Chapter 2.1, Problem 16E

To determine

To calculate: percentile and z-score of M and explain whether M has a high salary or a low salary.

Answer to Problem 16E

Here 48.28% player's salary on the World Champion 2008 Philadelphia Phillies baseball team is less than M's salary and percentile was 50%,

Explanation of Solution

Given:

  

Calculation:

M's salary in 2008 was $\$1,400,000$ . Since there were 14 salaries less than M's, his salary is at the percentile:

  $\begin{array}{l}\text{Percentile}=\frac{14}{29}\\ \approx 0.4828\\ =48.28\%\end{array}$

This means 48.28% player's salary on the World Champion 2008 Philadelphia Phillies baseball team less than M's salary. Note that we could also argue that since M's salary was the median, his percentile would be 50%.

The standardized score for M's salary is obtained below:

  $\begin{array}{l}z=\frac{x-\mu }{\sigma }\\ =\frac{1,400,000-3,388,617}{3,767,484}\\ \approx -0.53\end{array}$

M had a typical salary compared to the rest of the team since his percentile was 50%, but there were some players who made much more than he did since his z-score is negative, indicating a salary below the mean team salary.

Conclusion:

Therefore 48.28% player's salary on the World Champion 2008 Philadelphia Phillies baseball team is less than M's salary and percentile was 50%,