Average with sum of values equal to number of values

Question

I have a list of numbers. Each number can be any amount above 0 but under 1 million. There are 1 million numbers.

The numbers add up to 1 million.

Is it possible to calculate an average (Mean)? Normally calculating the mean does not work as 1 million / 1 million = 1 of course.

This is a bit of a random question but thanks.

Answer 1

Let us call your numbers $(X_i)_{1\leq i \leq 10^6}$. The mean is defined as $$ \mu = \frac{1}{10^6} \sum_{i=1}^{10^6} X_i=1$$ so the mean is $1$. You can either define it as the mean of this specific series or the probabilistic mean in both cases it will be $1$.