The average (arithmetic mean) of the even integers from 0 to 120 inclusive is how much greater than ...
The average (arithmetic mean) of the even integers from 0 to 120 inclusive is how much greater than the average (arithmetic mean) of the even integers from 0 to 60 inclusive?
Answer/Solution
30
Steps/Work
The sum of even numbers from 0 to N is 2 + 4 +...+ N
= 2(1 + 2 + ...+ N/2)
= 2(N/2)(N/2+1)/2 = (N/2)(N/2+1)
The average is (N/2)(N/2+1)/(N/2+1) = N/2
The average of the even numbers from 0 to 120 is 120/2 = 60
The average of the even numbers from 0 to 60 is 60/2 = 30
The answer is D.
= 2(1 + 2 + ...+ N/2)
= 2(N/2)(N/2+1)/2 = (N/2)(N/2+1)
The average is (N/2)(N/2+1)/(N/2+1) = N/2
The average of the even numbers from 0 to 120 is 120/2 = 60
The average of the even numbers from 0 to 60 is 60/2 = 30
The answer is D.