-500, -499, -498, ..., -1, 0, 1, ..., 498, 499, 500
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0
Because if you add -500 to 500, you get 0
If you add -499 to 499 its 0
If you do it for each number, negative and positive you will get 0
Anything divided by 0 is 0
so your mean is 0
Because if you add -500 to 500, you get 0
If you add -499 to 499 its 0
If you do it for each number, negative and positive you will get 0
Anything divided by 0 is 0
so your mean is 0
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((- 500 - 499 - 498 - ... - 1) + 0 + (1 + 2 + 3 + ... + 500))/1001 = 0