In the previous problem, the middle of the grade distribution is a C and C was the most likely grade to be assigned, so that is your best guess at this point for the grade earned by a randomly selected student.
If we have information on another variable that is related to grade, perhaps we can improve our guess.
Imagine that the professor says the following: “Over the past five years, I have collected information about attendance and grades. I find that there is a positive correlation between points and attendance, r = .90. Those people who attended every class tended to get 90 points and higher, those who attended most classes usually scored about 80-89 points, those who attended half of the classes scored between 70 and 79 points, those who came infrequently tend to score between 60 and 69 points, and those who never attended usually scored less than 60.”
Question 2: Imagine now that you were asked to predict how another student in the class would perform. If you learned that the student never attended class, what grade would you expect for this student?
Select an Answer:
A: 90 – 100 pts
Because we have a positive correlation, more attendance is associated with higher grades and less attendance with lower grades. For a student to get an A, they would probably have to attend all or almost all of the classes (i.e., a high score for attendance).
B: 80 – 89 pts
Because we have a positive correlation, greater attendance is associated with higher grades and less attendance with lower grades. For a student to get an B, they would have to attend most of the classes (i.e., a moderately high score for attendance). This student didn’t attend class at all.
C: 70 – 79 pts
C (70-79 points) would be a good guess if we had no other information (i.e., we didn’t know how much the student attended). We do know that this student did not attend class at all, and we have a positive correlation that indicates more attendance is associated with higher grades and less attendance with lower grades. To get a C, the student would likely have attended about 50% of the classes. This student didn’t attend any classes so it is unlikely that the student got a C.
D: 60 – 69 pts
You are on the right track. The student did not attend class at all and lower grades are associated with less attendance. However, those who received D grades were likely to attend some classes. Because this student didn’t attend any classes, it is unlikely that the student got a D.
F: < 60 pts
You are correct! Why? There is a positive relationship between attendance and grades. Not only will those who attend the most usually get the highest grades, but also those who attend the least classes will most likely get the lowest grades. A student who didn’t attend any classes at all is likely to score below 60 points and thus get a grade of F.