https://file.aiquickdraw.com/mathbot/file/1727323429649nnckujxk.jpg

### a. Mean and Median Scores
- **Traditional Classroom:**
  - Mean: 71.82
  - Median: 70.8

- **Flipped Classroom:**
  - Mean: 77.48
  - Median: 76.8

#### Comment on Differences:
The flipped classroom has both a higher mean and median score compared to the traditional classroom, indicating that students performed better overall in the flipped learning environment.

### b. Effect of Incorrect Score
If the score of 59.8 in the traditional class is incorrectly recorded as 598, the mean will be significantly affected, while the median will remain largely unchanged. This is because the mean is sensitive to extreme values, whereas the median is resistant to such outliers.

**Property Illustrated:** This demonstrates the robustness of the median compared to the mean when dealing with outliers.

Would you like more details or have any questions? Here are some related questions to consider:

1. How would the variance and standard deviation compare between the two classrooms?
2. What impact does the flipped classroom model have on student engagement based on these scores?
3. How does changing one score affect the range and interquartile range of the traditional classroom data?
4. Can we determine if the differences in means are statistically significant?
5. How would we graphically represent this data to show the difference in performance?

**Tip:** The median is often preferred over the mean as a measure of central tendency when dealing with skewed data or outliers.

Determine the mean and median score for each class. Comment on any differences. Suppose the score of 59.8 in the traditional course was incorrectly recorded as 598. How does this affect the mean? The median? What property does this illustrate?

This problem explores the comparison of mean and median exam scores between a traditional and a flipped classroom. It covers the impact of outliers on the mean and median, showing the robustness of the median when a score is incorrectly recorded. Suitable for Grades 10-12.

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