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

1 answer

To evaluate the statements about Groups A and B, we need to calculate the mean, median, and range for both groups, and assess their variability.

Data Sets:

  • Group A: 56, 14, 26, 28, 29, 45, 32, 80, 3, 10
  • Group B: 27, 24, 18, 19, 5, 16, 22, 10, 6, 20

Step 1: Calculate Mean

  • Group A:
    • Mean = (56 + 14 + 26 + 28 + 29 + 45 + 32 + 80 + 3 + 10) / 10 = 32.3 seconds
  • Group B:
    • Mean = (27 + 24 + 18 + 19 + 5 + 16 + 22 + 10 + 6 + 20) / 10 = 16.7 seconds

Step 2: Calculate Median

  • Group A (sorted): 3, 10, 14, 26, 28, 29, 32, 45, 56, 80
    • Median = (28 + 29) / 2 = 28.5 seconds
  • Group B (sorted): 5, 6, 10, 16, 18, 19, 20, 22, 24, 27
    • Median = (18 + 19) / 2 = 18.5 seconds

Step 3: Calculate Range

  • Group A:
    • Range = 80 - 3 = 77 seconds
  • Group B:
    • Range = 27 - 5 = 22 seconds

Step 4: Variability

  • Variability can be assessed through the range compared to the data points.
  • Group A has a wider range (77 seconds) compared to Group B (22 seconds), thus indicating higher variability.

Comparison of Statements:

  1. The mean time taken by Group A is higher than that of Group B. (True - Group A's mean is 32.3, Group B's mean is 16.7)
  2. The amount of variability of the time taken by Group A to thread a needle is higher than that of the time taken by Group B. (True - higher range indicates higher variability)
  3. The ranges of the time taken by Group A and Group B are the same. (False - Group A's range is 77 seconds, Group B's range is 22 seconds)
  4. The median time taken by members of Group A to thread a needle is higher than that of members of Group B. (True - Group A's median is 28.5, Group B's median is 18.5)

Conclusion:

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