To evaluate the statements about the data sets for Student Group A and Student Group B, we need to calculate the necessary statistics: the range, the median, and the mean for each group.
Student Group A:
Data: 56, 14, 26, 28, 29, 45, 32, 80, 3, 10
- Sorted Data: 3, 10, 14, 26, 28, 29, 32, 45, 56, 80
- Range: \(80 - 3 = 77\)
- Median: The middle value (average of the 5th and 6th values in sorted data): \((28 + 29) / 2 = 28.5\)
- Mean: \((3 + 10 + 14 + 26 + 28 + 29 + 32 + 45 + 56 + 80) / 10 = 32.3\)
Student Group B:
Data: 27, 24, 18, 19, 5, 16, 22, 10, 6, 20
- Sorted Data: 5, 6, 10, 16, 18, 19, 20, 22, 24, 27
- Range: \(27 - 5 = 22\)
- Median: The middle value (average of the 5th and 6th values): \((18 + 19) / 2 = 18.5\)
- Mean: \((5 + 6 + 10 + 16 + 18 + 19 + 20 + 22 + 24 + 27) / 10 = 15.7\)
Summary of Calculations:
- Group A
- Range: 77
- Median: 28.5
- Mean: 32.3
- Group B
- Range: 22
- Median: 18.5
- Mean: 15.7
Evaluating the Statements:
-
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 higher range and generally shows higher variability).
-
The ranges of the time taken by Group A and Group B are the same.
- False (Group A's range is 77, while Group B's range is 22).
-
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 vs. 18.5).
-
The mean time taken by Group A is higher than that of Group B.
- True (32.3 vs. 15.7).
Conclusion:
The false statement is: The ranges of the time taken by Group A and Group B are the same.