SOLUTION: The sum of 9 consecutive even numbers is 180. What is the result when the mean of these numbers is subtracted from the median?

Question 282032: The sum of 9 consecutive even numbers is 180. What is the result when the mean of these numbers is subtracted from the median?

Found 2 solutions by Fombitz, Mathematicians:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
1.
The average would be the sum divided by 9, since there are nine numbers.
2.
The median would be the 5th number
3.
The mean subtracted from the median would be

From eq. 1,

So then,

Answer by Mathematicians(84) (Show Source): You can put this solution on YOUR website!
First we need to find the sum of these 9 consecutive integers.
If we have some integer X, then (X + 1) will be the next integer, we want 9 integers total so we have:

Combining like terms we get:
plus the sum of (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8). You can either hand calculate this sum or you can use the formula n(n + 1)/2 is the sum of any numbers. So our n in this case is 8 so we have 8 * 9/2 = 36
So we have

So our 9 terms are:
16, 17, 18, 19, 20, 21, 22, 23, and 24. The mean is the average which is the middle number which is the mean.
So mean = 20 = median, mean - median = median - mean = 0
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