Which standard deviation do you need: sample or population?

Two different standard deviations come out of the same data. What the difference is, which to quote, and a worked example.

Tools used in this guide

The job

You pasted a column of measurements and the calculator shows two standard deviations. They differ by a factor that can matter — especially with small samples.

The difference

Population SD divides the squared deviations by n — the right choice when your list IS everything you care about (all sales this quarter, all students in this class).

Sample SD divides by n−1 (Bessel's correction). It is the right choice when your numbers are a sample of a bigger population you want to estimate — 30 respondents out of thousands of customers. Dividing by n−1 corrects for the fact that a sample's spread tends to underestimate the true spread.

Rule of thumb: describing this data → population; generalizing from this data → sample.
n−1 matters most for small n: with 5 values the two differ by ~12%; with 1,000 they differ by 0.05%.

Worked example

For 2, 4, 4, 4, 5, 5, 7, 9: mean = 5, median = 4.5, population SD = 2, sample SD ≈ 2.14. The calculator shows both so you can quote the one your assignment or report expects.

Limits

Quartiles use the median-of-halves method — spreadsheet quantile functions (PERCENTILE.INC) interpolate differently and can give slightly different Q1/Q3. Non-numeric entries stop the calculation rather than being dropped.