To compare the data sets for Student Group A and Student Group B, we first need to calculate the median, mean, range, and some measure of variability (like the standard deviation) for both groups.
Group A Data:
- 56, 14, 26, 28, 29, 45, 32, 80, 3, 10
- Sorted: 3, 10, 14, 26, 28, 29, 32, 45, 56, 80
- Median: The middle values are 28 and 29 (5th and 6th in order); thus, median = (28 + 29) / 2 = 28.5
- Mean: (3 + 10 + 14 + 26 + 28 + 29 + 32 + 45 + 56 + 80) / 10 = 3.3
- Range: 80 - 3 = 77
- Variability (standard deviation): We'll calculate this afterward.
Group B Data:
- 27, 24, 18, 19, 5, 16, 22, 10, 6, 20
- Sorted: 5, 6, 10, 16, 18, 19, 20, 22, 24, 27
- Median: The middle values are 18 and 19 (5th and 6th in order); thus, median = (18 + 19) / 2 = 18.5
- Mean: (5 + 6 + 10 + 16 + 18 + 19 + 20 + 22 + 24 + 27) / 10 = 14.7
- Range: 27 - 5 = 22
- Variability (standard deviation): We'll calculate this afterward.
Summary of Results
- Median (Group A) = 28.5, Median (Group B) = 18.5
- Mean (Group A) = 29.8, Mean (Group B) = 14.7
- Range (Group A) = 77, Range (Group B) = 22
Now let’s compare the statements given:
-
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 mean time taken by Group A is higher than that of Group B.
- True. (29.8 > 14.7)
-
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.
- This is likely true. Group A has a larger range and typically would have a higher variance and standard deviation, but we’ll calculate standard deviation for a precise statement.
-
The ranges of the time taken by Group A and Group B are the same.
- False. Group A has a range of 77 while Group B has a range of 22.
Conclusion:
The statement that is false is: "The ranges of the time taken by Group A and Group B are the same."