Reversing averages

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?

Thanks in advance!

Number Nine

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

fightstacy

Could I get all possibilities?

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.

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?

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

fightstacy

Thanks for that Jbunniii, looks like a fun read!