What Is a Weighted Average?
A weighted average (or weighted mean) is a calculation that takes into account the varying degrees of importance of the numbers in a data set. Unlike a simple arithmetic mean where all values contribute equally, a weighted average assigns different weights to each value, reflecting its relative significance.
The Formula
Weighted Average
Sum of weighted values divided by sum of weights.
WA = Sum(w*x) / Sum(w)
Each Contribution
How much each pair contributes to the total.
Contribution_i = w_i * x_i
Simple Average (Special Case)
When all weights are equal, it reduces to a simple mean.
If all w_i = 1: WA = Sum(x) / n
Common Applications
- Grades: Course grades where different assignments have different point values or percentages.
- Finance: Portfolio returns weighted by investment amounts.
- Statistics: Survey data where responses are weighted by sample sizes.
- Science: Averaging measurements with different levels of precision (weighted by inverse variance).
Tips
- Weights can be any positive numbers; they do not need to sum to 1 or 100.
- If all weights are equal, the weighted average equals the simple average.
- A higher weight means that value has more influence on the result.