Weighted Average Calculator
Calculate the average of a set of numbers where each number has a different weight.
Data Points and Weights
Understanding Weighted Average
A weighted average is a type of average that takes into account the relative importance or frequency of each value in a dataset. Unlike a simple average, where all values contribute equally, a weighted average assigns different 'weights' to each value.
Weighted Average Formula:
Where:
- Σ (Sigma) means 'sum of'
- Value = Each data point or number
- Weight = The importance or frequency assigned to each value
Weighted Average Examples
| Values | Weights | Weighted Average |
|---|---|---|
| 10, 20, 30 | 1, 1, 1 (Simple Average) | 20 |
| 10, 20, 30 | 1, 2, 1 | 20 |
| 80, 90, 70 | 0.2, 0.3, 0.5 (Course Grades) | 77 |
Frequently Asked Questions
What is a weighted average?
A weighted average is an average where some values contribute more than others to the final average. Instead of each data point contributing equally, each data point is multiplied by a predetermined weight.
How is a weighted average calculated?
To calculate a weighted average, multiply each value by its weight, sum these products, and then divide by the sum of all weights. Formula: Weighted Average = Σ(Value × Weight) / Σ(Weight).
When is a weighted average used?
Weighted averages are commonly used in academic grading (where different assignments have different importance), finance (e.g., portfolio returns), and statistics (e.g., calculating GPA, average cost of inventory). It is used whenever some data points are more significant than others.