Standard Deviation Calculator

Population and sample standard deviation, variance and more.

Standard Deviation Calculator

Fast online calculation engine

Enter Numbers (comma or newline separated)

Mean (Average)27.43

Median22.00

ModeNone

Std Deviation13.81

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What does Standard Deviation Calculator do?

Calculate both population and sample standard deviation from a data set, along with variance, mean and the sum of squared deviations. The working is shown step by step, which makes it useful for checking homework as well as real analysis.

How to Use Standard Deviation Calculator

1
Paste your dataAny list of numbers, in any common separator.
2
Choose sample or populationBoth are calculated; pick which to highlight.
3
Expand the workingSee each deviation squared if you need to show your method.

Key Features

Both sample (n − 1) and population (n) results, clearly labelled
Variance, mean and sum of squared deviations shown
Step-by-step working table of each deviation and its square
Coefficient of variation for comparing spread across different scales

Frequently Asked Questions

Should I use sample or population standard deviation?

Use sample (dividing by n − 1) when your data is a subset drawn from a larger group, which is almost always the case in research. Use population (dividing by n) only when you have measured every member of the group.

Why divide by n − 1 for a sample?

Because the sample mean is itself estimated from the data, which slightly understates the spread. Bessel’s correction compensates, giving an unbiased estimate of the population variance.

What does standard deviation actually tell me?

How far values typically sit from the mean. In a roughly normal distribution about 68% of values fall within one standard deviation of the mean and 95% within two.