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To find the mean, you need to add all the values and divide by the number of values.

Looking closely at the data, you'll notice that the first number is the negative of the last, the second number is the negative of the last but one and so on. This means that the sum of the pairs of numbers at the same position from each end is 0, and so the sum of all the numbers is 0.

If the sum is zero, then dividing this by any number greater than zero will lead to zero. The number of elements in the dataset is greater than zero.

Thus the mean of the dataset {-500, -499, -498, ..., -1, 0, 1, ..., 498, 499, 500} is 0.

If you want to know how many elements there were, then there are 500 - -500 + 1 = 1001 elements in the data set.

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Q: What is the mean of the following data set -500 -499 -498 ... -1 0 1 ... 498 499 500?
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