Arithmetic Mean Formula
The arithmetic mean formula calculates the average of a set of numbers by dividing their sum by the count.
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.