Population Standard Deviation Calculator

Calculate population standard deviation, population variance, and mean for a comma-separated numeric dataset.

Calculate population standard deviation

2Population variance: 4Mean: 5

How this tool works

Population standard deviation measures dispersion when the entered observations represent the complete population of interest. The calculator exposes mean and variance alongside the square-root result so each stage can be checked.

Population variance is the mean of squared differences between each value and the population mean. Population standard deviation is the square root of that variance.

How to use it

  1. Enter at least two numeric observations separated by commas.
  2. Confirm that the data represents the complete population rather than a sample.
  3. Read the mean, population variance, and population standard deviation.

Worked examples

Classic population example

Input
2, 4, 4, 4, 5, 5, 7, 9
Output
Population standard deviation 2

The mean is five and the average squared distance from that mean is four. Taking the square root of four produces a population deviation of two.

Constant observations

Input
6, 6, 6, 6
Output
Population standard deviation 0

Every observation equals the mean, so every deviation and squared deviation is zero. Their average and square root therefore remain zero.

Limitations

  • Use a sample-standard-deviation formula when observations are only a sample.
  • The tool does not handle weights, grouped frequencies, or missing-data conventions.