The weighted average takes into account the relative importance or weight of each data point in the calculation, which makes it more precise than a simple arithmetic mean. You can use a weighted average to calculate various weighted means in statistics, the weighted average cost of capital in finance, and other averages in scientific research.
Not everyone likes math, but it’s a vital part of many of the industries that keep modern society working. One of the more valuable but simple calculations that help these industries is the weighted average.
In this article, we’ll explore what a weighted average is, how it’s calculated, and how it’s used.
What is a weighted average?
A weighted average is a type of average that considers the weight or importance of each number in a set. This is useful when some numbers are more significant than others regarding their impact on the final result.
For example, when calculating a student’s final grade, the weight of each assignment or exam may be different. This results in a different grade than if all assignments and tests were weighed equally.
What is the difference between a weighted average and a simple average?
How is a weighted average calculated?
Calculating the weighted average involves a few simple steps, but it’s important to understand each step and how it affects the overall calculation. Here’s a step-by-step guide to calculating weighted average:
1. Determine the weight of each variable
The first step in calculating the weighted average is to determine the weight of each number in the set. The weight is typically represented as a percentage or a decimal, and it reflects the relative importance of that number to the overall calculation.
For example, in the grade calculation example we mentioned earlier, the three assignments have weights of 20%, 30%, and 50%, respectively.
2. Multiply each number by its weight
Next, you need to multiply each number in the set by its corresponding weight. This gives you the “weighted value” of each number, which considers its importance to the overall calculation.
For example, if you scored 80%, 90%, and 70% on the three assignments, the weighted values would be:
3. Add up the weighted values
Once you calculate the weighted value of each number, you need to add them up to get the total weighted value.
Using the example above, the total weighted value would be: 16% + 27% + 35% = 78%
4. Divide by the sum of the weights
Finally, divide the total weighted value by the sum of the weights to get the weighted average.
Using the example above, the sum of the weights is: 0.2 + 0.3 + 0.5 = 1
Dividing the total weighted value by the sum of the weights gives us: 78% / 1 = 78%
So the weighted average grade for the three assignments is 78%.
Let’s say you want to calculate the weighted average of three test scores. The first test is worth 30% of the final grade, the second test is worth 40%, and the third test is worth 30%. The scores are 80, 90, and 70. Using the formula above, the calculation would be:
Therefore, even though we used the same scores as the tests above, the weighted average of the three test scores is 81. This demonstrates how valuable incorporating a weighted average can be in a formula.
How can you use a weighted average?
The weighted average is a versatile concept many different fields use for various purposes. Here are some examples of how you can use a weighted average in finance, statistics, science, and other areas:
In the finance industry, the weighted average is used to calculate the weighted average cost of capital (WACC), which measures the overall cost of a company’s financing sources. WACC considers the weight of each financing source (such as debt and equity) and the cost of each source (such as interest rates and dividends).
WACC is an important metric for companies, as it helps them make decisions about investments, mergers and acquisitions, and capital structure.
Statisticians use the weighted average to calculate different types of weighted means, which are helpful in analyzing data sets with different distributions or sampling weights.
For example, the weighted arithmetic mean considers the relative frequency of each data point, while the weighted geometric mean is used for data sets with a logarithmic distribution. Weighted means are often used in survey research, epidemiology, and other fields where sampling weights are essential.
Scientists use the weighted average to calculate various types of averages in scientific research. This can range from the weighted average of the atomic mass of elements, the molecular weight of compounds, and experimental data.
These calculations consider the relative abundance or concentration of each component, which can affect the overall result. You may also see the weighted average used in meteorology, where they calculate the average temperature or precipitation over a given period.
Pros and cons of using a weighted average
Though the additional precision is helpful in many calculations, there are both upsides and downsides to using the weighted average in a calculation.
Here is a list of the benefits and drawbacks to consider.
- Reflects the importance of each data point. A weighted average can be useful when some data points are more important than others. By assigning weights to each data point, the weighted average reflects the relative importance of each point in the final calculation.
- Increases accuracy. A weighted average can increase the accuracy of the final calculation by giving more weight to more reliable data points. For example, in a survey, responses from a larger sample size may receive more weight as they’re likely to be more representative of the population.
- Allows for flexibility. The use of a weighted average allows for flexibility in the calculation. By adjusting the weights assigned to each data point, the final calculation can be tailored to specific needs.
- Complexity. Weighted averages can be more complex to calculate compared to simple averages, especially when the weights are not uniform. This can lead to errors in the calculation if not done carefully.
- Requires accurate weighting. The accuracy of the final calculation relies heavily on the accuracy of the weights assigned to each data point. If the weights are not accurate, the final result will also be inaccurate.
- Can be subjective. The weighting assigned to each data point can be subjective and influenced by personal biases or preferences. This can lead to different results depending on who assigns the weights.
Before using this calculation in your formula, make sure you consider whether any biases could be introduced into the data.
- The weighted average takes into account the relative importance or weight of each data point in the calculation.
- To calculate the weighted average, you first need to determine the weight of each data point in a set. Then, multiply each data point by its weight to get the “weighted value” of each data point.
- The weighted average is more precise than a simple arithmetic mean. Because of this, statisticians, scientists, and employees within the finance industry all use the calculation for different purposes.
View Article Sources
- Consumer Expenditures and Income: Calculation — U.S. Bureau of Labor Statistics
- Weighted Averaging — U.S. Environmental Protection Agency
- Weighted Average — CueMath