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 lies between the smallest and largest of the values $x_i$.
Distinctions involving this term
- Measures of center: The mean, median, and mode are different ways to summarize the middle of data, and they can be far apart. “Average” usually means the mean. The geometric mean averages growth factors and ratios, and the expected value is the mean of a probability distribution rather than of data.