With an example that if we replace each item of observation by the calculated mean, then the total of these replaced values will be equal to the sum of the given observations.
We take following three observations calculate their mean and replace the observations by the calculated mean:
Worker Wages |
A |
B |
C |
Daily wages (in Rs) |
100 |
150 |
200 |
Workers |
Wages (Rs.) X |
Mean X |
A B C |
100 150 200 |
150 150 150 |
N = 3 |
Σ X = 450 |
450 |
Thus we see that the total of replaced values (Rs. 450/-) is equal to the sum of the given observation.