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Reversing averages

  1. Feb 20, 2013 #1
    Hello!

    I was wondering if anyone had an effective way of extracting information from an average.

    I have a list of averages, they're acquired from inputs from 1 - 5, ..and I can see the amount of inputs used to get the average.

    An example would be

    60 inputs within the range 1 - 5
    Average = 2.88

    Is there a way to extract how many 1's 2's 3's 4's and 5's were used to get the average from this information?

    Thanks in advance!
     
  2. jcsd
  3. Feb 20, 2013 #2
    No. There are many combinations of numbers that produce the same average.
     
  4. Feb 20, 2013 #3
    Could I get all possibilities?
     
  5. Feb 20, 2013 #4

    Mark44

    Staff: Mentor

    No.

    When you take the average (mean) of a set of numbers, you lose detail about the numbers.

    Suppose you have a very simple set of numbers: {1, 2, 3}. The mean of this set of numbers is 2. This set, {1.1, 2, 2.9} also has a mean of 2, as does {1.01, 2, 2.99}. Any set of three numbers that add up to 6 would have a mean of 2.
     
  6. Feb 20, 2013 #5
    The thing is though, ..that the range 1 - 5 is whole numbers only, no fractions. ..this would surely decrease the amount of possibilities to few, ..am I wrong?
     
  7. Feb 20, 2013 #6

    jbunniii

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    You are right. You want to know how many ways there are to express N as the sum of M whole numbers. This is the sort of thing that is studied in the theory of partitions, a branch of number theory. See here for more:

    http://en.wikipedia.org/wiki/Partition_(number_theory)
     
  8. Feb 20, 2013 #7
    Thanks for that Jbunniii, looks like a fun read!
     
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