The mean of n numbers doubles as each number is doubled. Explain

Question

find mean

Answer 1

S₁ represents the sum of the original numbers

S₁ / n represents the mean of the first numbers.

 

2S₁ represents the sum of twice each of the original numbers

2S₁ / n represents the mean fo the sum of twice each of the original numbers.

 

2S₁ = 2(S₁)

 

QED

Answer 2

this is true; the mean is just the average. you should be able to devise some simple illustrations of this fact:

 

the average of 2, 3 and 4 is 3

the average of 4, 6 and 8 is 18/3 = 6, which is double the foregoing average.