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Math Help - easy mean problem

  1. #1
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    easy mean problem

    let x be a variable assuming the values 0,1,2,3.....k and let f_{0},f_{1},f_{2},f_{3},......,f_{k} be the corresponding cumulative frequency of the greater than type. Prove that the arithmetic mean of x is, \bar{x} = \frac{1}{N}(\sum_{i=1}^{k} F_{i}), where N is the total frequency.

    Thanks in advance!
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  2. #2
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    Re: easy mean problem

    Hey earthboy.

    For this problem, you might want to consider the definition of the mean in terms of the summation and what the frequency corresponds to in terms of the actual observation.

    Recall that the frequency for a variable says how many times it occurs so the observations in terms of the frequencies are F_i*i which gives the total number of observations.

    The mean is simply adding up all the observations and dividing by the total number.

    So write the frequencies in terms of the observations and relate that to the definition of the sample mean.
    Thanks from earthboy
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  3. #3
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    Re: easy mean problem

    Quote Originally Posted by chiro View Post
    Hey earthboy.

    For this problem, you might want to consider the definition of the mean in terms of the summation and what the frequency corresponds to in terms of the actual observation.

    Recall that the frequency for a variable says how many times it occurs so the observations in terms of the frequencies are F_i*i which gives the total number of observations.

    The mean is simply adding up all the observations and dividing by the total number.

    So write the frequencies in terms of the observations and relate that to the definition of the sample mean.
    Do you mean this:
    So the mean \bar{x}=\frac{0.(f_{0}-f_{1})+1.(f_{1}-f_{2})+2(f_{2}-f_{3})+....+k-1(f_{k-1}-f_{k})+kf_{k}}{N} where N=f_{0}

    expanding the numerator, all the terms would cancel out, leaving  \bar{x}=\frac{f_{1}+f_{2}+f_{3}......+f_{k}}{N}= \frac{1}{N} \sum_1^{k} f_{i}


    Thanks very much!
    Last edited by earthboy; December 6th 2012 at 09:22 PM.
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  4. #4
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    Re: easy mean problem

    You will have to use the fact that CF_(i+1) - CF_i = f_(i+1) where CF is the cumulative frequency and f is the normal frequency.
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