Four types of average
Not every situation calls for a simple arithmetic mean. This calculator offers four types, each suited to a different context.
Formulas
| Type | Formula | When to use |
|---|---|---|
| Arithmetic | Sum of values ÷ count | General case, all values equally weighted |
| Weighted | Σ(value × weight) ÷ Σ(weight) | When each value carries a different importance (e.g. grades with different weights) |
| Geometric | n-th root of the product of values | Growth rates, compounded percentage changes |
| Harmonic | n ÷ Σ(1/value) | Averages of rates, like average speed over equal-distance legs |
Example — weighted average
Grades 8 (weight 2), 6 (weight 3) and 9 (weight 5): average = (8×2 + 6×3 + 9×5) / (2+3+5) = (16+18+45)/10 = 7.9.
Tip
For weighted average, enter each pair as value:weight, comma separated — for example 8:2, 6:3, 9:5.
Frequently asked questions
What's the difference between arithmetic and weighted average?
In the arithmetic mean every value has equal weight; in a weighted average, each value can carry a different importance in the final result.
When should I use the geometric average?
It's ideal for calculating average growth rates, like average investment returns over several years.
When should I use the harmonic average?
It's best suited for averaging rates, like average speed over equal-distance trips taken in different times.
How do I enter weights for a weighted average?
Use the value:weight format for each item, separating items with commas — for example: 8:2, 6:3, 9:5.