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Math Help - Finding the median

  1. #1
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    Finding the median

    The sum of 5 consecutive integers is 10n + 5. What is the median of the 5 integers in terms of n?

    How can you prove that it must be 2n + 1?
    Last edited by dannyc; July 25th 2012 at 07:41 PM.
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  2. #2
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    Re: Finding the median

    Call the first of the consecutive integers "i". Then the next four integers are i+1, i+2, i+3, and i+4. The sum of those five numbers is i+ (i+1)+ (i+ 3)+ (i+ 4)+ (i+ 5)= 5i+ 10= 10n+ 5. Solve that for i in terms of n. The "median" is the middle number, i+ 2.
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  3. #3
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    Re: Finding the median

    How does 5i+10 imply 10n+5 ? I don't see it nor do I see how i + 2 implies 2n + 1.
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  4. #4
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    Re: Finding the median

    Quote Originally Posted by HallsofIvy View Post
    Call the first of the consecutive integers "i". Then the next four integers are i+1, i+2, i+3, and i+4. The sum of those five numbers is i+ (i+1)+ (i+ 3)+ (i+ 4)+ (i+ 2)= 5i+ 10= 10n+ 5. Solve that for i in terms of n. The "median" is the middle number, i+ 2.
    Quote Originally Posted by dannyc View Post
    The sum of 5 consecutive integers is 10n + 5. <--- your own words. Remember?
    What is the median of the 5 integers in terms of n?

    How can you prove that it must be 2n + 1?
    Quote Originally Posted by dannyc View Post
    How does 5i+10 imply 10n+5 ? I don't see it nor do I see how i + 2 implies 2n + 1.
    You are supposed to know what a median means or is.

    In your case the median is the 3rd term, that means (i + 2). Since i = 2n - 1 the term i + 2 = 2n + 1.
    Last edited by earboth; July 25th 2012 at 11:32 PM.
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  5. #5
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    Re: Finding the median

    Right, but I still do not know how we can set i + 2 = 2n + 1. Why can that conclusion be made algebraically?
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  6. #6
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    Re: Finding the median

    Quote Originally Posted by dannyc View Post
    Right, but I still do not know how we can set i + 2 = 2n + 1. Why can that conclusion be made algebraically?
    1.

    \underbrace{i+(i+1)+\overbrace{(i+2)}^{median}+(i+  3)+(i+4)}_{\text{according to HallsofIvy}} = \overbrace{10n+5}^{\text{according to dannyc}}

    5i+10=10n+5

    5i=10n-5=5(2n-1)

    \boxed{i=2n-1} Now add 2 on both sides of this equation:

    i+\color{red}2 \color{black}= (2n-1)+\color{red}2

    \boxed{i+2 = 2n+1}
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  7. #7
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    Re: Finding the median

    Quote Originally Posted by dannyc View Post
    How does 5i+10 imply 10n+5 ? I don't see it nor do I see how i + 2 implies 2n + 1.
    I don't know what you mean by "implies" here. I said they were equal and that is true because YOU said it was:
    "The sum of 5 consecutive integers is 10n + 5".
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