To determine which statement is true about the variability of the group times, we'll examine four key statistical measures: standard deviation, median, interquartile range (IQR), and mean for both groups. Let's list out the findings:
1. Standard Deviation:
- Group A: [tex]\(5.32\)[/tex]
- Group B: [tex]\(8.03\)[/tex]
Conclusion: The standard deviation of Group B is greater than that of Group A, indicating that the times in Group B are more spread out around the mean.
2. Median:
- Group A: [tex]\(49.5\)[/tex] seconds
- Group B: [tex]\(50.0\)[/tex] seconds
Conclusion: The median maze-completion time for Group B is slightly higher than that for Group A.
3. Interquartile Range (IQR):
- Group A: [tex]\(7.75\)[/tex] seconds
- Group B: [tex]\(13.0\)[/tex] seconds
Conclusion: The IQR of Group B is greater than that of Group A, suggesting that Group B's times have a wider spread in the middle 50% of the data.
4. Mean:
- Group A: [tex]\(49.6\)[/tex] seconds
- Group B: [tex]\(50.3\)[/tex] seconds
Conclusion: The mean maze-completion time for Group B is higher than that for Group A.
Given these findings, the correct statements about the variability of the group times are:
- The times in Group B have a greater standard deviation.
- The times in Group B have a greater interquartile range.
- The times in Group B have a greater mean.
The statement that says "The times in Group A have a greater median" is not true. Therefore, the correct statements are:
- The times in Group B have a greater standard deviation.
- The times in Group B have a greater interquartile range.
- The times in Group B have a greater mean.
Hence, the most accurate specific statement about the variability of the group times is:
- The times in Group B have a greater interquartile range.
