Formula
Each value is multiplied by its weight, then divided by the total weight:
Weighted mean = (value × weight, summed) / sum of weights
Equal weights give the same result as the arithmetic average.
Assumptions
- The two lists have the same count.
- Weights are zero or greater, and not all zero.
Worked example
Values 70, 80, and 90 with weights 1, 2, and 1 have a weighted mean of 80.
Input definitions
- Values
- The numbers being averaged.
- Weights
- How many times each value counts, in the same order.
Limitations
Results are rounded for display. This is a classroom calculation, not a measurement from a lab or a financial filing.
Questions
What if every weight is 1?
The result is the ordinary average.
Can a weight be zero?
Yes. That value drops out, as long as another weight is above zero.