Sometimes, all of the values in your data set will not be weighted the same. If you are calculating the mean of a data set where there are weighted values, you will need to account for these differences by using a weighted mean/average.
When calculating the weighted mean, it is important to keep the following formula in mind:
Sometimes in an academic course, exams are weighted for a certain percentage of the grade, and the final is weighted for a greater percentage.
Suppose a statistics course has four tests which comprise the course grade, but the final exam is weighted three times as much as the others.
A student receives the following scores:
What is this student's grade for the course? How do you find the mean?
You would first multiply each of the tests by their weights. Count each of the first three tests as each one test. However, count the final exam as three tests because it’s weighted three times as much:
This weighted average, or the weighted mean, is 87.5.
Assignment | Weight |
---|---|
Participation | 10% |
Homework | 25% |
Quizzes | 50% |
Tests | 15% |
In this class, Sam earned the following scores:
Assignment | Score |
---|---|
Participation | 100 |
Homework | 50 |
Quizzes | 70 |
Tests | 93 |
To calculate the weighted mean, we need to multiply each score that she received by the corresponding weight, add the values together, and divide by the total weight.
The weighted mean is 71.45, which tells us that Sam received a final grade of 71.45.
Source: Adapted from Sophia tutorial by Jonathan Osters.