How to use this tool
Enter the numeric observations and choose population or sample convention.
Population uses n; sample uses n−1 and requires at least two observations. Use the deviation table to inspect the working.
Variance = sum[(x−mean)²] / divisor; standard deviation = sqrt(variance)
Worked example
2 · standard deviation
Fixed example using the settings below. Monetary examples use USD; dates and times use their stated reference values. This example stays unchanged when you edit your calculation.
Example inputs
- Values: 2,4,4,4,5,5,7,9
- Convention: Population (divide by n)
Method illustration: For 2,4,4,4,5,5,7,9, population mean is 5 and standard deviation is 2.
Assumptions and limits
- Use population when the values are the whole population of interest; sample uses Bessel's n−1 correction and requires at least two values.
Check or report a result
Check the units, selected calculation and assumptions first. Compare the fixed example above with your inputs to identify what changed.
Report a calculation issue with the page address, hypothetical inputs, result displayed and result expected. Do not include passwords, bank details or other private information.