Standard Deviation Calculator
Paste your data. Choose sample (n − 1) or population (n).
How is standard deviation calculated?
Find the mean, subtract it from every value, square those differences, add them up, divide by n (population) or n − 1 (sample) to get the variance, then take the square root. Use the sample version when your numbers are a subset of a larger group, which is the usual case in surveys and experiments.
Start with the Average Calculator if you only need the mean, median or mode.
Frequently asked questions
What is the formula for standard deviation?
σ = √(Σ(x − μ)² ÷ N) for a population; for a sample, divide by n − 1 instead of N.
Why divide by n − 1 for a sample?
A sample tends to underestimate the spread of the full population, and dividing by n − 1 (Bessel's correction) compensates.
What does a high standard deviation mean?
The values are spread widely around the mean. A low one means they cluster close to it.
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