๐Ÿ“ŠSample vs Population Variance Calculator

Calculate population variance (divide by n) and sample variance (divide by n minus 1) for the same data set

How to Use the Sample vs Population Variance Calculator

The same data set can require a different variance formula depending on whether it represents the entire population or just a sample of it. Enter numbers separated by commas or spaces, and this tool calculates both population and sample variance side by side.

Population variance sums the squared deviations from the mean and divides by n, the total count. Sample variance instead divides by n-1, since a sample is only an estimate of a larger population โ€” this adjustment is known as Bessel's correction. The gap between the two values is largest for small n and shrinks as n grows.

Standard deviation is the square root of variance, expressed in the same units as your original data, which makes it easier to interpret how spread out the values are. Use sample variance when you only have part of the full picture, such as survey responses or experimental measurements, and population variance when you truly have every data point, such as every student's score in a class.

Frequently Asked Questions

Why are population and sample variance calculated differently?

Population variance divides by n because you have the entire population. Sample variance divides by n-1 instead, because a sample is only an estimate of the population, and dividing by n-1 corrects for that bias. This is called Bessel's correction.

Why can't I calculate this with fewer than 2 data points?

Sample variance divides by n-1, so with only 1 data point the denominator becomes 0 and the calculation is undefined. You need at least 2 values to get a sample variance result.