Formulas & tables/Mathematics/Probability/Variance of a random variable

Variance of a random variable

σ2=∑(xi−E(X))2pi\sigma^2=\sum (x_i-E(X))^2 p_i

Result unit: — (liczba)

What it describes

A measure of the dispersion of a random variable about its expected value.

Symbols

σ2\sigma^2
variance
xix_i
values of the variable
E(X)E(X)
expected value
pip_i
probabilities

Where it comes from

It measures how much the outcomes deviate from the expected value — a large variance means large risk and spread.

When to use it

Assessing the dispersion of a random variable and risk.

Example

Two games have E(X)=3E(X)=3 but different variances. Which is "safer"?
Substitutionwe compare the variances.
ResultThe one with the smaller variance — its outcomes lie closer to the mean.

Related formulas

Expected value Variance

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