The average, or arithmetic mean, is the single most common way to summarize a list of numbers with one representative value. This calculator accepts any list of numbers — grades, prices, measurements — separated by commas or spaces, and returns the mean along with the sum, count, minimum, and maximum.
The formula
For the values 12, 18, 25, 9, and 30: sum = 12+18+25+9+30 = 94, count = 5, so the average is 94 ÷ 5 = 18.8.
Mean vs. median vs. mode
| Measure | Definition | Best used when |
|---|---|---|
| Mean (average) | Sum divided by count | Data is fairly evenly distributed, without extreme outliers |
| Median | The middle value when sorted | Data has outliers that would skew the mean, e.g. income data |
| Mode | The most frequently occurring value | You want the single most common value in a data set |
Worked examples
| Data set | Average |
|---|---|
| 4, 8, 15, 16, 23, 42 | 18 |
| 85, 90, 78, 92 | 86.25 |
| 3, 3, 3, 3 | 3 |
Common mistakes
- Letting outliers dominate the picture. A single very large or small value can pull the mean away from what feels "typical" — the median is often a better summary in that case.
- Averaging averages. Combining several sub-group averages by simply averaging them again is inaccurate unless every sub-group has the same number of data points (this requires a weighted average instead).
Tips
- If your data has extreme outliers, calculate both the mean and the median to get a fuller picture.
- For grouped data with different sample sizes, use a weighted average rather than a simple average of averages.
Frequently asked questions
How do I calculate an average?
Add up all the numbers in the data set, then divide by how many numbers there are.
What's the difference between mean, median, and mode?
The mean is the sum divided by the count. The median is the middle value when the data is sorted. The mode is the value that appears most often. Each can tell a different story about the same data set.
Does the average calculator handle negative numbers?
Yes — enter negative numbers with a minus sign (e.g. -5) and they will be included correctly in the sum and average.
References
- Khan Academy — Free lessons on mean, median, and mode