Formulas & tables/Mathematics/Statistics/Variance

Variance

σ2=1n∑i=1n(xi−xˉ)2\sigma^2=\dfrac{1}{n}\sum_{i=1}^{n}(x_i-\bar{x})^2

Result unit: — (liczba)

What it describes

The mean of the squared deviations of the data from the mean — a measure of dispersion.

Symbols

σ2\sigma^2
variance
xix_i
data values
xˉ\bar{x}
mean
nn
number of data values

Where it comes from

The mean of the squared deviations from the mean — the larger it is, the more spread out the data are. We square the deviations so they do not cancel out.

When to use it

A measure of the spread of data; needed for the standard deviation.

Example

Data: 2, 4, 6 (mean = 4). Find the variance.
Substitutiondeviations: −2,0,2-2, 0, 2.
Resultσ2=4+0+43≈2.67\sigma^2=\dfrac{4+0+4}{3}\approx2.67.

Related formulas

Standard deviation Arithmetic mean

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