A measure of the average value

1. of a sample

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

2. of a distribution

For a random variable \(X\) with the distribution in question, the mean is equal to the expectation of the function
\[ f(X) = X \]