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How this calculator works
Standard deviation is the typical distance of the values from their mean. Use the population formula when your list is the entire group you care about, and the sample formula, which divides by n − 1, when the list is a sample used to estimate a larger group. The sample value is always slightly larger.
Formula
- Mean = Σx / n
- Population variance σ² = Σ(x − mean)² / n
- Sample variance s² = Σ(x − mean)² / (n − 1)
- Standard deviation = √variance
Worked example
2, 4, 4, 4, 5, 5, 7, 9
- Numbers
- 2, 4, 4, 4, 5, 5, 7, 9
Results = 2.1381
Sample standard deviation of 8 values. The population value is 2.
Frequently asked questions
Should I use sample or population standard deviation?
Use sample (n − 1) when your data is a sample from a larger group, which is the usual case in research and surveys. Use population (n) when you have every member of the group.
Why divide by n − 1?
A sample tends to underestimate the spread of the whole population. Dividing by n − 1, known as Bessel's correction, removes that bias from the variance estimate.
What does a large standard deviation mean?
The values are widely scattered around the mean. A small one means they cluster close to it.
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Results are estimates based on the values you enter and the published method shown above. They do not replace professional medical, financial or legal advice. Method reviewed October 7, 2026. About this site