To calculate the standard deviation for both datasets, we can follow these steps:
- Calculate the mean (average) of each dataset.
- Calculate the squared differences from the mean for each data point.
- Calculate the variance by averaging those squared differences.
- Take the square root of the variance to get the standard deviation.
Dataset A: 4, 5, 6, 12, 13
- Mean = (4 + 5 + 6 + 12 + 13) / 5 = 40 / 5 = 8
- 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
- Variance = (16 + 9 + 4 + 16 + 25) / 5 = 70 / 5 = 14
- Standard deviation = √14 ≈ 3.74
Dataset B: 4, 5, 7, 9, 10
- Mean = (4 + 5 + 7 + 9 + 10) / 5 = 35 / 5 = 7
- 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
- Variance = (9 + 4 + 0 + 4 + 9) / 5 = 26 / 5 = 5.2
- Standard deviation = √5.2 ≈ 2.28
Summary of Results
- The standard deviation of Dataset A is approximately 3.74.
- The standard deviation of Dataset B is approximately 2.28.
Conclusion
The standard deviation of Dataset A is larger than that of Dataset B, indicating that Dataset A has more variability.
Therefore, the correct response 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.
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