Weighted average
Elementary
A weighted average is an average in which some values count more than others.
High school
The weighted average of values $x_i$ with nonnegative weights $w_i$ is
\[\frac{\sum_i w_i x_i}{\sum_i w_i}.\]Values with larger weights count more.
Properties
- With equal weights, the weighted average is the ordinary mean.
- A weighted average always lies between the smallest and largest of the values $x_i$.