Question
Using the following symmetric box plots, compare the distributions. (Explain what the data is showing)
[25, 40, 55, 70, 85]
[60, 75, 80, 85, 100]
The first is grades with no homework, and the second is grades with homework
[25, 40, 55, 70, 85]
[60, 75, 80, 85, 100]
The first is grades with no homework, and the second is grades with homework
Answers
GPT-4o mini
To compare the distributions of the two sets of grades represented by symmetric box plots, we will analyze the provided data points for both scenarios: grades with no homework and grades with homework.
### Data Breakdown
1. **Grades with No Homework: [25, 40, 55, 70, 85]**
- **Minimum**: 25
- **Lower Quartile (Q1)**: 40
- **Median (Q2)**: 55
- **Upper Quartile (Q3)**: 70
- **Maximum**: 85
2. **Grades with Homework: [60, 75, 80, 85, 100]**
- **Minimum**: 60
- **Lower Quartile (Q1)**: 75
- **Median (Q2)**: 80
- **Upper Quartile (Q3)**: 85
- **Maximum**: 100
### Comparisons
- **Range**:
- The range for grades with no homework is **60** (85 - 25), whereas for grades with homework it is **40** (100 - 60). This indicates that the grades with no homework have more variability in performance compared to those with homework.
- **Median**:
- The median for grades with no homework is **55**, while the median for grades with homework is **80**. This suggests that, on average, students' performance improves significantly when homework is included.
- **Quartiles**:
- The lower quartile for no homework (40) is significantly lower than the lower quartile with homework (75), indicating that a larger proportion of students perform at a higher level when homework is assigned.
- The upper quartile for grades without homework (70) is also lower than the upper quartile for grades with homework (85), showing that even the better-performing students do better on average when homework is involved.
- **Overall Distribution Shape**:
- Both distributions are symmetric, but the shape indicates that when homework is assigned, there is a shift toward higher grades overall, with fewer low scores and a more concentrated upper end of the performance spectrum.
### Conclusion
The data reveals that the inclusion of homework seems to positively influence student grades, leading to a higher overall performance. Students exhibit improved consistency and higher scores when homework is part of their academic activities, as seen by the shifts in median and quartile values. The no-homework grades are more spread out with a significant low end, whereas the homework grades show less variability and a higher concentration of scores at the upper end. Overall, this suggests that homework could potentially play a critical role in enhancing student learning outcomes.
### Data Breakdown
1. **Grades with No Homework: [25, 40, 55, 70, 85]**
- **Minimum**: 25
- **Lower Quartile (Q1)**: 40
- **Median (Q2)**: 55
- **Upper Quartile (Q3)**: 70
- **Maximum**: 85
2. **Grades with Homework: [60, 75, 80, 85, 100]**
- **Minimum**: 60
- **Lower Quartile (Q1)**: 75
- **Median (Q2)**: 80
- **Upper Quartile (Q3)**: 85
- **Maximum**: 100
### Comparisons
- **Range**:
- The range for grades with no homework is **60** (85 - 25), whereas for grades with homework it is **40** (100 - 60). This indicates that the grades with no homework have more variability in performance compared to those with homework.
- **Median**:
- The median for grades with no homework is **55**, while the median for grades with homework is **80**. This suggests that, on average, students' performance improves significantly when homework is included.
- **Quartiles**:
- The lower quartile for no homework (40) is significantly lower than the lower quartile with homework (75), indicating that a larger proportion of students perform at a higher level when homework is assigned.
- The upper quartile for grades without homework (70) is also lower than the upper quartile for grades with homework (85), showing that even the better-performing students do better on average when homework is involved.
- **Overall Distribution Shape**:
- Both distributions are symmetric, but the shape indicates that when homework is assigned, there is a shift toward higher grades overall, with fewer low scores and a more concentrated upper end of the performance spectrum.
### Conclusion
The data reveals that the inclusion of homework seems to positively influence student grades, leading to a higher overall performance. Students exhibit improved consistency and higher scores when homework is part of their academic activities, as seen by the shifts in median and quartile values. The no-homework grades are more spread out with a significant low end, whereas the homework grades show less variability and a higher concentration of scores at the upper end. Overall, this suggests that homework could potentially play a critical role in enhancing student learning outcomes.