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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:
- 9
- 4
- 2
- 3
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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