If you are examining the height of a population, how would the variance be affected if everyone is wearing platform shoes that are exactly 3 inches tall?
It would have no effect on the variance.
The mean would shift up by 3 inches.
All measurements would also shift up by 3 in, so the differences between the mean and all other measurements would stay the same, and so would their squares, and the sum of their squares.
In short, variance would be unaffected.