Problem 2: During class, we have explored several ways in which averages

can be misleading and counterintuitive. Here is another surprising result.

Suppose a group of three math majors has a mean GPA of 3.0 and a group

of three physics majors has a mean GPA of 2.0. One of the physics majors

decides to change to a math major, so there are now four math majors and

two physics majors. The mean GPA for the four math majors is now less than

3.0 and the mean GPA for the two physics majors is now less than 2.0. Every

individual student's GPA remained the same, but by switching a student from

one group to the other, both averages decreased!

Explain how this is possible by constructing a specic example. (There are

multiple correct answers.) Choose GPAs for each of the six students so that

when a physics major changes to a math major, the math students' mean

GPA decreases from 3.0 and the physics students' mean GPA decreases from

2.0. (Remember that each student's GPA remains the same.) Include detailed

computations and explanations as part of your solution.

Problem

Thank you so much for helping me, I need some serious help with this subject!