# Reversing averages

1. Feb 20, 2013

### fightstacy

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?

2. Feb 20, 2013

### Number Nine

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

3. Feb 20, 2013

### fightstacy

Could I get all possibilities?

4. Feb 20, 2013

### 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.

5. Feb 20, 2013

### 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?

6. Feb 20, 2013

### 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/Partition_(number_theory)

7. Feb 20, 2013

### fightstacy

Thanks for that Jbunniii, looks like a fun read!