During a Budget Meeting, Local School Board Members Decided to Review

During a budget meeting, local school board members decided to review class size information to
determine if budgets were correct. Summary statistics are shown in the table.

$\begin{array}{|c|c|}\hline \bar{x} & 33.39 \text { students }\\\hline \text { s } & 5.66 \text {students }\\\hline \text { min}& 17 \\\hline \text {Q1} & 29 \\\hline \text {median} & 33 \\\hline \text {Q3} & 40 \\\hline \text {max }& 40 \\\hline\end{array}$

a. Notice that the third quartile and maximum class sizes are the same. Explain how this can be.
b. The school district declares that classes with fewer than 20 students are "too small". Would you consider a class of 20 students to be unusually small? Explain.
c. The school district sets the office supply budgets of their high schools on the enrollment of students. The district budgets each class $12 plus $0.75 per student, so a class with one student receives $12.75 and the classes with 40 students receive 12 + 0.75(40) = $42. What is the median class budget for office supplies? And the IQR?
d. What are the mean and standard deviation of the class office supply budgets?