Weighted Average Calculator

How to calculate weighted average?

A weighted average is a calculation that accounts for the relative importance, or weight, of each value in a data set. Unlike a simple average where all numbers are treated equally, a weighted average reflects the fact that some data points contribute more significantly to the final result than others.

Weighted Average = Σ (Value × Weight) / Σ Weights

Using the Weighted Average calculator: an example

Consider a student calculating their final course grade. If they received a Grade of 90 in a course worth 3 credits and a Grade of 80 in a course worth 4 credits, the credit hours serve as the weights for each respective grade.

Step-by-step calculation:

1. Multiply values by weights: (90 × 3 = 270) and (80 × 4 = 320).
2. Sum the products: 270 + 320 = 590.
3. Sum the total weights: 3 + 4 = 7 total credits.
4. Divide: 590 ÷ 7 = 84.28. The weighted average grade is 84.28.

Frequently Asked Questions

What is the difference between a simple and weighted average?

A simple average assumes all numbers contribute equally to the final value. A weighted average assigns specific levels of importance (weights) to each number, ensuring that higher-priority values have a larger impact on the result.

What happens if weights don't sum to 100?

The weights do not need to sum to 100 or 1. The weighted average formula works with any scale of weights because the total sum of products is divided by the sum of the weights used, effectively normalizing the result.

What are common real-world applications?

Weighted averages are essential in finance for calculating investment portfolio returns (where weights are dollar amounts), in education for Grade Point Average (GPA) calculations, and in business for inventory valuation and cost analysis.