Question

1. how did the average score of the bottom 10 students change from quiz 1 to quiz 3?

the way that the average score of the bottom 10 students change from quiz 1 to quiz 3 is by going from scores increasing, to 11 - 20 in which the the scores are decreasing which tanks the average. to add on i know this because since the upper 10 scholars were getting good scores which kept the average up, but then the bottom 10 students got horrible scores which tanked down the classes average which then led to the scores being bad. additionally i know this because the upper 10 scores from quiz 1 to 3 is 94, 96, 100, but scores from bottom 10 are 42, 40, 38 which tanked the good scores and made it horrible. showing how i know that the way that the average score of the bottom 10 students change from quiz 1 to quiz 3 is by going from scores increasing, to 11 - 20 in which the the scores are decreasing which tanks the average.

1. in the context of individual students’ performance versus class performance, what is the risk of using the class’s average score as a comparison metric rather than the individual student’s scores?

what is the risk of using “aggregate change” as a metric without considering the individual changes that comprise it?

Explanation:

Question 1: How did the average score of the bottom 10 students change from Quiz 1 to Quiz 3?

To determine the change in the average score of the bottom 10 students, we analyze the trend of their scores. Initially, the scores of the bottom 10 students were increasing. However, from Quiz 1 to Quiz 3, their scores shifted to a decreasing trend (e.g., scores like 42, 40, 38 are mentioned, indicating a decline). This decrease in individual scores of the bottom 10 students would lead to a decrease in their average score because the average is calculated as the sum of scores divided by the number of students. If the individual scores are decreasing, the sum will decrease, and thus the average (sum/10) will also decrease.

Using the class average as a comparison metric for individual performance has risks. The class average is influenced by all students' scores (both high and low). A high - performing student might have a score above the average, but if there are many low - scoring students, the average could be pulled down. Conversely, a low - performing student might seem better relative to the average if there are many high - scoring students. Also, the average doesn't show the distribution of scores (e.g., if scores are skewed, the average may not represent the typical student's performance). It can mask the true performance of an individual student, as it doesn't account for the unique performance trajectory or the specific strengths and weaknesses of each student.

When using "aggregate change" (total change across a group) without considering individual changes, we miss the details of how each component (individual) contributed to the aggregate. Some individuals might have had a large positive change, while others had a large negative change, but the aggregate could mask these differences. For example, in a class, the aggregate change in scores could be small, but some students might have improved a lot and others declined a lot. This lack of consideration of individual changes can lead to incorrect conclusions about the performance or behavior of the group members, as we don't know which individuals drove the aggregate change and in what way.

Answer:

The average score of the bottom 10 students decreased from Quiz 1 to Quiz 3. This is because their scores changed from an increasing trend to a decreasing trend (with scores like 42, 40, 38), so the sum of their scores reduced, leading to a lower average (since average = total score of bottom 10 / 10).

Question 2: In the context of individual students’ performance versus class performance, what is the risk of using the class’s average score as a comparison metric rather than the individual student’s scores?