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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 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.

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.

:)

1 answer

To determine which statement is false about the two groups, we can calculate the measures of center (mean and median) and variability (range and standard deviation) for both groups.

Group A:

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

  1. Median:

    • Sorting the data: 3, 10, 14, 26, 28, 29, 32, 45, 56, 80
    • The median (average of the 5th and 6th values): \( \frac{28 + 29}{2} = 28.5 \)

  2. Mean:

    • Sum: \( 56 + 14 + 26 + 28 + 29 + 45 + 32 + 80 + 3 + 10 = 2\sum48 \)
    • Mean: \( \frac{328}{10} = 32.8 \)

  3. Range:

    • Range: \( 80 - 3 = 77 \)

Group B:

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

  1. Median:

    • Sorting the data: 5, 6, 10, 16, 18, 19, 20, 22, 24, 27
    • The median (average of the 5th and 6th values): \( \frac{18 + 19}{2} = 18.5 \)

  2. Mean:

    • Sum: \( 27 + 24 + 18 + 19 + 5 + 16 + 22 + 10 + 6 + 20 = 20\sum13 = 168 \)
    • Mean: \( \frac{168}{10} = 16.8 \)

  3. Range:

    • Range: \( 27 - 5 = 22 \)

Comparing the Results:

  • Median:

    • Group A: 28.5
    • Group B: 18.5
    • Statement: True (Group A is higher)

  • Mean:

    • Group A: 32.8
    • Group B: 16.8
    • Statement: True (Group A is higher)

  • Range:

    • Group A: 77
    • Group B: 22
    • Statement: False (the ranges are not the same)

  • Variability (Implied by the range and standard deviation):

    • Group A has higher variability than Group B based on the range alone.
    • Statement: True

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