Weighted average is more complicated to calculate than arithmetic. As the name suggests, in the weighted average the various numbers have different relative values, or weights. For example, this average can be useful if you are trying to calculate your grade in a class where the various tests contribute different percentages to the final grade. The procedure to use will be slightly different if the sum of the weights equals 1 (or 100%) or is different.
Steps
Method 1 of 2: Calculate the Weighted Average If the Sum of Weights is 1
Step 1. Consider the numbers you want to average
You need to start compiling a list of the values you want to get the weighted average of. For example, if you are trying to calculate your final grade in a subject, write down all the grades you achieved in the partial exams.
For example, imagine you got 26 in the first assignment, 28 in the second and 22 in the oral
Step 2. Determine the weight of each number
Once you have the data, you need to know how much they "weigh" in the final average. For example, in your course the first assignment may be worth 20% of the final grade, the second 35% and the oral 45%. In this case, the sum of the weights is equal to 1 (or 100%).
To use these percentages in your calculations, you need to turn them into decimal numbers. The resulting values are referred to as "weights"
Advise:
converting a percentage to decimal is simple! Put the comma at the end of the percentage value, then move it two places to the left. For example, 75% becomes 0.75.
Step 3. Multiply each number by its weight (p)
When you have collected all the values, multiply each number (x) by the corresponding weight (p). You will need to run all products individually before adding them together.
For example, if you took 26 in the first assignment and that test is worth 20% of the final grade, multiply 26 x 0, 2. In this case, x = 26 and p = 0, 2
Step 4. Add the results to find the weighted average
The simple weighted average formula where the sum of the weights equals 1 is as follows: x1 (p1) + x2 (p2) + x3 (p3) and so on, where x represents each value of the set and p is the corresponding weight. To calculate the weighted average, simply multiply each number by its weight, then add the results. For instance:
The weighted average for the partial assignments and the oral exam would be as follows: 26 (0, 2) + 28 (0, 35) + 22 (0, 45) = 5, 2 + 9, 8 + 9, 9 = 24, 9. This means that your final grade would be very close to 25
Method 2 of 2: Calculate the Average If the Sum of Weights Doesn't 1
Step 1. Write down the numbers you want to average
When calculating a weighted average, the sum of the weights will not always be 1 (or 100%). Either way, you need to start collecting the data or values you want to know the averages of.
For example, imagine you want to calculate how many hours you slept on average at night over the course of 15 weeks. You got 4, 5, 7 or 8 hours of sleep each night
Step 2. Find the weight of each value
Once the data is known, find out the weights associated with it. For example, imagine that on average some of the 15 weeks you slept more than others. The weeks that best represent your nocturnal habits should have more "weight" than the others. You will use the number of weeks associated with the hours of sleep as your weight. For example, listing the weeks in order of weight:
- 9 weeks where you slept an average of 7 hours a night.
- 3 weeks where you slept 5 hours a night.
- 2 weeks of sleeping 8 hours a night.
- 1 week where you slept 4 hours a night.
- The number of weeks associated with the number of hours is the weight. In this case, you slept 7 hours a week for most of the period under review, while there were a few weeks where you slept more or less.
Step 3. Calculate the sum of all weights
To calculate the weighted average you need to find out what the sum of the weights is when you combine them. To do this, just add them together. In the case of your sleep study, you already know that the sum of the weights is 15, because you are examining your habits over the course of 15 weeks.
The weeks you have considered give the following sum: 3 weeks + 2 weeks + 1 week + 9 weeks = 15 weeks
Step 4. Multiply the values by the weights, then add the results
The next step is to multiply each data by the corresponding weight, as you did in the previous example, then you need to add the results. For example, if you are calculating how much you slept on average in the past 15 weeks, multiply the average number of hours of sleep per night by the corresponding number of weeks. You would get:
5 hours per night (3 weeks) + 8 hours per night (2 weeks) + 4 hours per night (1 week) + 7 hours per night (9 weeks) = 5 (3) + 8 (2) + 4 (1) + 7 (9) = 15 + 16 + 4 + 63 = 98
Step 5. Divide the result by the sum of the weights to find the mean
Once you multiply each value by its weight and add the results together, divide the number you get by the sum of all the weights. You will get the weighted average. For instance:
