To calculate a weighted average, multiply every value by its corresponding weight, add the weighted results, and divide by the total of all weights. Unlike a simple average, a weighted average allows some values to contribute more heavily than others.
Enter a list of numbers to calculate the mean, sum, count, median, mode, range, minimum, and maximum.
Multiply each value by its weight before combining the results.
What Is a Weighted Average?
A weighted average is a mean in which some observations influence the result more than others.
Each value is paired with a weight representing importance, frequency, credit, quantity, or probability.
The ordinary Average Calculator calculates a simple arithmetic mean, so weighted calculations should be completed separately using the method below.
Weighted Average Formula
Multiply each value by its weight. Add all weighted products and divide by the total weight.
When weights are percentages that total 100 percent, the weighted products can be added directly after converting the percentages to decimals.
When weights are quantities or credits, divide by their combined total.
Worked Example with Percentage Weights
Suppose three scores are 70, 80, and 90. Their weights are 20 percent, 30 percent, and 50 percent.
Multiply 70 by 0.20 to get 14, multiply 80 by 0.30 to get 24, and multiply 90 by 0.50 to get 45.
Adding the contributions gives a weighted average of 83.
Worked Example with Credit Hours
Suppose a three-credit course has a score of 80 and a six-credit course has a score of 90.
The weighted products are 240 and 540, giving a total of 780.
The total weight is nine credits. Dividing 780 by nine gives approximately 86.67.
Why a Simple Average Would Be Wrong
A simple average would treat each value as equally important.
For the two course scores, the simple average is 85, but the six-credit course should have twice the influence of the three-credit course.
The weighted result of approximately 86.67 reflects that difference.
Weights as Percentages
Percentage weights should normally total 100 percent.
Convert each percentage to a decimal before multiplying, such as 25 percent becoming 0.25.
When the percentages do not total 100 percent, divide the weighted total by the combined percentage weight.
Weights as Frequencies
A frequency can also act as a weight.
When a value of 10 occurs twice and a value of 20 occurs three times, the weighted total is 10 multiplied by two plus 20 multiplied by three.
Divide the result by five, the total frequency.
Weighted Average vs Simple Average
A simple mean assumes equal contribution from every observation.
A weighted mean assigns different levels of influence.
Read Average Formula Explained for the ordinary arithmetic-mean calculation.
Weighted Grades
Course grades often use weights for assignments, quizzes, projects, and examinations.
A final examination worth 50 percent affects the result more than a quiz worth 10 percent.
Confirm that the listed category weights total 100 percent before calculating the final grade.
Common Mistakes
Do not add the values before applying their weights.
Do not divide by the number of observations when the weights do not all equal one.
Do not mix percentages and whole-number weights without converting them into a consistent form.
Conclusion
A weighted average accounts for unequal importance by multiplying every value by its weight.
Add the weighted products and divide by the total weight.
Use the Average Calculator for simple means and this weighted method when values contribute unequally.
FAQs
What is a weighted average?
It is an average in which values have different levels of influence.
How do I calculate it?
Multiply each value by its weight, add the products, and divide by the total weight.
Must percentage weights total 100 percent?
They normally should, although a formula can normalise weights that total another amount.
Is a weighted average the same as a simple mean?
Only when every value has the same weight.
Can credit hours be used as weights?
Yes. Multiply each grade by its course credits and divide by total credits.