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Reversing averages

by fightstacy
Tags: averages, mathematics, mathematics advice
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fightstacy
#1
Feb20-13, 08:12 PM
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!
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Number Nine
#2
Feb20-13, 08:29 PM
P: 772
No. There are many combinations of numbers that produce the same average.
fightstacy
#3
Feb20-13, 08:32 PM
P: 4
Quote Quote by Number Nine View Post
No. There are many combinations of numbers that produce the same average.
Could I get all possibilities?

Mark44
#4
Feb20-13, 09:16 PM
Mentor
P: 21,397
Reversing averages

Quote Quote by fightstacy View Post
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.
fightstacy
#5
Feb20-13, 09:25 PM
P: 4
Quote Quote by Mark44 View Post
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?
jbunniii
#6
Feb20-13, 09:37 PM
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Quote Quote by fightstacy View Post
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
fightstacy
#7
Feb20-13, 09:40 PM
P: 4
Quote Quote by jbunniii View Post
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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