Standard Deviation Calculator
Standard deviation measures how spread out numbers are around their mean. Paste your data and choose whether it is a sample or a whole population.
Updated
Formula
Sample: s = √( Σ(x − x̄)² ÷ (n − 1) )
Population: σ = √( Σ(x − μ)² ÷ n )
Use the sample formula when your data is a subset of a bigger group (most research and surveys). Dividing by n − 1 corrects the tendency of a sample to underestimate spread.
Examples
Sample: 10, 12, 23, 23, 16, 23, 21, 16
Sample standard deviation = 5.237229
Population: 2, 4, 4, 4, 5, 5, 7, 9
Population standard deviation = 2
Important information
- For roughly bell-shaped data, about 68% of values lie within one standard deviation of the mean and about 95% within two.
Frequently asked questions
Sample or population — which should I choose?
Population only if your list contains every member of the group you care about. Otherwise choose sample.
What is variance?
Variance is the standard deviation squared — the average squared distance from the mean.
What does a high standard deviation mean?
The values are widely spread out. A low one means they cluster close to the mean.
What is the standard error?
The standard deviation divided by √n. It estimates how precisely the sample mean reflects the true mean.
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