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Standard Deviation Calculator

Standard Deviation Calculator is part of Toolspire and is ready as soon as this page loads. Sample divides by n − 1. Population divides by n. The headline is the sample figure, because a pasted list is usually a sample of something larger.

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On this page

What you can do here

Sample is the headline

Most pasted marks are a sample. The n − 1 divisor is the number in large type.

Population sits beside it

If your list is the entire class, not a sample, use the population figure in the detail.

The mean is shown too

You can see the centre the gaps were measured from, without opening the average page.

The sequence

How to use the Standard Deviation Calculator

  1. 1

    Paste every observation

    Leave out blanks. A double comma does not insert a zero; only real number tokens count.

  2. 2

    Pick the divisor your question names

    If the question says “sample” or does not say the list is complete, use the headline. If it says “population” or “entire data”, use the detail.

  3. 3

    Check 1, 2, 3

    Sample standard deviation 1 is the easy confirmation that n − 1 was used.

Worth knowing

  • Standard Deviation Calculator on Toolspire: both figures use the squared distance from the mean. They differ only in the divisor.
  • The sample standard deviation divides by n − 1. The population figure divides by n.
  • For 1, 2, 3 the sample standard deviation is 1 and the population figure is √(2/3), about 0.8165.
  • Fewer than two numbers is rejected. A single observation has no sample spread.

Why the two divisors disagree

Dividing the sum of squared gaps by n understates the spread when those observations are a sample from a larger population. The n − 1 divisor, Bessel’s correction, is the usual fix, and it is what spreadsheets call STDEV.S. STDEV.P divides by n. This page prints both and names them, so a homework question that says “population” is not answered with the sample formula by accident.

FAQ

Questions about Standard Deviation Calculator

Where does Standard Deviation Calculator run?

Standard Deviation Calculator runs in this tab on Toolspire. What you type or drop in is not sent to us and is not stored on a server.

Which standard deviation is the headline?

The sample one, dividing by n − 1. The population value, dividing by n, is in the detail and labelled.

What is the standard deviation of 1, 2 and 3?

The sample value is 1. The population value is the square root of 2/3, about 0.8165.

Why do I need two numbers?

With one number the gaps are zero and the sample divisor is zero. The page asks for a second observation.

Is this variance?

No. Variance is the average squared gap before the square root. The figures here are standard deviations, the square roots of those variances.

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