Weighted Average Calculator
Enter the values in a data set and their respective weights to calculate the weighted average.
Steps to Find the Weighted Average
To find the weighted mean, use the following formula:
x̄ = (x1 × w1) + (x2 × w2) + ... + (xn × wn) / w1 + w2 + ... + wn
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How to Find a Weighted Average
A weighted average, sometimes called a weighted mean, is an average value that reflects the varying amount of importance of each value in a data set. This is different from the arithmetic mean, where each value contributes equally when calculating the average.
Weighted averages are often used for applications such as sports statistics, class grades and GPA, job performance, credit scores, or calculating stock cost basis. A classic example of weighted averages is the school course, where homework is worth a smaller portion of the grade than the final exam.
Weighted Average Formula
To calculate a weighted average or weighted mean, you can use the following formula:
x̄ = (x1 × w1) + (x2 × w2) + … + (xn × wn) / w1 + w2 + … + wn
Thus, the weighted average x̄ is equal to the sum of the products of each weight and it’s value, divided by the sum of the weights.
For example, let’s use the weighted average formula to calculate a student’s GPA with the following courses and grades:
- class 1: 4 credits B (3.0)
- class 2: 3 credits A (4.0)
- class 3: 4 credits A- (3.7)
- class 4: 3 credits B+ (3.3)
GPA = (3.0 × 4) + (4.0 × 3) + (3.7 × 4) + (3.3 × 3) / 4 + 3 + 4 + 3
GPA = 12.0 + 12.0 + 14.8 + 9.9 / 4 + 3 + 4 + 3
GPA = 48.7 / 14
GPA = 3.48
This student’s GPA is 3.48.
This example should demystify how weighted averages work. You might also be interested in learning more about the geometric mean.