Paste a list of numbers (comma or newline separated) — pick population or sample depending on whether your data is the whole group or just part of it.
Population standard deviation divides the sum of squared deviations by N, used when your data represents the entire group you care about. Sample standard deviation divides by N−1 instead — a correction (Bessel's correction) that gives an unbiased estimate of the population's spread when your data is only a sample drawn from a larger population.
It measures spread, or variability, around the mean. A small standard deviation means most values sit close to the average; a large one means values are spread out over a wider range.
Squaring each deviation makes it positive, so values above and below the mean don't cancel each other out when summed, and it weights larger deviations more heavily than small ones — which is exactly the behavior we want from a measure of spread.
The Statistics Calculator covers mean, median, mode, range, variance, and standard deviation all together. This tool is a focused, standalone version for when you just need standard deviation specifically, with an explicit population-vs-sample toggle front and center.
Worked example: for the data set 2, 4, 4, 4, 5, 5, 7, 9 (n=8), the mean is 5. The population variance is 4, giving a population standard deviation of exactly 2. The sample variance (dividing by n−1=7 instead) is 32/7 ≈ 4.57, giving a sample standard deviation of about 2.14 — slightly larger, as Bessel's correction always produces.