# Average of infinity.

1. Feb 10, 2006

### heartless

Hello
I was watching lectures on Quantum Computing another day and I came up with a problem. I talked to my school teachers about it but everyone seemed to dodge my question except for one, my math team teacher who told me that without assuming anything it cannot be solved. Or we can take the lowest possible value and the highest, divide by 2 and that would be the average, or at last get 100 workers out of infinity and that would make an average of all.

Here's the problem:
What is the average of salaries of infinite number of workers, knowing that their salary can be any real number between 10 and a 1000?

What do you guys think about it?
Is it possible to solve it in any way? Or at least dig the problem to "average in terms of something"?

Thanks :)

2. Feb 10, 2006

### Orefa

This looks like a definition problem. In arithmetic, you average a group by adding up all values and dividing by the number of items. If you cannot add up the values and divide by their count then you cannot calculate the average. In your scenario, adding the values is impossible since you don't know them all. Dividing by infinity is also impossible, at least arithmetically. If you try to use a notion where it does not apply then you will have problems: what is the average color of a traffic light?

The purpose of an average value is to give a statistical indicator of the position of a group of values. Here, a median point (505) gives you a fair idea of where your group is located and this may be suitable for your purpose. Considering that the set of real numbers is infinite in both directions, this position extimate can even be considered highly accurate relative to the entire set. You just use the means you need to use in order to achieve your particular purpose and disregard what does not apply.

3. Feb 10, 2006

### chroot

Staff Emeritus
If each worker's salary is independent of the salaries of other workers, you don't need to look at an infinite number of such workers. You only need to look at one.

- Warren

4. Feb 10, 2006

### Mk

So what is the average of infinity and one? Infinity?

5. Feb 10, 2006

### chroot

Staff Emeritus
Infinity is not actually a number, so expressions involving infinity won't necessary behave like those involving real numbers. If you define an average as a sum divided by two, (infinity + 1)/2 = infinity.

- Warren

6. Feb 10, 2006

### krab

You have not given enough information. You also need to give the distribution function. I'm guessing you will say all salaries are equally likely. That would be called a uniform distribution. In that case it is indeed 505. No considerations of infinity are needed. As chroot said, if you asked What is the expectation value for just one salary, it would also be 505.

7. Feb 11, 2006

### AlphaNumeric

You can deal with the infinities just by taking limits as your number of workers goes to infinity. However, unless you're told some kind of distribution for the salaries, you've no idea other than it's going to be somewhere between 10 and 1000.