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Given Σ(xi − 5) = 9 and Σ(xi − 5)² = 45 for a dataset of 9 values x1, x2,..., x9, what is the standard deviation of the data?

1. 9
2. 4
3. 3
4. 2

Correct answer: 2

Solution

Variance = [sum(xi-5)^2 - (sum(xi-5))^2/n]/n = [45 - 81/9]/9 = (45-9)/9 = 4. Standard deviation = sqrt(4) = 2, which is option index 3. The stored index 1 (4) is the variance, not the SD.

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