The denominator difference
Population variance divides by n. Sample variance divides by n - 1. The n - 1 denominator corrects the tendency for a sample to underestimate the wider population's spread.
When to use each
- Population: use when your dataset contains every value you care about.
- Sample: use when your dataset is a sample used to estimate a larger population.
How to interpret the result
Standard deviation is in the same unit as the original data. A larger value means observations are more spread out around the mean. It does not say whether the data is normally distributed.
Common mistakes
- Choosing population mode because the result is slightly smaller.
- Using standard deviation without checking outliers.
- Comparing datasets with very different units or scales.
- Assuming standard deviation alone describes skewed data well.
Same data, two standard deviations
For the data 2, 4, 4, 9, 11, the mean is 6. The squared deviations are 16, 4, 4, 9 and 25, totaling 58. Population variance divides by 5, giving 11.6 and a population standard deviation of about 3.41. Sample variance divides by 4, giving 14.5 and a sample standard deviation of about 3.81.
The sample version is larger because it uses n - 1. Use population standard deviation when the data is the whole group being described. Use sample standard deviation when the data is a sample used to estimate a wider population.
Useful calculators
FAQ
Why is sample standard deviation larger?
Dividing by n - 1 makes the estimate larger to compensate for using a sample.
Does standard deviation require normal data?
No, but interpretation is easier for roughly symmetric distributions.
Should I report sample or population?
Report the method that matches the data and state it clearly.
Last reviewed: 2026-05-16.