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Standard Deviation Calculator

Calculate the mean, variance and standard deviation of a set of numbers, as a sample or a population.

Details

Your Results

What Standard Deviation Calculator does

Standard deviation measures spread: how far the values in a set typically sit from their mean. Two datasets can share a mean and describe entirely different situations, and this is the number that distinguishes them.

The distinction between sample and population matters. Sample standard deviation divides by n−1 to correct for the fact that a sample's own mean underestimates the spread of the population it came from.

  • Mean, variance and standard deviation
  • Sample (n−1) and population (n) modes, with the choice stated in the result
  • Comma-separated input

How to use Standard Deviation Calculator

  1. 1

    Enter your numbers

    Separate them with commas.

  2. 2

    Choose sample or population

    Population when your numbers are the entire group; sample when they are a subset you are generalising from.

  3. 3

    Read the results

    The mean, variance and standard deviation are shown together.

Example

Why the choice matters on small sets

Input

2, 4, 4, 4, 5, 5, 7, 9

Output

Mean                = 5
Population SD (n)   = 2
Sample SD (n−1)     ≈ 2.14

The gap between the two narrows as the dataset grows, and is negligible for large samples.

Limits and known behaviour

  • Sample standard deviation needs at least two values.
  • Standard deviation is heavily affected by outliers, because deviations are squared before averaging. One extreme value can dominate the result.
  • It describes spread around the mean, which is most meaningful for roughly symmetric distributions. For skewed data, quartiles describe the shape better.
  • Median, mode, quartiles and correlation are not calculated here.

Privacy and data handling

Runs entirely in your browser

  • The calculation runs in this page. Nothing you enter is transmitted or stored.
  • The tool works offline once the page has loaded.

Site-wide data handling, including analytics and advertising, is described in the privacy policy.

Frequently asked questions

Should I use sample or population?

Population if your numbers are the complete set you care about, such as the scores of every student in one class. Sample if they are a subset used to infer something about a larger group.

What does the number actually mean?

It is a typical distance from the mean, in the same units as your data. For roughly bell-shaped data, about two thirds of values fall within one standard deviation of the mean and about 95% within two.