Answer :
To determine which statement is true about the distributions of completion times for Group A and Group B, let's analyze and compare the key statistical measures: mean, median, and standard deviation.
1. Completion times for Group A:
[tex]\(4.5, 4.6, 5.0, 4.8, 4.4, 4.7, 5.2, 4.6, 4.8, 4.9\)[/tex]
2. Completion times for Group B:
[tex]\(5.5, 4.0, 4.2, 4.8, 4.1, 3.5, 3.9, 4.3, 4.4, 4.1\)[/tex]
Firstly, let's review the numerical values for the mean, median, and standard deviation for both groups:
- Mean of Group A: [tex]\(4.75\)[/tex]
- Mean of Group B: [tex]\(4.28\)[/tex]
- Median of Group A: [tex]\(4.75\)[/tex]
- Median of Group B: [tex]\(4.15\)[/tex]
- Standard Deviation of Group A: [tex]\(0.24\)[/tex]
- Standard Deviation of Group B: [tex]\(0.55\)[/tex]
Using these statistical measures, let's assess each of the statements:
1. "The students in Group A tended to complete the quiz in less time."
- Based on the means:
- Group A's mean time: [tex]\(4.75\)[/tex] minutes
- Group B's mean time: [tex]\(4.28\)[/tex] minutes
- Group A took, on average, more time to complete the quiz, not less. Therefore, this statement is false.
2. "The median of Group A is greater than the median of Group B."
- Median of Group A: [tex]\(4.75\)[/tex]
- Median of Group B: [tex]\(4.15\)[/tex]
- The median of Group A is indeed greater than the median of Group B. Hence, this statement is true.
3. "The means of both groups are about the same."
- The mean for Group A is [tex]\(4.75\)[/tex].
- The mean for Group B is [tex]\(4.28\)[/tex].
- The means are not about the same; there is a noticeable difference. This statement is false.
4. "The standard deviation of Group B is less than the standard deviation of Group A."
- Standard deviation of Group A: [tex]\(0.24\)[/tex]
- Standard deviation of Group B: [tex]\(0.55\)[/tex]
- The standard deviation of Group B is greater than that of Group A, indicating more variability in times for Group B. This statement is false.
Thus, the only true statement about the completion times of the groups is:
"The median of Group A is greater than the median of Group B."
1. Completion times for Group A:
[tex]\(4.5, 4.6, 5.0, 4.8, 4.4, 4.7, 5.2, 4.6, 4.8, 4.9\)[/tex]
2. Completion times for Group B:
[tex]\(5.5, 4.0, 4.2, 4.8, 4.1, 3.5, 3.9, 4.3, 4.4, 4.1\)[/tex]
Firstly, let's review the numerical values for the mean, median, and standard deviation for both groups:
- Mean of Group A: [tex]\(4.75\)[/tex]
- Mean of Group B: [tex]\(4.28\)[/tex]
- Median of Group A: [tex]\(4.75\)[/tex]
- Median of Group B: [tex]\(4.15\)[/tex]
- Standard Deviation of Group A: [tex]\(0.24\)[/tex]
- Standard Deviation of Group B: [tex]\(0.55\)[/tex]
Using these statistical measures, let's assess each of the statements:
1. "The students in Group A tended to complete the quiz in less time."
- Based on the means:
- Group A's mean time: [tex]\(4.75\)[/tex] minutes
- Group B's mean time: [tex]\(4.28\)[/tex] minutes
- Group A took, on average, more time to complete the quiz, not less. Therefore, this statement is false.
2. "The median of Group A is greater than the median of Group B."
- Median of Group A: [tex]\(4.75\)[/tex]
- Median of Group B: [tex]\(4.15\)[/tex]
- The median of Group A is indeed greater than the median of Group B. Hence, this statement is true.
3. "The means of both groups are about the same."
- The mean for Group A is [tex]\(4.75\)[/tex].
- The mean for Group B is [tex]\(4.28\)[/tex].
- The means are not about the same; there is a noticeable difference. This statement is false.
4. "The standard deviation of Group B is less than the standard deviation of Group A."
- Standard deviation of Group A: [tex]\(0.24\)[/tex]
- Standard deviation of Group B: [tex]\(0.55\)[/tex]
- The standard deviation of Group B is greater than that of Group A, indicating more variability in times for Group B. This statement is false.
Thus, the only true statement about the completion times of the groups is:
"The median of Group A is greater than the median of Group B."
