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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 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 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 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 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.
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1 answer

To compare the measures of center (mean and median) and variability (range and standard deviation) for the given data sets from Student Group A and Student Group B, we will analyze the data accordingly.

Data

  • 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

Calculating Measures of Center

  1. Mean:

    • Group A: \[ \text{Mean} = \frac{56 + 14 + 26 + 28 + 29 + 45 + 32 + 80 + 3 + 10}{10} = \frac{ 56 + 14 + 26 + 28 + 29 + 45 + 32 + 80 + 3 + 10 }{10} = \frac{ 312 }{10} = 31.2 \]
    • Group B: \[ \text{Mean} = \frac{27 + 24 + 18 + 19 + 5 + 16 + 22 + 10 + 6 + 20}{10} = \frac{ 27 + 24 + 18 + 19 + 5 + 16 + 22 + 10 + 6 + 20 }{10} = \frac{ 171 }{10} = 17.1 \]

  2. Median:

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

Calculating Measures of Variability

  1. Range:

    • Group A: \[ \text{Range} = 80 - 3 = 77 \]
    • Group B: \[ \text{Range} = 27 - 5 = 22 \]

  2. Standard Deviation (although not explicitly asked in your options, it's helpful for determining variability):

    • Group A will have a higher standard deviation than Group B, given the high outlier (80).

Summary of Findings

  • Means:

    • Group A mean (31.2) is higher than Group B mean (17.1).

  • Medians:

    • Group A median (28.5) is higher than Group B median (18.5).

  • Ranges:

    • Group A range (77) is not the same as Group B range (22).

Evaluating Statements

  1. The ranges of the time taken by Group A and Group B are the same. (False)
  2. The mean time taken by Group A is higher than that of Group B. (True)
  3. The median time taken by members of Group A to thread a needle is higher than that of members of Group B. (True)
  4. 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. (True)

Conclusion

The false statement is:

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