State four properties of the mean and illustrate each with a

State four properties of the mean and illustrate each
with an example.

Solution

1. The sum of the deviations from the mean is 0.

Ex. Consider 2, 5, 11.

Their mean is 6.

(2-6) + (5-6) + (11-6) = 0

****************

2.

If each observation is increased by a number p, the mean increases by p.

Let p = 2 in #1. Thus, we have the new numbers

4, 7, 13.

Thus, their new mean is 6 + 2 = 8.

******************

3.

If each observation is decreased by a number p, the mean decreases by p.

Let p = 2 in #1. Thus, we have the new numbers

0, 3, 9.

Thus, their new mean is 6 - 2 = 4.

*******************

4.

If each observation is multiplied by a number p, the mean gets multiplied by p.

Let p = 2 in the example in #1. Thus, we have the new numbers

4, 10, 22.

Thus, their new mean is 6*2 = 12.

****************