About this calculator
The working shows each step: the mean, the squared deviations, their sum, the variance and its square root.
How to use it
- Enter the numbers.
- Choose sample or population.
- Read the standard deviation and the working.
The formula
- x̄, μ
- mean
- n, N
- number of values
Worked example
2, 4, 4, 4, 5, 5, 7, 9
- The mean is 5 and the squared deviations add to 32.
- Population: √(32 ÷ 8) = 2. Sample: √(32 ÷ 7) = 2.138.
What the result means
In roughly bell-shaped data, about 68% of values lie within one standard deviation of the mean and 95% within two.
Assumptions
- Real numbers, at least two of them.
Limitations
- Very large or very small values are shown in scientific notation.
Frequently asked questions
Should I use sample or population?
Use sample (n − 1) when your data are a sample from a bigger group, which is most of the time. Use population (N) only when you have every member of the group.
Why divide by n − 1?
A sample’s values sit closer to the sample mean than to the true mean, so dividing by n slightly underestimates the spread. Dividing by n − 1 (Bessel’s correction) fixes that on average.
What is the coefficient of variation?
Standard deviation divided by the mean, as a percentage. It compares spread between data sets with different averages or units.
Last reviewed on 6 October 2026. Found a mistake? Tell us.