Arithmetic Mean Formula
Reference for the arithmetic mean formula (sum / count).
Compares arithmetic, geometric, and harmonic means with examples for statistics and data analysis.
The Formula
The arithmetic mean is the most common type of average. It represents the central value of a data set by adding all values together and dividing by the total count. It is widely used in statistics, science, economics, and everyday life.
Variables
| Symbol | Meaning |
|---|---|
| x̄ | The arithmetic mean (average) |
| x1, x2, ..., xn | The individual values in the data set |
| n | The number of values in the data set |
| Σ | Summation symbol — means "add all values together" |
Example 1
Find the mean of the test scores: 85, 92, 78, 95, 88
Add all values: 85 + 92 + 78 + 95 + 88 = 438
Count the values: n = 5
Divide: 438 / 5
Mean = 87.6
Example 2
A store sold items priced at $12, $8, $15, $8, $22, $10. What is the average price?
Sum: 12 + 8 + 15 + 8 + 22 + 10 = 75
Count: n = 6
Mean = 75 / 6
Mean = $12.50
When to Use It
The arithmetic mean is the right average when your data is evenly distributed without extreme outliers.
- Calculating grade point averages (GPA)
- Finding average temperatures, prices, or measurements
- Quality control — comparing individual measurements to the average
- Sports statistics — batting averages, scoring averages
- Financial analysis — average revenue, average cost per unit
Limitations
The arithmetic mean can be misleading when data contains extreme outliers. For example, if five employees earn $40,000, $42,000, $45,000, $48,000, and $500,000, the mean is $135,000 — which does not represent the typical salary. In such cases, the median (middle value) is a better measure of central tendency.
For rates of change or growth, use the geometric mean instead. For frequency data, use the mode.