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Median interpolation on logarithmic data

  1. Sep 14, 2009 #1
    1. The problem statement, all variables and given/known data
    Hello, I have a set of data that is grouped into bins. The bin sizes increase logarithmically by 10% (1.1 x the previous bin).

    2. Relevant equations
    Radius Frequency
    1.03 4924
    1.10 9938
    1.21 14009
    1.32 12269
    1.44 15813
    1.58 18723
    1.74 21471
    ... ...

    My total frequency is 612574
    I used excel's frequency function. For the first group any data that is greater than 1.03 and less than 1.10 is put into that group. So you can write it

    1.03<= x < 1.10

    so the lower class boundary is 1.03

    3. The attempt at a solution

    using the median interpolation formulae

    lower class boundary + ((n/2*[culmalative frequency of the previous classes])/frequency of class) * class width

    So for the 10% percentile:

    it lies in class 1.58.

    1.58 + (((612574/2)-56953)/18723) . (1.74 - 1.58)

    = 3.7107

    Which cannot be. Is this because im using logarithmic data? Is there a more suitable way?
  2. jcsd
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