If you want to calculate your percentage score on a test, you divide the number of points you scored by the number of points possible. Sometimes, the same process works to calculate your overall score in a class. But if your teacher assigns greater value to some scoring categories than others – also known as a weighted score – you'll have to add a few extra steps to your calculation process.
Before you start calculating weighted scores, let's review the basic skills you'll need to calculate weighted averages. The first is calculating percentages.
To calculate a percentage score, you divide the number of points earned by the number of points possible. Here are a couple of examples:
Example 1: If you earned 75 out of 100 possible points, your score is
Example 2: If you earned 16 out of 20 points on a pop quiz, your score is
Converting to and From Decimal Form
Usually, leaving your score in decimal form makes it easier to handle mathematically. That'll become important when you calculate your way through a weighted scoring method. But when it comes time to express your final answer, it's easier to read as a percentage.
To convert from decimal form to a percentage, multiply your result by 100. In the case of our two examples, you have:
To convert from percentage back to decimal form, you'd divide the percentage by 100. Give it a try with both examples – if you get it right, you'll end up with the same decimal value you started with.
Calculating an Average
There's one more skill you'll need to calculate weighted scores: A simple average, which in "math speak" is more properly called the mean. Let's say you want to know your average score after taking three tests, on which you received grades of 75%, 85% and 92% respectively.
To calculate the average, you'll first convert your percentages into decimal form, then add all your data points together and divide them by the number of data points you had. So, you have:
Which in this case, is:
Once you do the math, you arrive at:
If you convert that decimal back to percentage form, you'll see that your average score is 84 percent. In this particular example you didn't actually have to convert back and forth to percentage form, but it's a good habit to have.
Calculate the Weighted Average
Now, it's time to become your own weighted score calculator. Imagine that you're taking a class where the instructor thinks homework and tests are the most important part of the class. At the beginning of the class, he might warn you that homework will make up 40 percent of the score, tests will make up 50 percent of your score and pop quizzes will be the remaining 10 percent. The higher the percent or weight of a scoring element, the more it affects your overall score.
In order to calculate the weighted average under those terms, you'll first use the skills we just practiced to calculate your average in each category (homework, tests and pop quizzes). Let's say you end up with an average of 91% in homework, 89% in tests and 84% in pop quizzes.
- Homework: 0.91
- Tests: 0.89
- Pop quizzes: 0.84
- Homework: 0.91 × 0.4 = 0.364
- Tests: 0.89 × 0.5 = 0.445
- Pop quizzes: 0.84 × 0.1 = 0.084
First, convert divide each percentage by 100 to convert it into decimal form. In this example, that gives you:
Next, multiply each category by its appropriate weighting factor, expressed as a decimal. Since homework is 40% of your score, you'd multiply the homework category by 0.4; you'd multiply the test category by 0.5, and the pop quiz category by 0.1. This gives you:
After you've scaled each category according to its weight in the overall score, add the results together:
This is your weighted score, but it's still expressed in that easy-to-handle decimal form. To truly finish your work, multiply by 100 to convert it to the easy-to-read percentage form:
So your weighted score is 89.3%.
Other Places to Use a Weighted Score
For most people, school or university grades are where they're most likely to encounter the weighted score or weighted average. But you'll also see a weighted scoring model at work in statistics (especially for handling large data sets), in survey analysis, in investing and even in reviews of electronics or other items, when certain review criteria are assigned more importance than others.
- In percentage weighted scores, the sum of all the percentages must equal 100 to get your final score. However, this method allows you to know your minimum score before including the final grade. In the example, your score would be at least 42.5, even if you skipped the final and added zero to the total. If you got a 100 on the final, which adds 50, then the best you could hope for would be a 92.5.
About the Author
Lisa studied mathematics at the University of Alaska, Anchorage, and spent several years tutoring high school and university students through scary -- but fun! -- math subjects like algebra and calculus.