Question

What is the mean of the following data set?

-500, -499, -498, ..., -1, 0, 1, ..., 498, 499, 500

Answer 1

Use a smaller set, like -2' -1 0 1 2.
Add them
total is zero
Zero divided by 5 gives zero as mean.
Make a slightly bigger set from neg 7 to 7
Same total, same mean.
Therefore the mean of your set is zero.