Weighted mean

- A mean, or an average, is good when all data points are created equal. But sometimes, some data points are more important than others. Let's consider an academic course as our example. If the professor had four exams, and these were your four exam scores, calculating your average would be easy, 80%. But in many courses, instructors will also have quizzes, homework, and term papers.

In those cases, exams are usually worth more than quizzes, and homework, and term papers, may also have their own values. How do we figure out a student's average in a class like this? For this, we will use a weighted mean. Let's figure out how to calculate a weighted mean, and then discuss issues that should be considered in calculating and interpreting a weighted mean. So, let's look at how weighted means are calculated.

First, let's consider the weights of each category. Let's say our class has two exams, each worth 30% of the total grade. The quizzes are worth 10% of the grade, as is the homework. The term paper is worth 20% of the grade. Notice, the weights add up to 100%. Next, let's look at each student score in each category. 90% on exam one, 80% on exam two, the student's average on their quizzes was 75%, they got 100% on all of their homework, and they got an 85% on their term paper.

Now all we do, is multiply the score times the weight. 90% on exam one, with a weight of 30%, 0.30, that gives us a weight score of 27.0. We then do this for each category, multiply the score in each category by the weight for that category. Now that we have the weighted score for each category, we can add up all of the weighted scores, to get the weight mean.

This student, has an average of 85.5% for the course. This doesn't just work for students in a class, we could use weighted means to rate employees, or suppliers, we could use it to pick a home, or a school. And while we're presently looking at data that has already been collected, we can use weighted means to signal to others what we value. When a professor tells you that each exam is worth 30% of the grade, students get signals about the potential difficulty of exams, and also, how students should best use their time.

Which of course means, if you are going to use a weighted average, the categories and the weights of each category, are very important to consider. In general, there are no rules about which categories are chosen, there are certainly no rules about how weights for each category are determined. So, it's important, that when someone provides you with a weighted mean, that you question how the categories and weights were chosen. Equally as important, if you are the person in charge of developing a weighted mean, you need to carefully consider your choices in category and weight, it is likely your audience will ask you very specific questions about your calculations.

Finally, if you plan to use your weighted mean to motivate people, whether they be employees, students or suppliers, consider the messages they will receive when they see your rubric. If someone gave you this rubric, how would you react? How about if they gave you this one? As you can see, the weighted mean is simple, it's flexible, so, it's a very popular tool, but, it is also fairly arbitrary.

If you are using a weighted mean, be sure to take the time and effort to maximize the value of the data it will generate.