Calculate standard deviation and variance

Calculate population or sample spread in the original units for a numeric list.

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ToolStandard Deviation
Input
Output
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How it works

The mean is subtracted from each value, squared deviations are summed, and the total is divided by n for a population or n−1 for a sample before taking the square root. The result returns spread to the original units.

  • Population is the initial type.
  • Sample spread needs at least two values.

Worked example

Test Scores
Calculate the standard deviation of exam scores
Input
											85, 90, 78, 92, 88, 76, 95, 89
Output
												Type: population
Mean: 86.625
Variance: 38.484375
Standard Deviation: 6.203577596838779

When to use this

Quality samples estimate process spread, classes compare denominators, and measurement reports summarize variation beside a mean.

Edge cases

  • A single-value sample has no n−1 estimate.
  • An extreme observation can dominate squared deviations.
  • The square-root result keeps original units while variance does not.

References