Variance, Standard Deviation & Dispersion Calculators

Measure how spread out data are and how precise an estimate is.

26 calculators in this category.

Two data sets can share the same mean and still look very different. Measures of dispersion describe how far values typically fall from the centre, and they are essential for judging how much an average can be trusted.

This category includes the standard measures of spread, several relative and robust alternatives, and tools for error and uncertainty, including standard error, which describes the precision of an estimated mean rather than the spread of the raw data.

Calculators in this category

26 calculators

Key concepts

Variance and standard deviation
Variance is the average squared distance from the mean. Standard deviation is its square root, which returns the result to the original units.
Population and sample
A population value uses every member of the group. A sample value estimates it from a subset and divides by n − 1 to correct for bias in the variance.
Standard deviation and standard error
Standard deviation describes spread among observations. Standard error describes how much a sample statistic, such as the mean, would vary between samples.

Frequently asked questions

Should I divide by n or n − 1 when calculating variance?

Divide by n when your data are the entire population. Divide by n − 1 when your data are a sample used to estimate the population variance. The n − 1 version corrects the tendency of a sample to underestimate variation.

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