verba docent exempla trahunt ~Seneka
Take three numbers: 1, 2 and 3.
Mean value is 2
Differences between values and a mean are:
1-2 = -1
2-2 = 0
3-2 = 1
Sum of these differences is
-1 + 0 + 1 = 0
Zero-sum property states that no matter what numbers you start with, a result (sum of diiferences between them and their mean) would be 0