To determine which statement about the data sets is false, we need to calculate the mean, median, and range for both groups.
Student Group A: 56, 14, 26, 28, 29, 45, 32, 80, 3, 10
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Mean: \[ \text{Mean} = \frac{56 + 14 + 26 + 28 + 29 + 45 + 32 + 80 + 3 + 10}{10} = \frac{ 56 + 14 + 26 + 28 + 29 + 45 + 32 + 80 + 3 + 10 = 343}{10} = 34.3 \]
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Median: First, we sort the data: 3, 10, 14, 26, 28, 29, 32, 45, 56, 80. Since there are 10 numbers, the median is the average of the 5th and 6th values: \[ \text{Median} = \frac{28 + 29}{2} = 28.5 \]
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Range: \[ \text{Range} = 80 - 3 = 77 \]
Student Group B: 27, 24, 18, 19, 5, 16, 22, 10, 6, 20
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Mean: \[ \text{Mean} = \frac{27 + 24 + 18 + 19 + 5 + 16 + 22 + 10 + 6 + 20}{10} = \frac{ 27 + 24 + 18 + 19 + 5 + 16 + 22 + 10 + 6 + 20 = 147}{10} = 14.7 \]
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Median: Sort the data: 5, 6, 10, 16, 18, 19, 20, 22, 24, 27. The median is the average of the 5th and 6th values: \[ \text{Median} = \frac{18 + 19}{2} = 18.5 \]
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Range: \[ \text{Range} = 27 - 5 = 22 \]
Now, let's compare the statements:
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Mean time:
- Group A: \(34.3\)
- Group B: \(14.7\)
- True: "The mean time taken by Group A is higher than that of Group B."
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Variability:
- Group A's range: \(77\)
- Group B's range: \(22\)
- True: "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."
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Median time:
- Group A: \(28.5\)
- Group B: \(18.5\)
- True: "The median time taken by members of Group A to thread a needle is higher than that of members of Group B."
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Ranges:
- Group A’s range: \(77\)
- Group B’s range: \(22\)
- False: "The ranges of the time taken by Group A and Group B are the same."
Thus, the false statement is: "The ranges of the time taken by Group A and Group B are the same."