Standard Deviation Calculator

Sample or population standard deviation, from any list of numbers.

Use "sample" when your numbers are a subset of a larger population; use "population" when they're the entire group you care about.

Sample standard deviation
2.1381
Mean
5.0000
Variance
4.5714

Sample standard deviation divides by n−1 instead of n (Bessel's correction), which corrects for the tendency to underestimate variability from a sample alone.

A worked example

For 2, 4, 4, 4, 5, 5, 7, 9, the mean is 5, the population standard deviation is exactly 2, and the sample standard deviation is about 2.14.

Frequently asked questions

What does standard deviation actually tell you?

How spread out the numbers are from the mean — a small standard deviation means values cluster tightly around the average; a large one means they're spread widely.

When should I use sample vs. population standard deviation?

Use population when your numbers represent the entire group you care about. Use sample when your numbers are just a subset used to estimate something about a larger group — sample standard deviation's n−1 divisor corrects for that estimation.