Variance Calculator
Calculate sample variance or population variance for a list of numbers. Enter values separated by commas and choose the variance type to measure how spread out the data is.
Separate each number with a comma.
Choose sample variance if your values are a sample, or population variance if they represent the full population.
How This Calculator Works
Variance measures how spread out a set of numbers is around the mean. This calculator first finds the mean, then calculates the squared distance of each value from the mean, sums those squared differences, and divides by the appropriate divisor.
Sample variance divides by n - 1, while population variance divides by n. Sample variance is usually used when your values are only part of a larger group.
Formula
Sample Variance = Sum of (x - mean)^2 / (n - 1)
Population Variance = Sum of (x - mean)^2 / n
Example
If your values are 10, 12, 15, 18, and 20, the calculator first finds the mean, then measures how far each number is from that mean. Those differences are squared, added together, and divided by either 4 for sample variance or 5 for population variance.
Frequently Asked Questions
What is variance?
Variance is a measure of how far values in a data set are spread out from the mean.
What is the difference between sample and population variance?
Sample variance uses n - 1 in the denominator, while population variance uses n. Sample variance is used when the data is only a sample.
Why do squared differences matter?
Squaring prevents positive and negative differences from canceling each other out and gives more weight to larger deviations.
Can variance be negative?
No. Variance is always zero or positive because it is based on squared values.
How is variance related to standard deviation?
Standard deviation is the square root of variance. It is often easier to interpret because it uses the same units as the original data.