How to Calculate Weighted Average: A Guide

Understanding how to calculate weighted average is useful in a variety of contexts, including academics and business, financial analysis, and strategic decision-making. Unlike a simple average, which assigns equal weight to all numbers, a weighted average prioritizes some data points over others.

Whether you're calculating employee performance evaluations, estimating the expected value of a random variable, or determining stock weighted average prices, mastering this method can lead to more accurate conclusions and better decisions.

What is the weighted average?

A weighted average, also known as a weighted mean, is a type of mean in which each value in a data set is multiplied by a weight indicating its relative importance. To calculate the final average, add the weights and divide by the total weight. This differs from the arithmetic mean, which assumes that all values have equal importance.

The weighted average is used across various fields-finance, economics, and even education. In accounting, weighted average accounts are often used to determine the cost of goods sold or to value inventory consistently. Since each component has a different weight, and often represents different values, a regular average would misrepresent the data.

Using a weighted average when evaluating career options helps you balance different salary levels over time. Salary.com's personal salary report can further assist you in your career by offering carefully chosen and customized details about your position, business, background, and factors that affect compensation.

What is the purpose of a weighted average?

The primary goal of a weighted average is to provide an accurate representation of a situation in which not all factors are equal. It is frequently used in real-world applications where decision making is based on multiple data points with different weights. For example, investors use it to compute the weighted average price of stocks purchased at different prices. With a variety of assessment components, including quizzes, assignments, and projects, each with a specific weight, it aids in determining the final average of students in schools.

In economics, the weighted average is used to calculate expected values based on probabilities assigned to different outcomes, particularly when looking at a random variable. Similarly, HR departments use this technique in employee performance evaluations, where different tasks or KPIs have varying degrees of importance. In short, a weighted average is useful for summarizing and simplifying complex data in a fair and meaningful way.

Advantages and disadvantages of weighted average

The weighted average's primary benefit is its capacity to take each value's relative significance into consideration. When factors of different importance are included in the data set, it yields a more accurate and trustworthy result than a simple average. This approach is very adaptable, enabling users to give important factors the right weights, and it is very helpful in domains such as project management, statistics, finance, and education.

But it has some disadvantages as well. First of all, more specific information is needed to calculate a weighted average, namely, an understanding of each value and its value-corresponding weight. Additionally, there is room for error: improper weight assignment and errors in weighted average calculations can skew results.

Finally, the procedure can get complicated, particularly when working with big data sets or manually calculating results without the use of programs like Google Sheets or Excel. In these software's, you can calculate the weighted average using SUMPRODUCT and SUM functions, making the process efficient for large data sets. Despite these drawbacks, when precise analysis is needed, the advantages frequently exceed the difficulties.

How to calculate weighted average

Now that you understand what a weighted average is and why it's important, let's walk through the step-by-step process to calculate a weighted average manually. Below is a simplified guide for performing this calculation manually.

Step 1: List all the values and their corresponding weights.

Begin by identifying each value and its assigned weight. These could include test scores, stock prices, or any other set of measurable data. The weight denotes the relative importance of that value.

For example, if you have three grades-90, 85, and 80-with weights of 0.4, 0.3, and 0.3, you should start by organizing them in a simple table or list.

Step 2: Multiply each value by its weight.

Before adding the weighted sum, multiply each value by its corresponding weight. Continuing from our example, you would calculate:

• 90 x 0.4 = 36
• 85 x 0.3 = 25.5
• 80 x 0.3 = 24

Step 3: Add up all the weighted values.

Next, sum all of the weighted values you calculated. In this case, the total weighted sum would be: 36 + 25.5 + 24 = 85.5. This number represents the combined impact of each grade according to its relative significance.

Step 4: Check that the weights add up to 1.

After adding the weighted values, finish the calculation by dividing the total weighted sum by the sum of all weights. It's essential to verify that the sum of the weights equals 1 (or 100% if using percentages).

In our example, 0.4 + 0.3 + 0.3 = 1, so everything checks out. If the weights sum does not equal one, divide the total weighted sum by the total weight to calculate the correct final average.

The result, 85.5, is your weighted average-a more precise reflection of performance compared to a regular average where each score is weighted equally.

Other examples

Let's explore a couple of other scenarios where weighted average calculations are used in real life. In the previous example, we determined the weighted average price of a stock bought at different times and prices. The following examples will show how weighted average calculations apply in investing:

In investing, suppose you buy the same stock at different prices: 100 shares at $10 and 200 shares at $12. First, multiply each share count by its price:

• 100 x 10 = 1000
• 200 x 12 = 2400

Then add them: 1000 + 2400 = 3400. Now divide the total weighted sum by the total number of shares: 3400 ÷ 300 = $11.33. That's your weighted average price per share-a critical figure for any investor making buy-sell decisions.

We've covered definitions, formulas, and worked examples-now you're ready to use weighted average in your own calculations.

Learning how to calculate weighted average is a valuable skill that will help you make more informed decisions. Whether you're working on a school project, managing investments, or analyzing employee data, understanding the weighted average formula helps you evaluate outcomes more accurately. Always remember to consider the assigned weight of each data point, multiply it correctly, double-check that all the weights add up, and interpret your results in context.