Author:
John Stephens
Date Of Creation:
22 January 2021
Update Date:
1 July 2024
Content
The weighted average, also known as the weighted average, is a little more difficult to calculate than the conventional arithmetic mean. As the name suggests, a weighted average is a mean or a mean in which the component numbers have different values or weights. For example, you need to find a weighted average when calculating grades in class, where tests make up different proportions of your total score. The procedure you use to calculate may differ slightly depending on whether the total weighted value is 1 (or 100%) or not.
Steps
Method 1 of 2: Calculate the weighted average when the weights add up to 1
Collect the numbers you want to average. You will begin by putting together a list of numbers to calculate the weighted average. For example, if you want to find a weighted average of grades in class, the first thing to do is write them down.
- For example, maybe your overall score is 82 for the oral test, 90 for the written test, and 76 for the semester exam.
Determine how important each number is. Once you have the numbers, you need to know how important each of them is, or how valuable it is in your average score. For example, in your class, the oral test 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%).- To use percentages in your problem, you need to convert them to decimals. The conversion result is called "weighting".
Advice: Converting percent to decimals is very simple! Place the decimal comma at the end of the percentage value, then shift two places to the left. For example, 75% would be 0.75.
Multiply each number by their weight (w). Once you have the numbers, pair each number (x) with their respective weight (w). You will multiply each pair of numbers and weights together and then add them together to get the average.
- For example, if your total oral test score is 82 and the proportion in the total score on the oral exam is 20%, multiply 82 x 0.2. In this case, x = 82 and w = 0.2.
Add together results to find the weighted average. The basic formula for finding the weighted average when the sum of weights equals 1 is x1 (w1) + x2 (w2) + x3 (w3), etc., where x is each number in your number and w is their respective weight. To find the weighted average, 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 would 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%.
Method 2 of 2: Sum the weights is not equal to 1
Write down the numbers you want to average. When you calculate a weighted average, the different weights don't always add up to equal 1 (or 100%). Either way, start by gathering numbers, or single numbers for which you want to find the mean.
- For example, you might want to know how many hours of sleep you sleep on average for 15 weeks per night, but the number of hours you sleep varies from week to 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 total weight associated with each number. For example, suppose over a 15-week period, on average, there are weeks where you sleep at night more than others. The weeks that best represent how much you usually sleep have more weight than other weeks. You will use the number of weeks relative to the number of hours you sleep as your weight.For example, put the weeks in the following weighted order:- 9 weeks when you sleep an average of 7 hours per night.
- 3 weeks when you sleep 5 hours per night.
- 2 weeks when you sleep 8 hours per night.
- 1 week when you sleep 4 hours per night.
- The number of weeks associated with the number of hours of sleep is weight. In this case, you sleep 7 hours per night for most weeks, while having relatively fewer weeks than you sleep for more or less hours.
Sum the weights. To calculate the weighted average, you need to find out how much the weights are worth when adding them together. To do this, add up the weights. In the case of your sleep study, you already know that the total weights are 15, since you are looking at your sleep patterns that take place over a 15-week period.- The total number of weeks added is as follows: 3 weeks + 2 weeks + 1 week + 9 weeks = 15 weeks.
Multiply the numbers by their weights and add the result. Next, multiply each number in your numbers by their respective weights, just as you would for the case of summing the weights equal to 1 (or 100%). Add together the results. For example, if you calculate the average number of hours of sleep per night over a period of 15 weeks, multiply the average number of hours of sleep per night by the corresponding number of weeks. You will get:- 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 total weight to find the mean. After multiplying each number by its weight and adding up the results, divide the results you find by the total weight. You will find a weighted average. For example:
- 98/15 = 6.53. This means you get an average of 6.53 hours of sleep per night over a 15 week period.
