How this calculation works
Standard deviation describes the spread of observations around their arithmetic mean in the original measurement unit. Choose population when the list is the entire group of interest, or sample when it is being used to estimate a wider population’s spread. That choice changes the divisor, not the data.
Worked example
This example uses illustrative inputs. Your current result is shown above.
For 2, 4, 4, 4, 5, 5, 7 and 9, the mean is 40/8 = 5. Squared deviations sum to 9 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = 32. Population variance is 32/8 = 4 and standard deviation is √4 = 2.
Assumptions and limits
- Population mode needs at least one value; sample mode needs at least two.
- Observations must be in the same unit and receive equal weight.
- Standard deviation describes spread; it is not a confidence interval or the standard error of the mean.
Questions people ask
Which mode should I choose?
Choose population for a complete group you only want to describe. Choose sample when using observed data to estimate a larger population’s variance. The sampling design still matters to inference.
Why does sample mode give a larger number?
For the same data it divides the squared deviations by n − 1 rather than n. This adjustment accounts for estimating the mean from the sample.