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For five observations, sum of (xi - 10) = 5 and sum of (xi - 10)² = 25. The standard deviation of the transformed observations 2x1+7, 2x2+7, 2x3+7, 2x4+7, 2x5+7 is
- 8
- 16
- 4
- 2
Correct answer: 4
Solution
Let yi = xi-10. Then sum yi = 5 and sum yi² = 25 with n=5. Mean of yi = 5/5 = 1. Variance of yi = (sum yi²)/n - (mean yi)² = 25/5 - 1 = 5-1 = 4. SD of yi = SD of xi = 2. For zi = 2xi+7 = 2(xi-10)+27: standard deviation of zi = |2| * SD(xi) = 2*2 = 4.
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