Average Formulas
“Average” can mean several different measures of the centre of a data set.
Formulas
| Average | Formula / rule |
|---|---|
| Arithmetic mean | x̄ = Σx ÷ n |
| Median | middle value of the sorted data (mean of the two middle values if n is even) |
| Mode | most frequent value(s) |
| Weighted mean | Σ(w·x) ÷ Σw |
| Geometric mean | (x₁ × x₂ × … × xₙ)^(1/n) |
| Harmonic mean | n ÷ Σ(1/x) |
Example
Data: 2, 3, 3, 8, 14
- Mean: 30 ÷ 5 = 6
- Median: 3 (the third value)
- Mode: 3
Mean 6, median 3, mode 3 — the single large value pulls the mean up.
Which to use
- Mean for symmetric data without outliers.
- Median for skewed data such as incomes or prices.
- Mode for categories or the most common option.
- Geometric mean for average growth rates: returns of +10% and −10% average to √(1.1 × 0.9) − 1 ≈ −0.5% per period.
- Harmonic mean for averaging rates over equal distances, like the average speed of a round trip.