How the Average Calculator Works
An average tells you what is typical in a list of numbers. There are three common kinds: the mean, the median and the mode. The Average Calculator works out all three for any list of numbers, and also gives you the count, the sum, and the smallest and largest values.
What you enter
- Numbers: your list, separated by commas, spaces, semicolons or new lines (the default is 12, 18, 25, 40, 55).
- Every item must be a number. If one is not, the calculator tells you which one.
The three averages
| Average | How it is found |
|---|---|
| Mean | Add all the numbers, then divide by how many there are |
| Median | Sort the numbers and take the middle one (for an even count, the mean of the two middle ones) |
| Mode | The number that appears most often (there may be none, or more than one) |
A worked example
The default list is 12, 18, 25, 40, 55:
| Result | Value |
|---|---|
| Count | 5 |
| Sum (12 + 18 + 25 + 40 + 55) | 150 |
| Mean (150 / 5) | 30 |
| Median (the middle of the sorted list) | 25 |
| Mode | None (every value appears once) |
| Smallest / largest | 12 / 55 |
Chart: the numbers
The bars show each number. The mean is 30, and the median is 25:
12 █████████ 18 █████████████ 25 ██████████████████ median 40 █████████████████████████████ 55 ████████████████████████████████████████
More examples
| List | Mean | Median | Mode |
|---|---|---|---|
| 2, 3, 3, 5, 7, 3, 9 | 4.5714 | 3 | 3 |
| 4, 8, 15, 16 | 10.75 | 11.5 | None |
| 1, 1, 2, 2, 3 | 1.8 | 2 | 1, 2 |
| 20, 22, 24, 26, 500 | 118.4 | 24 | None |
Which average to use
- Mean: best for evenly spread data, such as test scores or daily temperatures.
- Median: best when a few numbers are extreme, such as house prices or salaries.
- Mode: best for the most popular choice, such as the most common shoe size.
Chart: one extreme number
The list 20, 22, 24, 26, 500 has one very large value. It pulls the mean up, but the median stays with the typical numbers:
mean ████████████████████████████████████████ 118.4 median ████████ 24
Tips
- A list can have no mode (all different) or several modes (a tie).
- The answers are rounded to 4 decimal places, and a small non-zero answer is never shown as 0.
- For the spread of the numbers (standard deviation and variance), use the Statistics Calculator.
This tool gives an estimate for general information only. For grades or official statistics, follow the method required.