Standard deviation calculator
Calculate population or sample standard deviation, with the mean, variance and denominator used in the calculation.
Enter the observations and choose population for the entire dataset or sample to estimate dispersion from a sample.
Result
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How to use this calculator
Enter the observations and choose population for the entire dataset or sample to estimate dispersion from a sample.
Formula and method
Standard deviation is the square root of variance: σ=√[Σ(x−μ)²/n], or s=√[Σ(x−x̄)²/(n−1)] for a sample.
Worked example
For 2; 4; 4; 4; 5; 5; 7; 9, the mean is 5 and the population standard deviation is 2.
Limits and interpretation
Sample calculations need at least two observations. Standard deviation has the same units as the data. It is not a confidence interval and does not imply normally distributed data.
Frequently asked questions
How should I interpret the result?
For 2; 4; 4; 4; 5; 5; 7; 9, the mean is 5 and the population standard deviation is 2.
What inputs and assumptions are required?
Sample calculations need at least two observations. Standard deviation has the same units as the data. It is not a confidence interval and does not imply normally distributed data.