What is the Weighted Average?
A weighted average is an average that accounts for the relative importance of the different factors that you include in the average.
Averages are standard statistical tools that you can use to find an approximate middle point in a set of numbers. The problem with finding the mean of a set of numbers is that it does not account for the relative importance of those numbers. Weighted averages correct for this flaw, assigning importance to each number and factoring that importance in when calculating the average. Weighted averages are valuable because they provide more information than a simple average without requiring much additional information — just the information needed to assign weights to each number.
College professors regularly use weighted averages when assigning final grades in their classes. Think about a class where 25% of the grade comes from homework, 35% comes from quizzes, and the remaining 40% comes from the final exam. The professor uses weighted averages to determine each student’s final grade weighting homework grades at .25, quiz grades at .35, and the final at .4.
Finding a weighted average is like comparing the weights of two buckets of rocks as opposed to counting the number of rocks in each…
Each bucket may contain 10 rocks, but a three-pound stone is going to count for more than a pebble. Similarly, a more heavily weighted number in a set is going to count more than a lightly weighted one.
A weighted average is an average that accounts for the importance of each number that you’re averaging. When you find the average (or mean) of a set of numbers, usually, all you have to do is add the numbers, then divide the sum by the number of values you added. Weighted averages assign importance (or weight) to each number.
A weighted average can be more useful than a regular average because it offers more nuance. It reduces the weight of data that is less important, allowing more material data to have a more significant effect on the result. You can also use it to correct for deficiencies in a dataset. For example, if you’re assessing a sprinter’s average sprint times, you might want to weight sprints from the past three months more heavily than sprints from the year previous to account for the sprinter’s improvement over time.
One of the most common examples of a weighted average is the grade you receive in a class. For example, the class syllabus could state that homework is 20% of your final grade, quizzes 30%, and exams 50%. Rather than finding the simple average of every graded assignment, the professor weights those grades based on the type of task. Tests are two and a half times more important than homework assignments, and quizzes are 50% more important than homework.
In sports, statisticians use weighted averages to calculate an athlete’s performance. For example, in Major League Baseball, people calculate slugging percentage using a weighted average. Singles have a weight of one, doubles a weight of two, triples a weight of three, and home runs a weight of four.
Manufacturers can use weighted averages to determine the cost of their raw materials. If the manufacturer buys 200 units at $5 per unit from one supplier and 500 units at $3 per unit from another, it needs to use a weighted average to find the average cost per unit accurately. This is important for determining sales prices and profitability.
Similarly, investors can use weighted averages to determine their portfolios’ performances. If an investor puts $30,000 in company ABC and $10,000 in company XYZ, they should weight their returns 3:1 to find the average return for their portfolio. Bond investors can use a similar calculation to find the average interest rate of their portfolio.
The weighted average method is a method of determining the average cost of a product or investment. Companies frequently use this method to track inventory costs. Investors can use it to track the cost basis for investments where First-In, First-Out (FIFO) or Last-In, First-Out (LIFO) cost bases aren’t used.
The benefit of using the weighted average method is that it is easier to track. Systems such as FIFO or LIFO require individual tracking for every unit. That means that businesses have to track every unit of every item in inventory, and investors must track the cost basis for every share that they own.
The downside of the weighted average costing method is that it is less precise. If a business purchases raw materials at very different prices, the weighted average won’t adequately reflect the lowest or highest cost paid. This could result in the company pricing goods too low, leading it to lose money on sales where it used components purchased at a high price. In theory, sales from the goods made with low-cost batches of supplies make up for these losses, but this does not always happen.
You should use a weighted average when you want to assign more importance to some numbers in a dataset than others. One scenario where this is useful is where one event can have multiple positive or negative results, but the magnitude of the positive or negative result is variable.
An example of this in baseball is slugging percentage. This particular batting average compares the number of hits (positive results) a player gets to the number of times they go up to bat, but not every hit is created equal. A double is more valuable (more positive) than a single, a triple more valuable than a double, and a home run more valuable still.
Using a weighted average offers more insight into the value of each of a player’s at-bats.
The most crucial difference between averages and weighted averages is that weighted averages assign importance to each number in a set of numbers. A regular mean or average does not.
Outliers tend to have a smaller impact on weighted averages than in typical averages. You can assign a low weight to outliers to reduce their impact on the weighted mean.
Averages tend to find a central tendency in a set of numbers. A weighted average does not because it is heavily based on the assigned weights.
Another difference is that weighted averages can be biased or subjective. Each number in the set must have a weight. How to assign weights is generally an individual decision. Two people with the same dataset can assign weights in entirely different ways, which produces two different weighted averages. Because typical means don’t involve subjective weights, they cannot be biased in the same way.
To calculate weighted averages, you need to start with a set of numbers. Weighted averages are frequently used to calculate class grades, so imagine a set of grades that looks like this.
Once you have the set of numbers, you must assign a weight to each. The list of assignments includes homework, quizzes, and exams. You can make a table with the grades and the type of task, such as:
The syllabus states that homework assignments are worth 25% of the final grade, quizzes, 35%, and exams 40%. The next step is to multiply each grade by its corresponding weight.
Finally, sum the results and divide it by the sum of the weights to find the final weighted average.
25% + 28.7% + 24.5% + 23.75% + 40% + 25% + 21% + 28.8% = 216.75%
.25 + .35 + .35 + .25 + .4 + .25 + .35 + .4 = 2.6
216.75% / 2.6 = 83.365%
One of the most significant disadvantages of using weighted averages is that the calculations can be complicated. This is especially true as the size of the data set grows. Modern tools, like Excel, can make finding weighted averages much easier.
To start, make two columns, one containing each number and another containing the weight for each number. Then, use the SUMPRODUCT function to multiply each number by its weight and to sum the results.
Next, use the SUM function to find the sum of all the weights. Finally, divide the SUMPRODUCT of the numbers by the SUM of the weights to find the weighted average.
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