Introduction:

Weighted averages are used in a variety of contexts, including calculating final grades in a course, determining investment returns and various statistical analyses. A weighted average is an average where each number being averaged is assigned a weight according to its importance or relevance. In this article, we will discuss how to calculate a weighted average with a step-by-step guide.

Step 1: List Your Numbers and Weights

First, create a list of the numbers for which you want to calculate the weighted average. Next, assign each number a corresponding weight. The weight assigned to each number should be indicative of its importance relative to the other numbers in the list.

For example, suppose you want to find the weighted average of exam scores for a class that has three exams with weights 40%, 30%, and 30%. Write down the scores and corresponding weights like this:

Exam 1: Score = 90, Weight = 40%

Exam 2: Score = 80, Weight = 30%

Exam 3: Score = 85, Weight = 30%

Step 2: Multiply Each Number by Its Weight

Now, multiply each number by its weight. This will give you the “weighted” value for each number.

Example:

Weighted Exam 1 Score = (90 * 0.4) = 36

Weighted Exam 2 Score = (80 * 0.3) = 24

Weighted Exam 3 Score = (85 * 0.3) = 25.5

Step 3: Determine the Sum of the Weights

Add up the weights assigned to all numbers in your list. This sum is essential for calculating the weighted average correctly.

Example:

Sum of Weights = (0.4 + 0.3 + 0.3) = 1

Step 4: Calculate the Weighted Average

Now we are ready to calculate the weighted average! Divide the sum of the weighted values by the sum of the weights.

Weighted Average = (Sum of Weighted Values) / (Sum of Weights)

Example:

Weighted Average = (36 + 24 + 25.5) / 1

Weighted Average = 85.5

Conclusion:

Calculating a weighted average is an essential tool for many applications, particularly where individual values in a dataset carry different levels of importance. By following these simple steps, you can easily compute a weighted average for any set of numbers with assigned weights.