(Solved) If the sum of an odd number of consecutive integers is 0, what is the median?

smorgan6616

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11 years ago

If the sum of an odd number of consecutive integers is 0, what is the median?

If the sum of an odd number of consecutive integers is zero, what is the median?

I have no idea, please help!

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askollmeyer

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11 years ago

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txgalbiolclas

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11 years ago

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nursing2

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11 years ago

Since the sum is zero, there must be some negative numbers in the set.

Let the sum of the negative numbers be N
Let the sum of the positive number be P

So the sum of the numbers in the set is:
N + 0 + P = 0
Since there are an odd number of consecutive integers, N = -P

Thus the median is 0.

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lengjacinto

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11 years ago

answer is 0 ..take consecutive numbers like -1 ,0 and 1
or -3 ,-2 ,-1, 0, 1, 2, 3

in both cases the sum is zero
So median will be the middle term which in both is zero

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rizabove

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11 years ago

I don't know if there is a specific way as to how to solve this problem, but I do know what the answer is. I used the guess and check system and it wasn't too hard to figure it out. I started out using three integers and after I did -2+(-1)+0, I realized they couldn't be negative, because when you add a negative, it is just like subtracting. At least not all of the integers. Then I wondered if I could do -1 as my first integer, then 0 and then 1. And it worked! -1+0=-1. So -1+1=0. This is correct because -1, 0, and 1 all come together to make 0 and there is an odd number of them. The median is the number in the middle. So, 0 is the median. Actually, I just figured out the algebraic way to do this as I was typing. Since the sum is 0, you know there has to be at least one negative in your expression. So, use the algebraic equation -n+0+n, or -n+(-n)+0+n+n. Just make sure that as many consecutive negatives you have on the left side of the zero, there is an equal amount on the other side. Thus, the answer to this problem is always 0, because 0 is always in the middle in a consecutive set of data that adds up to 0.

Your median is 0.

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