Reversing averages

by fightstacy
 P: 4 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!
 P: 772 No. There are many combinations of numbers that produce the same average.
P: 4
 Quote by Number Nine No. There are many combinations of numbers that produce the same average.
Could I get all possibilities?

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Reversing averages

 Quote by fightstacy Could I get all possibilities?
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.
P: 4
 Quote by Mark44 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.
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?
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 Quote by fightstacy 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?
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/Partiti...mber_theory%29
P: 4
 Quote by jbunniii 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/Partiti...mber_theory%29
Thanks for that Jbunniii, looks like a fun read!

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