A Physical Education Instructor Administered a Leadership Aptitude Survey and Ranked

Short Answer

A physical education instructor administered a leadership aptitude survey and ranked the scores (X) of the 15 students. A tennis tournament was held for the same students and their order of finish is shown below (Y). Calculate the correlation between leadership aptitude and the finish in the tennis tournament.
$$\begin{array} { | l | l | l | l | } \hline \text { Student } & \boldsymbol { X } & \boldsymbol { Y } & \\\hline & & & \\\hline 1 & 1 & 9 & \\\hline 2 & 2 & 10 & \\\hline 3 & 3 & 3 & \\\hline 4 & 4 & 12 & \\\hline 5 & 5.5 & 5 & \\\hline 6 & 5.5 & 1 & \\\hline 7 & 7 & 15 & \\\hline 8 & 8 & 13 & \\\hline 9 & 9 & 8 & \\\hline 10 & 10 & 11 & \\\hline 11 & 11 & 2 & \\\hline 12 & 12 & 7 & \\\hline 13 & 13 & 4 & \\\hline 14 & 14 & 6 & \\\hline 15 & 15 & 14 & \\\hline\end{array}$$