3/13 Arithmetic mean – properties
The arithmetic mean is the most commonly used measure of central tendency. It allows you to summarize a dataset with just one number.
Let's calculate arithmetic means for the following sets of numbers:
| Set |
Sum |
Arithmetic mean |
| 1, 2, 3 |
6 |
2 |
| 2, 2, 2 |
6 |
2 |
| 0, 2, 4 |
6 |
2 |
| -10 ,2, 14 |
6 |
2 |
| -1000, 2, 1004 |
6 |
2 |
| -1000, 503, 503 |
6 |
2 |
Observe that:
- All datasets in this group have the same arithmetic mean.
- The arithmetic mean can't be less than the minimal element of the set or greater than the maximal.
- Adding two values with a sum equal to the doubled arithmetic mean doesn't change the mean.
- The arithmetic mean doesn't have to be an element in the dataset. (In the final example, the number 2 does not appear in the dataset.)
