Calculate the sample standard deviation for the dataset {3, 5, 7, 9} using sample formula s = sqrt(sum (x - bar{x})^2 / (n - 1)).
Answer and explanation
Correct answer: D. sqrt(20/3)
- Step 1: Compute sample mean: bar{x} = (3 + 5 + 7 + 9) / 4 = 24 / 4 = 6. Step 2. Compute squared deviations: (3-6)^2 = 9, (5-6)^2 = 1, (7-6)^2 = 1, (9-6)^2 = 9. Step 3. Sum deviations: 9 + 1 + 1 + 9 = 20. Step 4. Divide by (n - 1) = 3: s^2 = 20 / 3 => s = sqrt(20/3). Answer: sqrt(20/3). Why not the others: sqrt(5) divides by n = 4 (population standard deviation); 2.5 is an approximation of range.
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