Compute the sample standard deviation for the data values 2, 4, 6, 8, 10.

Compute the sample standard deviation for the data values 2, 4, 6, 8, 10.

• A. 3.1623
• B. 2.0
• C. 3.0
• D. 4.0

Answer: (A)

This question tests how to compute a sample standard deviation, which measures how spread out the data are around the mean using the n−1 denominator. First find the mean: (2 + 4 + 6 + 8 + 10) / 5 = 6. Then compute each squared deviation from the mean: (2−6)² = 16, (4−6)² = 4, (6−6)² = 0, (8−6)² = 4, (10−6)² = 16. The sum of these squared deviations is 40. For a sample, divide by n−1: 40 / (5−1) = 10, which is the sample variance. The sample standard deviation is the square root of the variance: sqrt(10) ≈ 3.1623. So the value listed as approximately 3.1623 is the correct one. (Note: using the population formula would give sqrt(40/5) = sqrt(8) ≈ 2.828, which is a different measure.)

This question tests how to compute a sample standard deviation, which measures how spread out the data are around the mean using the n−1 denominator.

First find the mean: (2 + 4 + 6 + 8 + 10) / 5 = 6. Then compute each squared deviation from the mean: (2−6)² = 16, (4−6)² = 4, (6−6)² = 0, (8−6)² = 4, (10−6)² = 16. The sum of these squared deviations is 40. For a sample, divide by n−1: 40 / (5−1) = 10, which is the sample variance. The sample standard deviation is the square root of the variance: sqrt(10) ≈ 3.1623.

So the value listed as approximately 3.1623 is the correct one. (Note: using the population formula would give sqrt(40/5) = sqrt(8) ≈ 2.828, which is a different measure.)