The data shows the number of seconds it took two randomly selected groups to thread a needle. Compare the measures of center and variability of these data sets.
Student Group A: 56, 14, 26, 28, 29, 45, 32, 80, 3, 10
Student Group B: 27, 24, 18, 19, 5, 16, 22, 10, 6, 20
Which of the following statements about these data sets is false?
(1 point)
Responses
The mean time taken by Group A is higher than that of Group B.
The mean time taken by Group A is higher than that of Group B.
The ranges of the time taken by Group A and Group B are the same.
The ranges of the time taken by Group A and Group B are the same.
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.
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.
The median time taken by members of Group A to thread a needle is higher than that of members of Group B.
The ranges of the time taken by Group A and Group B are the same. (This statement is false, as the range of Group A (77 seconds) is higher than the range of Group B (22 seconds).)
The statement that is false is: "The mean time taken by Group A is higher than that of Group B."
Let's compare the measures of center and variability for both groups:
Measures of Center:
- Mean of Group A: (56 + 14 + 26 + 28 + 29 + 45 + 32 + 80 + 3 + 10) / 10 = 33.3
- Mean of Group B: (27 + 24 + 18 + 19 + 5 + 16 + 22 + 10 + 6 + 20) / 10 = 16.7
Since 33.3 > 16.7, the mean time taken by Group A is indeed higher than that of Group B. So, the given statement is true, not false.
Measures of Variability:
- Range of Group A: 80 - 3 = 77
- Range of Group B: 27 - 5 = 22
Since 77 > 22, the range of the time taken by Group A is higher than the range of Group B. So, the given statement is true, not false.
The only statement that does not hold true is the last one: "The median time taken by members of Group A to thread a needle is higher than that of members of Group B." Without calculating the medians, we cannot determine if this statement is true or false based on the given data.