To analyze the statements regarding the time taken by both groups to thread a needle, let’s calculate the measures of center and variability for both groups.
Data for Group A:
- Data: 56, 14, 26, 28, 29, 45, 32, 80, 3, 10
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Mean: \[ \text{Mean} = \frac{(56 + 14 + 26 + 28 + 29 + 45 + 32 + 80 + 3 + 10)}{10} = \frac{ 3 + 10 + 14 + 26 + 28 + 29 + 32 + 45 + 56 + 80}{10} = \frac{ 3 + 10 + 14 + 26 + 28 + 29 + 32 + 45 + 56 + 80}{10} = \frac{ 432}{10} = 43.2 \]
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Median:
- Ordered data: 3, 10, 14, 26, 28, 29, 32, 45, 56, 80
- Middle values: 28 and 29 \[ \text{Median} = \frac{28 + 29}{2} = 28.5 \]
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Range: \[ \text{Range} = 80 - 3 = 77 \]
Data for Group B:
- Data: 27, 24, 18, 19, 5, 16, 22, 10, 6, 20
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Mean: \[ \text{Mean} = \frac{(27 + 24 + 18 + 19 + 5 + 16 + 22 + 10 + 6 + 20)}{10} = \frac{ 27 + 24 + 18 + 19 + 5 + 16 + 22 + 10 + 6 + 20}{10} = \frac{ 147}{10} = 14.7 \]
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Median:
- Ordered data: 5, 6, 10, 16, 18, 19, 20, 22, 24, 27
- Middle values: 18 and 19 \[ \text{Median} = \frac{18 + 19}{2} = 18.5 \]
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Range: \[ \text{Range} = 27 - 5 = 22 \]
Summary of Calculations:
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Group A:
- Mean = 43.2
- Median = 28.5
- Range = 77
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Group B:
- Mean = 14.7
- Median = 18.5
- Range = 22
Comparison of Statements:
- "The mean time taken by Group A is higher than that of Group B." - True (43.2 > 14.7)
- "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)
- "The ranges of the time taken by Group A and Group B are the same." - False (77 ≠ 22)
- "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 (based on range and presumed standard deviation, Group A has more variability).
Conclusion:
The false statement is: "The ranges of the time taken by Group A and Group B are the same."