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

Similar to previous sections about median and mode, and mean, in this section we practice calculating the median, mode, and mean of given data sets in word problems. The mean, median, and mode are measures of central tendency. A measure of central tendency is a value that represents the centre of a set of data. Also, in this section, we are given data sets in word problems and asked to figure out which measure of central tendency best describes the data. The mode is the best measure of central tendency for data that represents frequency of choice. In contrast, the median is the best measure if a data set contains unusually large or small numbers in relation to the rest of the data. Finally, either the median or mean can be used as a measure of central tendency if all of the numbers in a set of data are close together.

7th Grade7th