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Statistics: How to find mean of bins

  1. Sep 11, 2010 #1
    1. The problem statement, all variables and given/known data
    Hi

    Say I have the following bin sizes, where the number in paranthesis is the amount of data points contained in the bin:

    20-29 : (2)
    30-39 : (7)
    40-49 : (12)
    50-59 : (14)

    How would I go about and find the mean for this binned data? I know that I should use

    [tex]
    mean = \frac{1}{N}\sum\limits_j {n_j x_j },
    [/tex]

    where bin j corresponds to a value xj and contains nj elements. But in my case, what are the values of the bins?
     
  2. jcsd
  3. Sep 11, 2010 #2

    statdad

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    Homework Helper

    You usually treat this as a weighted mean problem. Think this way: if you needed to select one value from inside each bin, what value (intuitively) would be the one to pick if you didn't want to over- or under-estimate typical values in the bin? That's the value you use for x.
     
  4. Sep 11, 2010 #3
    I would use the average value of the data samples in that particular bin. Would you also do that?
     
  5. Sep 11, 2010 #4

    statdad

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    Homework Helper

    No - you need to use a number that comes from the bins, not the collected data.
     
  6. Sep 11, 2010 #5
    Then the average of the bin-size, i.e. for 20-29 it is 24.5?
     
  7. Sep 11, 2010 #6

    statdad

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    Homework Helper

    Yes - it's called the midpoint of the bin.
     
  8. Sep 12, 2010 #7
    Thanks, it is kind of you to help me.

    Best wishes,
    Niles.
     
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