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This article was co-written by Mario Banuelos, PhD. Mario Banuelos is an assistant professor of mathematics at California State University, Fresno. With over eight years of teaching experience, Mario specializes in mathematical biology, optimization, statistical modeling for genome evolution, and data science. Mario holds a bachelor’s degree in mathematics from California State University, Fresno, and a doctorate in applied mathematics from the University of California, Merced. Mario teaches at both the high school and college levels.
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The weighted average, also known as the weighted mean, is a bit more difficult to calculate than the normal arithmetic mean. As the name suggests, a weighted average is the average or average in which the component numbers have different values or weights. For example, you might need to find the weighted average of your class score, where tests account for different proportions of your total score. The procedure you use for the calculation may differ slightly depending on whether the sum of the weights is equal to 1 (or 100%).
Steps
Calculate the weighted average when the weights add up to 1
- For example, maybe your total score is 82 for the oral test, 90 for the written test, and 76 for the semester exam.
- To use percentages in a problem, you need to convert them to decimals. The resulting transformation is called the “weight”.
Tip: Converting percentages to decimals is simple! Place a decimal point at the end of the percentage value, then move two places to the left. For example, 75% would be 0.75.
- For example, if your total oral exam score is 82 and your oral exam share of the total score is 20%, multiply 82 x 0.2. In this case, x=82 and w=0.2.
- The weighted average of your oral, written, and final exam scores will be as follows: 82(0.2) + 90(0.35) + 76(0.45) = 16.4 + 31, 5 + 34.2 = 82.1. This means your course GPA is 82.1%.
The sum of the weights is not equal to 1
- For example, maybe you want to know how many hours you slept each night on average for 15 weeks, but the number of hours of sleep varies each week. You can sleep 5, 8, 4, or 7 hours a night.
- 9 weeks when you sleep an average of 7 hours a night.
- 3 weeks when you sleep 5 hours a night.
- 2 weeks when you sleep 8 hours a night.
- 1 week when you sleep 4 hours a night.
- The number of weeks associated with the number of hours of sleep is the weight. In this case, you sleep 7 hours a night for most of the week, while there are relatively fewer weeks than you sleep for more or less hours.
- The total weeks add up as follows: 3 weeks + 2 weeks + 1 week + 9 weeks = 15 weeks.
- 5 hours per week (3 weeks) + 8 hours per week (2 weeks) + 4 hours per week (1 week) + 7 hours per week (9 weeks) = 5(3) + 8(2) + 4(1) + 7(9) = 15 + 16 + 4 + 63 = 98
- 98/15 = 6.53. This means you slept an average of 6.53 hours per night over a 15-week period.
This article was co-written by Mario Banuelos, PhD. Mario Banuelos is an assistant professor of mathematics at California State University, Fresno. With over eight years of teaching experience, Mario specializes in mathematical biology, optimization, statistical modeling for genome evolution, and data science. Mario holds a bachelor’s degree in mathematics from California State University, Fresno, and a doctorate in applied mathematics from the University of California, Merced. Mario teaches at both the high school and college levels.
This article has been viewed 34,709 times.
The weighted average, also known as the weighted mean, is a bit more difficult to calculate than the normal arithmetic mean. As the name suggests, a weighted average is the average or average in which the component numbers have different values or weights. For example, you might need to find the weighted average of your class score, where tests account for different proportions of your total score. The procedure you use for the calculation may differ slightly depending on whether the sum of the weights is equal to 1 (or 100%).
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