Standard Deviation Calculator

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Sample vs. population standard deviation

Both measure how spread out values are around the mean, but they divide by a slightly different number: population standard deviation divides the sum of squared differences by n (the full count), while sample standard deviation divides by n−1. The n−1 adjustment (called Bessel's correction) compensates for the fact that a sample's mean is only an estimate of the true population mean, which would otherwise cause sample variance to systematically underestimate the true population variance.

Frequently asked questions

Which one should I use? Use "sample" if your data is a subset drawn from a larger population you're trying to describe (the far more common case in practice); use "population" only if your data genuinely represents the entire group of interest, with nothing left out.

What does a large standard deviation mean? It means the values are widely spread out from the mean; a small standard deviation means the values cluster tightly around the mean — it's a direct measure of variability or consistency in the data.

What is variance, and how does it relate to standard deviation? Variance is the standard deviation squared (or equivalently, standard deviation is the square root of variance) — variance is useful mathematically, while standard deviation is easier to interpret since it's in the same units as the original data.