Question

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

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

Answer 1

To evaluate the statements about the data sets for Student Group A and Student Group B, we need to calculate the necessary statistics: the range, the median, and the mean for each group.

### Student Group A:
Data: 56, 14, 26, 28, 29, 45, 32, 80, 3, 10
- **Sorted Data**: 3, 10, 14, 26, 28, 29, 32, 45, 56, 80
- **Range**: \(80 - 3 = 77\)
- **Median**: The middle value (average of the 5th and 6th values in sorted data): \((28 + 29) / 2 = 28.5\)
- **Mean**: \((3 + 10 + 14 + 26 + 28 + 29 + 32 + 45 + 56 + 80) / 10 = 32.3\)

### Student Group B:
Data: 27, 24, 18, 19, 5, 16, 22, 10, 6, 20
- **Sorted Data**: 5, 6, 10, 16, 18, 19, 20, 22, 24, 27
- **Range**: \(27 - 5 = 22\)
- **Median**: The middle value (average of the 5th and 6th values): \((18 + 19) / 2 = 18.5\)
- **Mean**: \((5 + 6 + 10 + 16 + 18 + 19 + 20 + 22 + 24 + 27) / 10 = 15.7\)

### Summary of Calculations:
- **Group A**
- Range: 77
- Median: 28.5
- Mean: 32.3
- **Group B**
- Range: 22
- Median: 18.5
- Mean: 15.7

### Evaluating the Statements:
1. **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 (Group A has a higher range and generally shows higher variability).

2. **The ranges of the time taken by Group A and Group B are the same.**
- False (Group A's range is 77, while Group B's range is 22).

3. **The median time taken by members of Group A to thread a needle is higher than that of members of Group B.**
- True (28.5 vs. 18.5).

4. **The mean time taken by Group A is higher than that of Group B.**
- True (32.3 vs. 15.7).

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