If you are examining the height of a population, how would the variation be affected if everyone is wearing platform shoes that are exactly 3 inches tall?
The variation will not be affected in any way.
Let's calculate the variations in both cases:
Case 1 - without platform shoes
Let the set of heights be
Let's calculate the mean and variation:
Case 2 - with platform shoes
Let now the set of heights be
Let's calculate mean and variation:
So we can see that the mean is increased by 3.
So we see, that the variation remains unchanged if the same number is added to (or substracted from) all data in a set.