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.