worldofcalcsAverage Calculator
Average (mean)
66.2
331 ÷ 5
Median
67
Mode
None
Range
44
Count
5
Mean, median, mode and range
The average usually means the mean: add up the values and divide by how many there are. The median (middle value) and mode (most common value) describe the centre of the data in other ways, and the range shows how spread out it is. This calculator gives all of them at once.
Average formulas
Mean = sum ÷ count · Median = middle value · Mode = most frequent value · Range = largest − smallest
For the median, sort the numbers; with an even count, it is the mean of the two middle values. There can be more than one mode, or none if every value appears once.
Which average to use
- The mean is best for data without extreme values, such as marks in a class.
- The median is better when a few values are very large or small, such as salaries or house prices.
- The mode is useful for the most common size, choice or category.
- To find a percentage from total marks, use the percentage calculator.
Worked example
- Marks: 45, 67, 89, 72, 58
- Sum = 331, count = 5, so mean = 331 ÷ 5 = 66.2
- Sorted: 45, 58, 67, 72, 89, so the median is 67
- No mark repeats, so there is no mode
- Range = 89 − 45 = 44
How one large value moves the mean
Each set has the same middle values; the last one includes one very large value.
| Numbers | Mean | Median |
|---|---|---|
| 10, 20, 30, 40, 50 | 30 | 30 |
| 10, 20, 30, 40, 500 | 120 | 30 |
The median barely moves, which is why it is used for skewed data such as incomes.