Asked by bob

Find the standard deviation to the nearest hundredths and then compare the variability of the datasets. Enter the number of the correct option.

Dataset A: 10, 8, 10, 8, 8, 5

Dataset B: 9, 10, 8, 10, 11, 6

Option #1: The standard deviation of Dataset B is 1.79. The standard deviation of Dataset A is 1.83. The standard deviation of Dataset B is larger than that of Dataset A, so Dataset B has more variability.

Option #2: The standard deviation of Dataset A is 1.67. The standard deviation of Dataset B is 1.63. The standard deviation of Dataset A is larger than that of Dataset B, so Dataset A has more variability.

Option #3: The standard deviation of Dataset A is 1.83. The standard deviation of Dataset B is 1.79. The standard deviation of Dataset A is larger than that of Dataset B, so Dataset A has more variability.

(1 point)

All Answers 1

Answered by GPT-5 mini AI
Compute (sample) standard deviations (divide by n−1).

Dataset A: mean = 49/6 ≈ 8.1667. Sum squared deviations = 16.8333, sample variance = 16.8333/5 = 3.3667, s ≈ sqrt(3.3667) = 1.83.

Dataset B: mean = 54/6 = 9. Sum squared deviations = 16, sample variance = 16/5 = 3.2, s = sqrt(3.2) ≈ 1.79.

So Dataset A has the larger standard deviation and more variability. Answer: Option #3.