Question

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 median time taken by members of Group A to thread a needle is higher than that of members of 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.
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 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.
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Answer 1

The false statement is: "The ranges of the time taken by Group A and Group B are the same."

Work:
- Group A sorted: 3, 10, 14, 26, 28, 29, 32, 45, 56, 80
- Median = (28 + 29)/2 = 28.5
- Mean = 323/10 = 32.3
- Range = 80 − 3 = 77
- SD ≈ 23.0 (greater variability)

- Group B sorted: 5, 6, 10, 16, 18, 19, 20, 22, 24, 27
- Median = (18 + 19)/2 = 18.5
- Mean = 167/10 = 16.7
- Range = 27 − 5 = 22
- SD ≈ 7.5

Thus medians and means for Group A are higher, and Group A shows more variability; the ranges are not the same.