To compare the variability of the datasets using standard deviation, first, let's calculate the standard deviation for both Dataset A and Dataset B.
Dataset A: 11, 7, 12, 8, 9, 5
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Calculate the mean: \[ \text{Mean} = \frac{11 + 7 + 12 + 8 + 9 + 5}{6} = \frac{52}{6} \approx 8.67 \]
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Calculate the squared deviations from the mean:
- \( (11 - 8.67)^2 \approx 5.44 \)
- \( (7 - 8.67)^2 \approx 2.78 \)
- \( (12 - 8.67)^2 \approx 11.11 \)
- \( (8 - 8.67)^2 \approx 0.44 \)
- \( (9 - 8.67)^2 \approx 0.11 \)
- \( (5 - 8.67)^2 \approx 13.49 \)
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Calculate the variance: \[ \text{Variance} = \frac{5.44 + 2.78 + 11.11 + 0.44 + 0.11 + 13.49}{6} \approx \frac{33.37}{6} \approx 5.56 \]
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Calculate the standard deviation: \[ \text{Standard Deviation} = \sqrt{5.56} \approx 2.36 \]
Dataset B: 10, 8, 10, 8, 8, 4
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Calculate the mean: \[ \text{Mean} = \frac{10 + 8 + 10 + 8 + 8 + 4}{6} = \frac{58}{6} \approx 9.67 \]
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Calculate the squared deviations from the mean:
- \( (10 - 9.67)^2 \approx 0.11 \)
- \( (8 - 9.67)^2 \approx 2.78 \)
- \( (10 - 9.67)^2 \approx 0.11 \)
- \( (8 - 9.67)^2 \approx 2.78 \)
- \( (8 - 9.67)^2 \approx 2.78 \)
- \( (4 - 9.67)^2 \approx 32.11 \)
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Calculate the variance: \[ \text{Variance} = \frac{0.11 + 2.78 + 0.11 + 2.78 + 2.78 + 32.11}{6} \approx \frac{40.67}{6} \approx 6.78 \]
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Calculate the standard deviation: \[ \text{Standard Deviation} = \sqrt{6.78} \approx 2.60 \]
Comparison of Standard Deviations:
- Standard Deviation of Dataset A: approximately 2.36
- Standard Deviation of Dataset B: approximately 2.60
The rounded values could lead to:
- The final standard deviation calculations indicate that Dataset B has a higher standard deviation than Dataset A, implying that Dataset B has greater variability.
Therefore, the correct response is:
The standard deviation of Dataset A is 2.36. The standard deviation of Dataset B is 2.60. The standard deviation of Dataset B is larger than that of Dataset A, so Dataset B has more variability. However, this statement does not match the provided options. Therefore, please verify the details above to check for any discrepancies, as the calculations do suggest differing values than your listed responses.
1 answer