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Math Help - arithmetic mean

  1. #1
    rcs
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    arithmetic mean

    the arithmetic mean of a set of 50 numbers is 38. if two numbers 45 and 55 are discarded the mean of the remaining set of numbers is ____ .

    need little help on this guys.

    thanks
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  2. #2
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    Re: arithmetic mean

    Better answer below. *disregard this*
    Last edited by tricxta; August 3rd 2012 at 11:52 PM.
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  3. #3
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    Re: arithmetic mean

    Quote Originally Posted by rcs View Post
    the arithmetic mean of a set of 50 numbers is 38. if two numbers 45 and 55 are discarded the mean of the remaining set of numbers is ____ .

    need little help on this guys.

    thanks
    You are told \displaystyle \begin{align*} \frac{t_k + t_{k + 1} + t_{k + 2} + \dots + t_{k + 49}}{50} = 38 \implies t_k + t_{k + 1} + t_{k + 2} + \dots + t_{k + 49} = 1900 \end{align*}. Two of these terms are 45 and 55, so removing them gives

    \displaystyle \begin{align*} t_k + t_{k + 1} + t_{k + 2} + \dots + t_{k + 49} - 45 - 55 &= 1900 - 45 - 55 \\ &= 1800 \end{align*}

    There are now 48 terms, so the mean of these 48 terms will be \displaystyle \begin{align*} \frac{1800}{48} = 37.5 \end{align*}.
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    rcs
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    Re: arithmetic mean

    thanks sir... but how did you get 1900?
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    Re: arithmetic mean

    Quote Originally Posted by rcs View Post
    thanks sir... but how did you get 1900?
    50 \times 38 = 1900
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    Re: arithmetic mean

    If the arithmetic mean is 38, then their sum is 50*38 = 1900...
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  7. #7
    rcs
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    Re: arithmetic mean

    you are all God's gifts to all not so good in mathematics... God Bless guys
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  8. #8
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    Re: arithmetic mean

    Quote Originally Posted by Prove It View Post
    You are told \displaystyle \begin{align*} \frac{t_k + t_{k + 1} + t_{k + 2} + \dots + t_{k + 49}}{50} = 38 \implies t_k + t_{k + 1} + t_{k + 2} + \dots + t_{k + 49} = 1900 \end{align*}. Two of these terms are 45 and 55, so removing them gives

    \displaystyle \begin{align*} t_k + t_{k + 1} + t_{k + 2} + \dots + t_{k + 49} - 45 - 55 &= 1900 - 45 - 55 \\ &= 1800 \end{align*}

    There are now 48 terms, so the mean of these 48 terms will be \displaystyle \begin{align*} \frac{1800}{48} = 37.5 \end{align*}.
    Thank you King of Proofs ProveIt
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