Progress rate. Grade Point Average (GPA) and Progress Rate (PR) are two variables of crucial importance to students and schools. While each class’s GPA data is typically bell shaped, the PR data is quite different. Here is a histogram and summary statistics from a large class of business students in a European university, where PR is determined as the share of the 60 yearly European Credit Transfer and Accumulation System (ECTS) points achieved by any student.

a) Which is a better summary of the typical PR, the mean or the median? Explain.

b) Which is a better summary of the spread, the IQR or the standard deviation? Explain.

c) From a Normal model, about what percentage of students are within one standard deviation of the mean PR?

d) What percentage of students actually are within one standard deviation of the mean PR?

e) Explain the problem in using the Normal model for these data.