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Standard Deviation Calculator

Enter your numbers to get both the sample and the population standard deviation, plus variance, mean and more.

Your details

Result

Standard deviation (sample, N−1)

2.1381

population (N): 2.0000

Count
8
Mean
5
Median
4.5
Mode
4
Sum
40
Min · Max
2 · 9
Range
7
Sample variance
4.5714
Population variance
4.0000
  • Use the sample figure if your numbers are a sample of a bigger group; use the population figure if they are the whole group.

Good to know: Use the sample figure (N−1) if your numbers are a sample of a bigger group, and the population figure (N) if they are the whole group.

About this tool

Full descriptive statistics for any data set: sample and population standard deviation, variance, mean, median, mode, sum, min, max and range.

Formula

variance = Σ(x − mean)² ÷ N (population) or ÷ (N−1) (sample); standard deviation = √variance.

Reference values

  • Use N−1 when data is a sample
  • SD of 0 means all values are identical
  • Range ignores all but the extremes

Questions people ask

What does standard deviation tell me?

How spread out the numbers are around the average. A small value means they cluster close together.

Sample or population — which should I use?

Use sample if the data is a subset of something larger, which is the usual case.

What does a standard deviation of 0 mean?

Every value is identical.

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How we calculate this

We use the standard published formula or definition for this calculation, and we show the working so you can check it.

Spotted a mistake? Tell us and we'll check it. How we check our calculators