A measure of the average deviation from the average value

1. of a sample

Given a sample of \(n\) values \(x_i\) with mean \(\mu\), the variance is defined as
\[ \frac{1}{n}\sum_{i=1}^{n}\left(x_i - \mu\right)^2 \]
where \(\sum\) is the summation sign.

2. of a distribution

For a random variable \(X\) with the distribution in question and having a mean of \(\mu\), the variance is equal to the expectation of the function
\[ f(X) = \left(X - \mu\right)^2 \]