Concept

Weighted Mean

The weighted mean, or the weighted average, of a numerical data set is a type of mean used when some data values are weighted more than others. This mean is defined as the sum of the product of the weights

w

and associated data values

x,

divided by the sum of the weights.

$Weighted Mean = \frac{w _{1} x _{1} + w _{2} x _{2} + \dots + w _{n} x _{n}}{w _{1} + w _{2} + \dots + w _{n}}$

As an example, consider three $100 -$ point assignments that are worth different percentages of the total grade of a course. The following table shows the scores of a student on each assignment.

Assignment	Score	Weight
Exam	$60$	$50 % = 0.5$
Quiz	$80$	$20 % = 0.2$
Term Paper	$90$	$30 % = 0.3$

Decimal forms of the percentages are used in the formula to find the weighted mean of the student.

Weigthed Mean = \frac{6 0 \cdot 0 . 5 + 8 0 \cdot 0 . 2 + 9 0 \cdot 0 . 3}{0 . 5 + 0 . 2 + 0 . 3} = 73

If the weights are equal — regardless of the value — then the weighted mean equals the arithmetic mean.

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