# Mean

A measure of the average value

Given a sample of \(n\) values \(x_i\), the mean is defined as

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

**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

\[
f(X) = X
\]