Variance and standard deviation are the most widely used measures of data spread in statistics.
