EVERYDAY MATH · FREE INTERACTIVE CALCULATOR
Standard Deviation Calculator
Calculate sample and population standard deviation with worked variance. Change the inputs below to calculate a result immediately. No account required.
Count
8Mean
5Population standard deviation
2Sample standard deviation
2.1381How to calculate the answer
Population variance divides summed squared deviations by n; sample variance divides by n − 1.
Worked example
For 2, 4, 4, 4, 5, 5, 7, 9, population standard deviation is 2.
For the example inputs shown above, the calculated results are:
| Count | 8 |
|---|---|
| Mean | 5 |
| Population standard deviation | 2 |
| Sample standard deviation | 2.1381 |
How to interpret this result
Sample standard deviation requires at least two observations.
These figures illustrate the displayed method using the default inputs. Change the inputs to explore another case, and check units and conventions relevant to the problem.
Population and sample statistics differ
Population standard deviation divides the sum of squared deviations by the population count; sample standard deviation usually uses one fewer degree of freedom.
Interpret variability
A larger standard deviation means observations are more spread around the mean in the original units, but comparisons should consider the scale and distribution.
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Frequently asked questions
Population or sample standard deviation?
Use population if you have every value, sample if the values are a subset of a larger group.
Why divide by n−1 for a sample?
It corrects the bias in estimating the population variance.
What does a large deviation mean?
The values are more spread out.
Sources and further reading
Last updated: . Results are estimates for information only and are not financial, medical or professional advice.