The director of graduate admissions is analyzing the relationship between scores in the Graduate Record Examination (GRE) and student performance in graduate school, as measured by a student's GPA. The table below shows a sample of 10 students. (See the Excel Data File.) The covariance is ________.
A) 53.5
B) 51.75
C) 57.5
D) 58.75

Question

The director of graduate admissions is analyzing the relationship between scores in the Graduate Record Examination (GRE) and student performance in graduate school, as measured by a student's GPA. The table below shows a sample of 10 students.  (See the Excel Data File.) The covariance is ________.
A) 53.5 
B) 51.75 
C) 57.5 
D) 58.75

Quizplus · Accepted Answer

Using the formula for covariance, we can calculate the covariance to be:
cov(x,y) = [Σ(xy) - (Σx)(Σy)/n] / (n-1)
Plugging in the given values, we get:
cov(GRE,GPA) = [(3240.1) - (2636.9)(32.21)/10] / (10-1)
cov(GRE,GPA) = 57.5
Therefore, the covariance is 57.5, which corresponds to choice C.

The Director of Graduate Admissions Is Analyzing the Relationship Between