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Standard Deviation Calculator
Dispersion Analytics
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About the Standard Deviation Calculator
Standard deviation measures how spread out numbers are around their average. A small value means the data is tightly grouped; a large value means it is widely scattered.
How to use the Standard Deviation Calculator
- Enter your numbers separated by commas.
- Choose Sample (nβ1) if your data is a sample of a larger group or Population (N) if it is the whole group.
- Press Calculate to see the mean, variance and standard deviation.
Formula and method
Population: Ο = β(Ξ£(x β ΞΌ)Β² Γ· N)
Sample: s = β(Ξ£(x β xΜ)Β² Γ· (n β 1))
Worked example
For 15, 22, 18, 30, 25 the mean is 22. The squared deviations add up to 138. Population variance is 27.6 (Ο β 5.25) and sample variance is 34.5 (s β 5.87).
A worked data set. For 2, 4, 4, 4, 5, 5, 7, 9 the mean is 5. The population standard deviation is 2 and the sample standard deviation is about 2.14.
When to use the Standard Deviation Calculator
- Measuring how spread out a set of results is.
- Comparing the consistency of two data sets that have the same mean.
- Preparing statistics for a report, a lab or a class.
Common mistakes to avoid
- Using the population formula for a sample. A sample uses n β 1 in the denominator.
- Reading a large standard deviation as bad without considering the size of the mean.
Tips
- Use the sample formula in most real-world cases, where you have only part of the data.
- In a normal distribution about 68% of values fall within one standard deviation of the mean.
Frequently Asked Questions
A sample tends to under-estimate the spread of the full population. Dividing by n β 1 (Bessel's correction) corrects that bias.
Use the population version when you have every value. Use the sample version when your data is only a part of a larger group.
The values are all close to the mean.