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.

Question

Student A: 56, 14, 26, 28, 29, 45, 32, 80, 3, 10
Student 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 amount of variability of the time taken by Group A 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 is higher than the amount of variability of the time taken by Group B.

The median time taken by Group A is higher than that of Group B.
The median 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 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.

Answer 1

To evaluate the statements, we first need to calculate the measures of center (mean and median) and variability (range) for the two groups.

Group A Data: 56, 14, 26, 28, 29, 45, 32, 80, 3, 10

1. Calculating the mean for Group A:

   • Sum = 56 + 14 + 26 + 28 + 29 + 45 + 32 + 80 + 3 + 10 = 343
   • Mean = Sum / Number of values = 343 / 10 = 34.3

2. Calculating the median for Group A:

   • Ordered Data: 3, 10, 14, 26, 28, 29, 32, 45, 56, 80
   • Median = (28 + 29) / 2 = 28.5

3. Calculating the range for Group A:

   • Range = Max - Min = 80 - 3 = 77

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Group B Data: 27, 24, 18, 19, 5, 16, 22, 10, 6, 20

1. Calculating the mean for Group B:

   • Sum = 27 + 24 + 18 + 19 + 5 + 16 + 22 + 10 + 6 + 20 = 147
   • Mean = Sum / Number of values = 147 / 10 = 14.7

2. Calculating the median for Group B:

   • Ordered Data: 5, 6, 10, 16, 18, 19, 20, 22, 24, 27
   • Median = (18 + 19) / 2 = 18.5

3. Calculating the range for Group B:

   • Range = Max - Min = 27 - 5 = 22

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Now we can analyze the statements:

1. The amount of variability of the time taken by Group A is higher than the amount of variability of the time taken by Group B.

   • True: The range for Group A (77) is higher than the range for Group B (22).

2. The median time taken by Group A is higher than that of Group B.

   • True: Median for Group A is 28.5, while for Group B it is 18.5.

3. The mean time taken by Group A is higher than that of Group B.

   • True: Mean for Group A is 34.3, while for Group B it is 14.7.

4. The ranges of the time taken by Group A and Group B are the same.

   • False: The range for Group A is 77, and the range for Group B is 22. They are not the same.

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