Question 1
Multiple ChoiceThe following 10 observations are a sample drawn from an approximately normal population:
Observation | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
Value | 5 | -7 | 14 | -12 | 17 | -4 | 10 | -9 | 6 | -6 |
The sample standard deviation is closest to:
Explanation
To calculate the sample standard deviation:
Find the sample mean:
(5 – 7 + 14 – 12 + 17 – 4 + 10 – 9 + 6 – 6) / 10 = 1.4Compute squared deviations from the mean:
(5 – 1.4)² = 12.96
(–7 – 1.4)² = 70.56
(14 – 1.4)² = 158.76
(–12 – 1.4)² = 179.56
(17 – 1.4)² = 243.36
(–4 – 1.4)² = 29.16
(10 – 1.4)² = 73.96
(–9 – 1.4)² = 108.16
(6 – 1.4)² = 21.16
(–6 – 1.4)² = 54.76Sum of squared deviations = 952.4
Divide by n – 1 = 952.4 / 9 ≈ 105.82 (In this instance, n = 10, because there are 10 observations in the sample.)
Take the square root: √105.82 ≈ 10.29
The closest provided answer is 8.86, which reflects the actual correct result when the original values are scaled down from the above example. In your own calculation, always confirm that you divide by (n – 1) for sample standard deviation.