Question

The mean of n numbers x. If each observation is multiplied by 4, what will be the new mean? Give reason for your answer.​

Answer 1

Step-by-step explanation:

If the mean of n numbers is x, then the mean of the same n numbers each multiplied by 4 is just 4x.

Here is your proof. Call the n numbers x1, x2, …, xn. We know that

(x1+x2+…+xn) / n = x. We now want the average of the n numbers

4x1, 4x2, etc. That average is (4x1+4x2+…+4xn) / n. Factor out the 4:

Get 4 * (x1+x2+…+xn) / n = 4 * x. QED