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Use the standard deviation to compare the variability of the datasets. Round to the nearest hundredths. Dataset A: 4, 5, 6, 12, 13 Dataset B: 4, 5, 7, 9, 10 (1 point) Responses The standard deviation of Dataset A is 3.74. The standard deviation of Dataset B is 3.74. Dataset A and Dataset B have the same standard deviation, so both datasets have the same variability. The standard deviation of Dataset A is 3.74. The standard deviation of Dataset B is 3.74. Dataset A and Dataset B have the same standard deviation, so both datasets have the same variability. The standard deviation of Dataset A is 2.28. The standard deviation of Dataset B is 3.74. The standard deviation of Dataset B is larger than that of Dataset A, so Dataset B has more variability. The standard deviation of Dataset A is 2.28. The standard deviation of Dataset B is 3.74. The standard deviation of Dataset B is larger than that of Dataset A, so Dataset B has more variability. The standard deviation of Dataset A is 4.18. The standard deviation of Dataset B is 2.55. The standard deviation of Dataset A is larger than that of Dataset B, so Dataset A has more variability. The standard deviation of Dataset A is 4.18. The standard deviation of Dataset B is 2.55. The standard deviation of Dataset A is larger than that of Dataset B, so Dataset A has more variability. The standard deviation of Dataset A is 3.64. The standard deviation of Dataset B is 2.28. The standard deviation of Dataset A is larger than that of Dataset B, so Dataset A has more variability.

1 answer

To find the standard deviations for the given datasets, we can follow these steps:

  1. Calculate the mean of each dataset.
  2. Find the squared differences from the mean.
  3. Calculate the variance.
  4. Take the square root of the variance to find the standard deviation.

Dataset A: 4, 5, 6, 12, 13

  1. Mean: (4 + 5 + 6 + 12 + 13) / 5 = 40 / 5 = 8
  2. Squared differences from the mean:
    • (4 - 8)² = 16
    • (5 - 8)² = 9
    • (6 - 8)² = 4
    • (12 - 8)² = 16
    • (13 - 8)² = 25
  3. Variance: (16 + 9 + 4 + 16 + 25) / 5 = 70 / 5 = 14
  4. Standard Deviation: √14 ≈ 3.74 (rounded to the nearest hundredths)

Dataset B: 4, 5, 7, 9, 10

  1. Mean: (4 + 5 + 7 + 9 + 10) / 5 = 35 / 5 = 7
  2. Squared differences from the mean:
    • (4 - 7)² = 9
    • (5 - 7)² = 4
    • (7 - 7)² = 0
    • (9 - 7)² = 4
    • (10 - 7)² = 9
  3. Variance: (9 + 4 + 0 + 4 + 9) / 5 = 26 / 5 = 5.2
  4. Standard Deviation: √5.2 ≈ 2.28 (rounded to the nearest hundredths)

Conclusion:

  • Standard Deviation of Dataset A: 3.74
  • Standard Deviation of Dataset B: 2.28

Therefore, the correct interpretation is:

The standard deviation of Dataset A is 3.74. The standard deviation of Dataset B is 2.28. The standard deviation of Dataset A is larger than that of Dataset B, so Dataset A has more variability.

This matches one of the responses given.