Chapter 3.1, Problem 3.6E

To determine

To calculate the value of percentile and z score for Madson’s salary and then explain it.

Answer to Problem 3.6E

Percentile: 50^th percentile

Z score: -0.53

Explanation of Solution

Given:

Player	Salary	Player	Salary	Player	Salary
Burrell, Pat	1,42,50,000	Romero, J. C.	32,50,000	Kendrick, Kyle	4,45,000
Howard, Ryan	1,00,00,000	Feliz, Pedro	30,00,000	Dobbs, Greg	4,40,000
Myers, Brett	85,83,333	Helms, Wes	24,00,000	Ruiz, Carlos	4,25,000
Rollins, Jimmy	80,00,000	Werth, Jayson	17,00,000	Condrey, Clayton	4,20,000
Eaton, Adam	79,58,333	Madson, Ryan	14,00,000	Coste, Chris	4,15,000
Utley, Chase	77,85,714	Durbin, Chad	9,00,000	Rosario, Francisco	3,95,000
Lidge, Brad	63,50,000	Taguchi, So	9,00,000	Zagurski, Mike	3,92,500
Moyer, Jamie	60,00,000	Bruntlett, Eric	6,00,000	Lahey, Tim	3,90,000
Gordon, Tom	55,00,000	Hamels, Cole	5,00,000	Mathieson, Scott	3,90,000
Jenkins, Geoff	50,00,000	Victorino, Shane	4,80,000

  

Variable	Salary
n	29
Mean	3388617
Standard deviation	3767484
Minimum	390000
Quartile 1	440000
Median	1400000
Quartile 3	6000000
Maximum	14250000

Formula used:

  $\text{Percentile = }\left(\frac{\text{No}\text{. of values less than }x+0.5}{\text{Total no}\text{. of values }}\right)\times 100$

  $\text{z score = }\frac{x-\mu }{\sigma }$

Calculation:

  $\begin{array}{c}\text{Percentile = }\left(\frac{\text{No}\text{. of values less than }x+0.5}{\text{Total no}\text{. of values }}\right)\times 100\\ =\left(\frac{14+0.5}{29}\right)\times 100\\ ={50}^{\text{Th }}\text{percentile}\end{array}$

  $\begin{array}{l}z\text{- score}=\frac{\begin{array}{r}\hfill 1400000\end{array}-3388617}{3767484}\\ z\text{- score}=-0.53\end{array}$

The 50^th percentile shows that the madson’s salary is more than 50% of the other player’s salary while the z score equal to -0.53, means that madson’s salary is 0.53 standard deviation less than mean.