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Take the first ten positive integers. If each number is first multiplied by -1 and then increased by 1, what is the variance of the resulting set of numbers?

1. 8.25
2. 6.5
3. 3.87
4. 2.87

Correct answer: 8.25

Solution

The transformation of the first ten positive integers by multiplying by -1 and then adding 1 results in the set {-1, -2, -3, -4, -5, -6, -7, -8, -9, -10}. The variance of this set is calculated to be 8.25, which reflects the spread of the numbers around their mean.

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