Standard Deviation Calculator

What is the Standard Deviation Calculator?

Calculate sample and population standard deviation and variance. Standard deviation measures how far values typically sit from the average, so two data sets with the same mean can be told apart.

How to use the Standard Deviation Calculator

1. Paste or type your numbers into the box (a sample is pre-filled so you can see how it works).
2. Results update automatically as you type; you can also press Calculate.
3. Read the output: sample standard deviation (s), population standard deviation (σ), sample variance, mean.
4. Use the 📊 chart to see the result visually, then copy or share it.

Formula and method

Worked example

With the sample input, the Standard Deviation Calculator returns sample standard deviation (s): 6.82432623571; population standard deviation (σ): 6.3835726674; sample variance: 46.5714285714.

Where the Standard Deviation Calculator helps in real life

Two classes both average 72% on an exam. The class with a standard deviation of 4 performed consistently, while the class with 15 had a wide spread of results.

A manufacturer weighs 50 bags of flour labelled 1 kg. A small standard deviation shows the filling machine is consistent.

Common mistakes to avoid

• Using the population formula for a sample, which understates spread.
• Comparing standard deviations of data in different units.
• Ignoring outliers that inflate the result.
• Treating standard deviation as the full range.

💡 Practical tip: In roughly bell-shaped data, about two thirds of values fall within one standard deviation of the mean.

Tips for better results

• Use the sample standard deviation when your data is a sample of a larger group.
• Look at the coefficient of variation to compare different scales.
• Plot the data to spot outliers before trusting the figure.

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