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Standard Deviation Calculator

Calculate the population or sample standard deviation of a list of numbers.

Separate numbers with a comma or a new line, e.g. 2, 4, 4, 5, 9.

Data type

Population: use when the entered values are the complete group you're analysing. Sample: use when they're a sample taken from a larger population.

Worked example

For 2, 4, 4, 4, 5, 5, 7, 9 as a population, the standard deviation is 2.

How it works

Standard deviation measures how spread out a set of numbers is from its mean. This tool uses two different, standard formulas depending on your choice above: the population formula divides by the number of values, while the sample formula divides by one fewer than the number of values (to correct for estimating from a sample). The two are never mixed. A sample standard deviation needs at least 2 values, since dividing by one fewer than 1 is undefined.

What this result means

Standard deviation measures how spread out your numbers are from the mean — a small value means the numbers cluster close to the mean, a large value means they are widely spread.

Common mistakes

  • Using sample standard deviation when your numbers are actually the entire population — the two formulas can give noticeably different answers on small data sets.

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