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How do I calculate the standard deviation of a data set?

Short answer

Standard deviation measures how spread out your numbers are around the mean: you find the mean, average the squared differences from it to get the variance, then take the square root. The browser-based standard deviation calculator gives both the population and sample standard deviation from a pasted list, with nothing uploaded.

What the formula does

Standard deviation tells you the typical distance of a value from the mean. The steps are: calculate the mean, subtract it from each value and square the result, average those squared differences to get the variance, then take the square root of the variance. A small standard deviation means the numbers cluster close to the mean, while a large one means they are widely scattered.

Population versus sample

There are two versions. The population standard deviation divides the summed squared differences by the count of values, and is used when your data covers the entire group. The sample standard deviation divides by the count minus one, and is used when your data is a sample drawn from a larger group. The calculator reports both so you can pick the correct one, and it does the arithmetic in your browser.

Step by step

  1. Open the calculator. Open the standard deviation calculator in your browser.
  2. Enter your numbers. Paste your list separated by commas, spaces or new lines.
  3. Read the result. Read the population and sample standard deviation, plus the variance and mean.

Frequently asked questions

What is the difference between population and sample standard deviation?

The population version divides by the number of values, while the sample version divides by that number minus one. Use the sample version when your data is a sample of a larger group.

Does it also show the variance?

Yes. The variance is the square of the standard deviation and is reported alongside it.

Is my data private?

Yes. The whole calculation runs in your browser with nothing sent to a server.

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