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Given that ∑(i=1 to 18) (xᵢ − 8) = 9 and ∑(i=1 to 18) (xᵢ − 8)² = 45, find the standard deviation of the observations x₁, x₂,..., x₁₈.
- 3/2
- 3/4
- 9/4
- 4/9
Correct answer: 3/2
Solution
Using di = xi - 8: variance = 45/18 - (9/18)² = 2.5 - 0.25 = 2.25, so the standard deviation = sqrt(2.25) = 3/2.
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