Answer to Question #238972 in Statistics and Probability for shykie

Question

Compute and interpret the correlation coefficient for the aptitude scores and grade point averages in Exercise 8 on page 373.

Answer 1

Since, the data is incomplete, we assume as follows:

Compute and interpret the correlation coefficient for the aptitude scores and grade point averages given as:

Aptitude scores (X) (out of 100) : 78, 85, 92, 98, 52

Grade point average (Y) (out of 10): 8, 9, 9, 9, 5

Solution:

X Values

∑ = 405

Mean = 81

∑(X - M_x)² = SS_x = 1276

Y Values

∑ = 40

Mean = 8

∑(Y - M_y)² = SS_y = 12

X and Y Combined

N = 5

∑(X - M_x)(Y - M_y) = 119

R Calculation

r = ∑((X - M_y)(Y - M_x)) / $\sqrt{(SS_x)(SS_y)}$

r = 119 / $\sqrt{(1276)(12)}$ = 0.9617

This is a strong positive correlation, which means that high X variable scores go with high Y variable scores (and vice versa).