Standard Deviation Calculator

Compute standard deviation, variance, mean and the full set of descriptive statistics.

What the Standard Deviation Calculator does

Standard deviation is the typical distance between a value and the mean, in the same units as the data. Small means tightly clustered; large means widely scattered. Use the sample formula when your numbers are a subset drawn from a bigger group.

Formula

  • σ = √(Σ(x − μ)² ÷ n)
  • s = √(Σ(x − x̄)² ÷ (n − 1))

Inputs explained

InputUnitRequiredNotes
NumberstextYesSeparate values with commas, spaces or new lines.
Data set typeone of 2 optionsYes

How to use it

  1. Choose Data set type.
  2. Enter Numbers.
  3. Select Calculate.

Worked example

Five delivery times in minutes: 28, 31, 27, 35, 29.

Numbers
28, 31, 27, 35, 29
Type
Sample

Mean 30, sample standard deviation ≈ 3.16 minutes.

Frequently asked questions

Should I use sample or population?

Population when your data is the entire group you care about. Sample when it is a subset used to estimate a larger population — that covers most real analysis.

What counts as a high standard deviation?

It depends on scale. Compare it to the mean using the coefficient of variation, which is shown above as a percentage.

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