Adding a Constant

Compare the dotplots of the old and new list:

O O O O Old: --+---------+---------+---------+---------+-- 0 5 10 15 20 O O O O New: --+---------+---------+---------+---------+-- 0 5 10 15 20

The dotplots or histograms look the same, except that the new histogram has been shifted 10 units to the right. Therefore, the new average should be 10 units larger than the old average, but the new SD should be equal to the old SD. This may be verified by actual computations for the list 11, 13, 14, 14: i.e. new average equals 13, new SD equals 1.414.

Subtracting by a constant will move the histogram to the left instead of to the right. Therefore the average will also move left, the SD will remain unchanged.