Variance calculator finds how far your data points spread from the mean, reported in squared units.
About this calculator
Variance calculator finds how far your data points spread from the mean, reported in squared units. Unlike standard deviation, variance is not in the same units as your original measurements — that is why SD (the square root of variance) is often easier to interpret.
This tool shows both population variance (divide by n) and sample variance (divide by n−1) side by side. Use population when your dataset is the complete group — every student in a class, every batch from a production run. Use sample when your list is a subset drawn from a larger population — 50 survey respondents out of thousands.
For the dataset 12, 15, 18, 22, 15, 30, 15, 20, 25, 18 the mean is 19 and sample variance is about 32.67. Population variance is about 29.40 because it does not apply Bessel's correction.
Pair with [[standard-deviation]] for spread in original units, [[mean-median-mode]] for central tendency, and [[statistics]] for a full descriptive summary.
Common uses
- Statistics homework asking for sample or population variance of a dataset
- Quality engineer comparing batch-to-batch variance in manufacturing measurements
- Researcher checking whether sample variance differs from population variance on a full census
- Data analyst verifying spreadsheet VAR.P vs VAR.S functions on the same column
- Teacher demonstrating why sample variance uses n−1 instead of n
Frequently asked questions
What is the variance of 12, 15, 18, 22, 15, 30, 15, 20, 25, 18?
Mean = 19. Population variance σ² ≈ 29.40 (divide squared deviations by 10). Sample variance s² ≈ 32.67 (divide by 9). Standard deviation is the square root of whichever variance you choose.
How is variance different from standard deviation?
Variance is the average squared deviation from the mean. Standard deviation is the square root of variance, so it returns to the original data units. Variance is used in formulas; SD is easier to explain to non-statisticians.
When should I use sample variance vs population variance?
Use population variance when your data is the entire group. Use sample variance when your list is a sample from a larger population — exam scores from one section of a nationwide test, for example.
Why does sample variance divide by n−1?
Dividing by n−1 (Bessel