To evaluate the statements about the two groups and determine which one is false, we can calculate the mean, median, and range for both Group A and Group B.
Group A data:
56, 14, 26, 28, 29, 45, 32, 80, 3, 10
Group B data:
27, 24, 18, 19, 5, 16, 22, 10, 6, 20
Calculations
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Mean:
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Group A:
\[ \text{Mean} = \frac{56 + 14 + 26 + 28 + 29 + 45 + 32 + 80 + 3 + 10}{10} = \frac{ 56 + 14 + 26 + 28 + 29 + 45 + 32 + 80 + 3 + 10}{10} = \frac{ 10 + 3 + 32 + 80 + 45 + 5 + 29 + 45 + 32 + 80}{10} = 32.3 \] -
Group B:
\[ \text{Mean} = \frac{27 + 24 + 18 + 19 + 5 + 16 + 22 + 10 + 6 + 20}{10} = \frac{ 27 + 24 + 18 + 19 + 5 + 16 + 22 + 10 + 6 + 20}{10} = 16.7 \]
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Median:
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Group A (sorted): 3, 10, 14, 26, 28, 29, 32, 45, 56, 80
- Median: (28 + 29) / 2 = 28.5
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Group B (sorted): 5, 6, 10, 16, 18, 19, 20, 22, 24, 27
- Median: (18 + 19) / 2 = 18.5
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Range:
- Group A: \[ \text{Range} = 80 - 3 = 77 \]
- Group B: \[ \text{Range} = 27 - 5 = 22 \]
Summary of Results
- Mean:
- Group A: 32.3 (Higher than Group B's 16.7)
- Median:
- Group A: 28.5 (Higher than Group B's 18.5)
- Range:
- Group A: 77 (Not the same as Group B's 22)
Evaluating the Statements
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The ranges of the time taken by Group A and Group B are the same.
- False (Group A's range is 77, Group B's range is 22).
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The mean time taken by Group A is higher than that of Group B.
- True (32.3 > 16.7).
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The amount of variability of the time taken by Group A to thread a needle is higher than the amount of variability of the time taken by Group B.
- True (Group A has a larger range, indicating more variability).
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The median time taken by members of Group A to thread a needle is higher than that of members of Group B.
- True (28.5 > 18.5).
Conclusion
The false statement is: The ranges of the time taken by Group A and Group B are the same.