Reversing Averages: Extracting Info from an Average

  • Thread starter fightstacy
  • Start date
In summary, there is no effective way to extract the specific numbers used to calculate an average from the average itself. This is due to the fact that there are many combinations of numbers that can produce the same average. Additionally, when taking the average of a set of numbers, you lose detail about the specific numbers. This concept is studied in the theory of partitions in number theory, which explores the various ways to express a number as a sum of other numbers.
  • #1
fightstacy
4
0
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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  • #2
No. There are many combinations of numbers that produce the same average.
 
  • #3
Number Nine said:
No. There are many combinations of numbers that produce the same average.

Could I get all possibilities?
 
  • #4
fightstacy said:
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.
 
  • #5
Mark44 said:
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?
 
  • #6
fightstacy said:
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/Partition_(number_theory)
 
  • #7
jbunniii said:
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)

Thanks for that Jbunniii, looks like a fun read!
 

1. How do you reverse an average?

To reverse an average, you need to know the total sum of all the data points used to calculate the average. Then, you can multiply the average by the number of data points and subtract the total sum from that value. This will give you the missing data point that was used to calculate the average.

2. Can you reverse an average if you only have the average value?

No, you cannot reverse an average if you only have the average value. You need to know at least one other data point in order to calculate the missing data point. If you only have the average, you would need to know the total sum of all the data points used to calculate the average.

3. Why is reversing an average useful?

Reversing an average can be useful because it allows you to extract information from an average that you may not have otherwise been able to obtain. This can be helpful in situations where you need to know the value of a missing data point or want to analyze the data in a different way.

4. Are there any limitations to reversing an average?

Yes, there are limitations to reversing an average. This method only works if the data set is evenly distributed and does not have any outliers. It also assumes that all the data points were used to calculate the average, which may not always be the case.

5. Can you use the same method to reverse any type of average?

Yes, you can use the same method to reverse any type of average, whether it is a mean, median, or mode. However, it is important to note that the results may vary depending on the type of average used and the characteristics of the data set.

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