Want to find the arithmetic mean for ungrouped or grouped data instead? Use the arithmetic mean calculator.
How to Use the Weighted Mean Calculator
This weighted mean calculator helps you find the weighted average of a dataset and see how the value was obtained. To use the calculator:
- Enter your data values in the Data Values input field. You should separate the values either using commas, spaces, tabs, or line breaks.
- Enter the matching weights in the Weights input field. You should separate the weights either using commas, spaces, tabs, or line breaks.
- Click Calculate.
The calculator will instantly return the weighted mean and show you how exactly the value was computed using your own data.
Note. The number of values should be equal to the number of weights for the calculator to work. If your data is in Excel, Google Sheet, or a text document, you can copy and paste them in the calculator input fields.
What Is Weighted Mean?
The weighted mean (or weighted average) is a type of mean in which some data points count more than others. Unlike the average, which treats all the values equally, the weighted mean accounts for the varying weights when finding the average.
For example, final exams tend to carry more weight than quizzes and homework. In this case, using the arithmetic mean would be wrong because it would not account for the varying weights.
Weighted Mean Formula
The weighted mean formula is:
Where:
- x̄w is the weighted mean.
- xi is each data value.
- wi is the weight for each value.
- wixi is the product of each value and its weight.
- Σwixi is the sum of all weighted products.
- Σwi is the sum of all weights.
Note. Sometimes, the weighted mean formula may be written in the expanded format as shown below.
How to Calculate Weighted Mean
To calculate the weighted mean by hand:
- Multiply each value by its weight and sum them
- Add all the weights.
- Divide the sum of the weighted products by the sum of the weights
Example
A student receives the following scores in three course components:
| Component | Score | Weight |
|---|---|---|
| Assignment | 78 | 20 |
| Midterm exam | 84 | 30 |
| Final exam | 90 | 50 |
Find the weighted average score.
Solution
By definition, the weighted mean formula is: x̄w = Σwixi / Σwi
Using the expanded form of the formula and substituting the values, we get:
x̄w = [78(20) + 84 (30) + 90 (50)]/(20+30+50)
= 8580/100
= 85.8
Alternatively, you can find the weighted average of the same data using these simple steps:
Step 1: Multiply each value by its weight and sum them
Multiplying each score (xi) by the weight (wi) and summing, we get:
Σwixi = 78(20) + 84 (30) + 90 (50)
= 1560 + 2520 + 4500
= 8580
Step 2: Add all the weights
The sum of all weights is: Σwi = 20 + 30 + 50
= 100
Step 3: Divide the Σwixi by the sum of the weights
Recall, the weighted mean formula is: x̄w = Σwixi / Σwi
Substituting the values and solving, we get:
x̄w = 8580 / 100
= 85.8
Therefore, the weighted mean score is 85.8.
Frequently Asked Questions
A weighted mean is an average where each value is multiplied by a weight before the average is calculated. Values with larger weights have more influence on the final result.
This calculator finds the weighted mean of a dataset using data values and their corresponding weights. It also shows the weighted product table and a clear step-by-step solution.
The weighted mean formula is: x̄w = Σwixi / Σwi, where xi represents each value and wi represents the corresponding weight.
Yes. Weighted mean and weighted average usually mean the same thing.
Use a weighted mean when some values are more important than others. For example, use it for course grades with different weights, GPA with credit hours, or averages involving different quantities.
If all weights are equal, the weighted mean is the same as the regular arithmetic mean.
