## Reversing averages

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?

 No. There are many combinations of numbers that produce the same average.

 Quote by Number Nine No. There are many combinations of numbers that produce the same average.
Could I get all possibilities?

Mentor

## 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.

 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?

Blog Entries: 1
Recognitions:
Gold Member
Homework Help
 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

 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!