Standard Deviation Calculator
Calculate mean, variance, and standard deviation for up to 5 values. Supports both population and sample standard deviation.
Results
What is it?
Standard deviation measures how spread out data values are from the mean. A low standard deviation means values cluster tightly around the mean; a high one means they are widely dispersed. Population SD (Ļ) is used when you have every member of a group; Sample SD (s) is used when your data is a sample drawn from a larger population ā it applies Bessel's correction (dividing by nā1) to reduce bias.
How to use
Enter up to 5 data values, then select how many values you are using from the dropdown (this controls which values contribute to the mean). The calculator computes the mean, both variants of variance, and both variants of standard deviation.
Example scenario
Test scores: 10, 20, 30, 40, 50 (n=5). Mean = 30. Squared deviations: 400, 100, 0, 100, 400. Sum of squares = 1000. Population variance = 200, Ļ = 14.14. Sample variance = 250, s = 15.81.
Pro tip
Use the Empirical Rule (68-95-99.7 Rule) with normally distributed data: ~68% of values fall within Ā±1Ļ, ~95% within Ā±2Ļ, and ~99.7% within Ā±3Ļ. This rule is used extensively in quality control (Six Sigma) and exam grading (bell curves).