Mr. Randall is analyzing the statistics on the past three exams for one of his students.
Exam. Percent. Percentile rank.
Unit A. 67%. 91st
Unit B. 63%. 66th
Unit C. 71%. 50th
a) Which exam do you think was the most difficult for this student? Explain your answer.
b) Which exam do you think was the most difficult for this class? Explain your answer.
c) Mr. Randall thought the student's most impressive exam was unit A. Explain his reasoning.
Explain in detail
a) Based on the percentiles, we can see that exam Unit C had the lowest percentile rank of 50th, indicating that it was the most difficult for this student. Even though the student scored 71% on this exam, many other students scored higher, resulting in a lower percentile rank.
b) To determine which exam was the most difficult for the class, we should look at the average percentile rank for each exam. If we add up the percentile ranks for all three exams (91 + 66 + 50) and divide by 3, we get an average percentile rank of 69th. This means that Unit C was the most difficult exam for the class as well.
c) Mr. Randall's reasoning for thinking that Unit A was the most impressive exam for the student could be based on the fact that even though the student scored 67%, they achieved a high percentile rank of 91st. This indicates that the student outperformed a majority of their classmates on this particular exam, making it the most impressive performance relative to their peers.