Question

24 mark for review administrators at a state university computed the mean gpa (grade point average) for juniors and seniors majoring in either physics or chemistry. the results are displayed in the table below. when juniors and seniors are grouped together, could physics majors have a higher mean gpa than chemistry majors? physics chemistry juniors 2.8 3.0 seniors 3.2 3.6 overall? ? a no. the physics majors’ mean gpa for juniors and seniors must be 3.0, while the chemistry majors’ mean gpa for juniors and seniors must be 3.3. b no. there is not enough information to determine the mean gpa for each major, but it must be higher for chemistry majors than for physics majors. c yes. it could happen. whether it does happen depends on the number of juniors and seniors in each major. d yes. it could happen. whether it does happen depends on the variability of the gpas within each of the four groups of students.

Explanation:

Step1: Recall weighted - mean concept

The overall mean GPA is a weighted - mean of the junior and senior mean GPAs. The weights are the number of juniors and seniors in each major.

Step2: Analyze the situation

We know the mean GPAs for juniors and seniors separately for physics and chemistry majors. But to find the overall mean GPA for each major, we need to know the number of juniors and seniors in each major. If there are a large number of juniors in physics (with a lower GPA of 2.8) and a large number of seniors in chemistry (with a higher GPA of 3.6), or vice - versa, the overall mean can vary.

Answer:

C. Yes. It could happen. Whether it does happen depends on the number of juniors and seniors in each major.