You are viewing the article How to Calculate Weighted Average at **Lassho.edu.vn** you can quickly access the necessary information in the table of contents of the article below.

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%).

## Steps

### Calculate the weighted average when the weights add up to 1

**Collect the numbers you want to average.**You’ll start by putting together a list of numbers to calculate a weighted average. For example, if you want to find the weighted average of grades in class, the first thing you should do is write down the scores.

^{[1] X Research Source}

- For example, maybe your total score is 82 for the oral test, 90 for the written test, and 76 for the semester exam.

**Determine the importance of each number.**Once you have the numbers, you need to know how important each number is, or what value, in your GPA results. For example, in your class, the oral exam accounts for 20% of the total score, while the written test is 35% and the final exam is 45%. In this case, the sum of the weights equals 1 (or 100%).

^{[2] X Research Source}

- 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.

**Multiply each number by their weight (w).**After you get the numbers, pair each number (x) with their respective weight (w). You would multiply each pair of numbers and weights together, then add them together to get the average.

^{[3] X Research Sources}

- 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.

**Add the results together to find the weighted average.**The basic formula for finding a weighted average when the sum of the weights equals 1 is x1(w1) + x2(w2) + x3(w3), etc., where x is each number in your sequence and w are their respective weights.

^{[4] X Research Source}To find a weighted average, you simply multiply each number by its weight and add the results together. For example:

- 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

**Write down the numbers you want to average out.**When you calculate a weighted average, the different weights do not always add up to 1 (or 100%). Either way, start by aggregating the data, or single numbers, for which you want to find the average.

^{[5] X Research Sources}

- 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.

**Find the weight of each number.**Once you have the numbers, find the sum of the weights attached to each number. For example, let’s say over a 15-week period, on average, there are weeks when you sleep more nights than others. The weeks that are most representative of how much sleep you usually get will have more weight than the other weeks. You will use the number of weeks associated with the hours of sleep as the weight. For example, put the weeks in order of weight like this:

^{[6] X Research Source}

- 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.

**Calculate the sum of the weights.**To calculate the weighted average, you need to figure out how much the weights are worth when you add them together. To do this, add up the weights. In the case of your sleep study, you already know that the sum of the weights is 15, since you’re looking at your sleep patterns over a 15-week period.

^{[7] X Research Sources}

- The total weeks add up as follows: 3 weeks + 2 weeks + 1 week + 9 weeks = 15 weeks.

**Multiply the numbers by their weights and add up the results.**Next, multiply each number in your data series by their respective weights, just as you did for the 1 (or 100%) total weight case. Add the results together. For example, if you calculate the average nightly sleep hours over a period of 15 weeks, multiply the average hours of sleep per night by the corresponding number of weeks. You will get:

^{[8] X Research Resources}

- 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

**Divide the result by the sum of the weights to find the mean.**After multiplying each number by its weight and adding the results, divide the result by the total weight. You will find the weighted average. Example:

^{[9] X Research Source}

- 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%).

Thank you for reading this post How to Calculate Weighted Average at **Lassho.edu.vn** You can comment, see more related articles below and hope to help you with interesting information.

**Related Search:**