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Statistics 101

Introduction
Arithmetic mean
3. Arithmetic mean – properties
Median
Mode
Summary

Instruction

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.)