Free calculator
Weighted average
An average where every value has its own weight: grades of varying importance, an average price from purchases of different sizes. Add rows as needed.
Weighted average calculation
Enter a weight for every value. Empty rows are skipped.
- Weighted average
- —
How the weighted average is calculated
An ordinary (arithmetic) average gives all values the same importance. A weighted average assigns each value a weight; values with a higher weight pull the result more:
weighted average = (value₁ × weight₁ + value₂ × weight₂ + …) / sum of weights
A step-by-step example
Values 3, 5 and 9 with weights 1, 2 and 3:
- Multiply each value by its weight:
3×1 = 3,5×2 = 10,9×3 = 27. - Add up the products:
3 + 10 + 27 = 40. - Add up the weights:
1 + 2 + 3 = 6. - Divide:
40 / 6 = 6.67.
The weighted average is 6.67, closer to nine than the ordinary average of 5.67, because nine has the largest weight.
Repeated values as weights
A weight can also be a count of occurrences. The average of the numbers 2, 2, 2, 5, 5 can be calculated as a weighted average of two rows: value 2 with weight 3 and value 5 with weight 2: (2×3 + 5×2) / 5 = 3.2.
Where the weighted average is used
- School: grade averages where an exam counts more than an oral test; at university, the credit-weighted grade average.
- Purchasing and inventory: the average purchase price across several deliveries at different prices and quantities.
- Investment: the average portfolio return weighted by position size.
- Statistics: price indices where every item is weighted by its share of consumption; surveys weighted by group representation in the population.
- Marketing: average order value across channels of different sizes.
Where to go next
You can do the maths. But what next? How to turn customers who bought once into customers who buy repeatedly is the subject of the book Opakovaný prodej.