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If ∑(i=1 to 9) (x_i - 5) = 9 and ∑(i=1 to 9) (x_i - 5)² = 45, then the standard deviation of the 9 items x1, x2,..., x9 is:

1. 4
2. 2
3. 3
4. 9

Correct answer: 2

Solution

The standard deviation is calculated as the square root of the variance. Given that the sum of squared deviations from the mean is 45 for 9 items, the variance is 45/9 = 5, and the standard deviation is the square root of 5, which is approximately 2.

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