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# Weighted Average Definition

The weighted average or weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead it is used in computing a kind of arithmetic mean of a set of numbers in which some elements of the set carry more importance (weight, frequency, or relative importance) than others. The notion of weighted mean plays a role in descriptive statistics and also occurs in a more general form in several other areas of mathematics.

If all the weights are equal, then the weighted mean is the same as the arithmetic mean. While weighted means generally behave in a similar fashion to arithmetic means, they do have a few counterintuitive properties, as captured for instance in Simpson's paradox.

## Examples

Grades are oftentimes computed using a weighted average:

• Suppose that homework counts 25%, quizzes 25%, and tests 50%.

• If Norman has a homework grade of 85%, a quiz grade of 75%, and a test grade of 90%, then

• To calculate Norman's overall grade based on these weighted averages = (0.25)(85) + (0.25)(75) + (0.50)(90)

• Norman's Overall Grade = 85%

### Sources

“Weighted Arithmetic Mean.” Wikipedia, Wikimedia Foundation, 16 Apr. 2020, en.wikipedia.org/wiki/Weighted_arithmetic_mean.

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