Weighted Average

College/University

Definition

A method to find the mean in a set of numbers. The weighted average takes into consideration that some components in the set of numbers are more important than others. The average is calculated by multiplying each number with its assigned weight before adding them together and dividing it to find the average.

Worked examples

Grades: $ 85\times0.6 + 90\times0.4 = 51 + 36 = 87$

Tests worth 60% and homework 40%; multiply each score by its weight, add, then divide by total weight (here 1.0).

$\frac{3\times10 + 5\times20 + 2\times15}{3+5+2} = \frac{30+100+30}{10} = 16$

Three items at $10, five at $20, two at $15; weights are the counts, so divide the sum by the total count.

Common mistakes

$\frac{85 + 90}{2} = 87.5$ → $85\times0.6 + 90\times0.4 = 87$ Taking the simple average ignores the weights; you must multiply each value by its weight first.
$85\times0.6 + 90\times0.4 = 87$ (forget to divide) → $\frac{85\times0.6 + 90\times0.4}{0.6+0.4} = 87$ When weights don't sum to 1, you must divide the weighted sum by the total weight.
$\frac{3\times10 + 5\times20}{3\times5}$ → $\frac{3\times10 + 5\times20 + 2\times15}{3+5+2}$ Add the weights in the denominator, don't multiply them; and include all terms from the numerator.

Where you'll use it next

Weighted averages appear in computing grade point averages, analyzing survey data with different sample sizes, portfolio returns in finance, and expected values in probability and statistics.

Found in 1 StudyPug lesson

Application of Averages

Grade 7 Math

Discover how to apply mean, median, and mode to everyday data, from test scores to salaries, and decide which average tells the truest story.

7th Grade7th