Mean (Average) Formula
Reference for arithmetic mean formula Mean = Σx/n.
Compares arithmetic, geometric, and harmonic mean with guidance on when each best represents a data set.
The Formula
Mean (x̄) = Σx / n
The mean is the sum of all values divided by the number of values. It is the most widely used measure of central tendency in statistics.
Variables
| Symbol | Meaning |
|---|---|
| x̄ | The mean (pronounced "x-bar") |
| Σx | The sum of all data values |
| n | The number of data values |
Example 1
Find the mean of: 12, 15, 18, 22, 33
Σx = 12 + 15 + 18 + 22 + 33 = 100
n = 5
Mean = 100 / 5
Mean = 20
Example 2
A student's test scores are: 85, 90, 78, 92, 88, 95. What is the average?
Σx = 85 + 90 + 78 + 92 + 88 + 95 = 528
n = 6
Mean = 528 / 6
Mean = 88 — The student's average test score is 88.
When to Use It
Use the mean formula when:
- You need a single number to represent a data set
- The data has no extreme outliers that would skew the result
- Calculating grade point averages, batting averages, or financial averages
- You need a baseline for further statistical calculations (like standard deviation)
Key Notes
- The mean is sensitive to outliers — a single extreme value pulls it significantly; when data is skewed (e.g. incomes, house prices), the median is usually a better measure of the "typical" value
- The arithmetic mean works for additive quantities (temperatures, scores); for multiplicative growth rates or ratios, use the geometric mean: (x₁ × x₂ × … × xₙ)^(1/n)
- Weighted mean accounts for unequal importance: x̄ = Σ(wᵢxᵢ) / Σwᵢ — used for GPA (credit-weighted), stock portfolios (value-weighted), and survey results (population-weighted)
- The mean is the unique value that minimizes the sum of squared deviations (Σ(xᵢ − x̄)²) — this property makes it the foundation for least-squares regression and analysis of variance (ANOVA)