Guide

What is standard deviation?

Standard deviation is a measure of spread. It answers: typical distance from the average. A small value means the numbers huddle near the mean. A large value means they fan out.

The problem it solves

The mean alone can hide a mix. Two classes can both average 70. One might be a tight cluster around 70; the other might mix 40s and 100s. Standard deviation is the usual one-number summary of that difference.

Units

It is the positive square root of variance, so the result uses the original units — points, millimetres, seconds — not squared units. Variance is useful in formulas; standard deviation is easier to read next to the data.

Population SD ≈ √(average of (x − μ)²)

Same centre, different spread

You can hold the mean fixed and change only the spread. The dashed line on a plot is still the mean; the cloud of points gets tighter or wider. That is what the number is trying to capture.

Common mistakes

• Treating SD as a percentage of “goodness.” It is a distance in the data’s units unless you convert it (for example with the coefficient of variation).
• Comparing SDs across different units without scaling.
• Ignoring outliers. One extreme value inflates squared deviations.

How Standard Deviation Calculator helps

Paste a list on Android, calculate, and read the headline SD next to mean, variance, and a graph of the same numbers. In-app lessons include a tight-vs-spread comparison with a shared mean.

Download Standard Deviation Calculator

Related guides

• How to calculate standard deviation
• The two standard deviation formulas
• How to read a standard deviation

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