Standard Deviation Calculator

Enter a list of numbers separated by commas to find the mean, variance, and standard deviation - a measure of how spread out the values are.

Standard Deviation Calculator

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Numbers (comma-separated)

Type

Standard deviation

2.4

Mean

5.2

Variance

5.76

Use "Population" if your numbers are the entire group; use "Sample" if they're a sample from a larger group.

The formulas

Population: sigma = sqrt( sum((x - mean)^2) / N ) Sample: s = sqrt( sum((x - mean)^2) / (N - 1) )

Example

Data: 4, 8, 6, 5, 3, 2, 8, 9, 2, 5. Mean = 5.2. Population standard deviation ≈ 2.4; sample standard deviation ≈ 2.53 (slightly higher, since it divides by N-1 instead of N).

Step-by-step guide

Enter your numbers, separated by commas.
Choose population or sample depending on whether your data represents the whole group or just part of it.
Read the mean, variance, and standard deviation.

Common mistakes

Using "population" when your data is really a sample of a larger group - this understates the true standard deviation slightly.

Confusing variance with standard deviation - variance is in squared units, while standard deviation (its square root) is in the same units as your original data.

Frequently asked questions

Population vs. sample - which should I use?

Use population if your numbers include every member of the group you care about. Use sample if your numbers are a subset used to estimate something about a larger group - this is the more common case in research and statistics.

What does a high standard deviation mean?

A higher standard deviation means the values are more spread out from the mean; a lower one means they're clustered closer together.

Why is sample standard deviation always slightly higher?

Dividing by N-1 instead of N (called Bessel's correction) compensates for the tendency of a sample to underestimate the true variability of the full population.

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