Question

1. Rowdy Rho Fraternity is in danger of losing campus approval if they do not raise the mean GPA of the entire group to at least 2.2. This terms GPA’s are 1.8, 2.0, 2.0, 2.0, 2.0, 1.9, 1.8, 2.3, 2.5, 2.3, 1.9, 2.2, 2.0, 2.3.

1. What is the mean GPA? Is RR Fraternity going to lose its campus approval?
2. Rod claims he made a 2.0 because he was sick for 6 weeks. He believes he would have made a 3.9 if he had been well. Would Rod have saved the fraternity with a 3.9 GPA?
3. Suppose the college had required the fraternities to have a median GPA of 2.2. Would Rod have saved the fraternity if he had earned a 3.9 GPA?
4. What can you say about the effect of and exceptionally high (or low) value on the mean and the median?

Answer 1

a) Mean = Total sum/ n = 29/14 = 2.07

The mean GPA is 2.07.

Yes, RR Fraternity is going to lose its campus approval because the mean value is less than the required approval rating.

b) Yes, Rod would have saved the fraternity with a 3.9 GPA.

c) Median is the middle value when data is arranged in a ascending order.

We cannot be certain that he would have saved the fraternity with a 3.9 GPA. As we are not certain that the middle value would have a 2.2 GPA value.

d) Mean is adversely influenced by these exceptional high (or low) value.

Median is a good measure of the average value when the data include exceptionally high or low values because these have little influence on the outcome.