Question

exercises 15 and 16 refer to the dotplot and summary statistics of salaries for players on the world champion 2008 philadelphia phillies baseball team.

salary (millions)

variable n mean std. dev. min q1 med q3 max
salary 29 3388617 3767484 390000 440000 1400000 6000000 14250000

1. baseball salaries brad lidge played a crucial role as the phillies \closer,\ pitching the end of many games throughout the season. lidges salary for the 2008 season was $6,350,000.

(a) find the percentile corresponding to lidges salary. explain what this value means.
(b) find the z - score corresponding to lidges salary. explain what this value means.

Explanation:

Step1: Sort data and count

Sort 29 - player salaries. Count how many are less than Lidge's salary.

Step2: Calculate percentile

Percentile $=\frac{\text{Number of salaries}<\text{Lidge's salary}}{n}\times100$.

Step3: Calculate z - score

$z=\frac{x - \text{Mean}}{\text{Std. dev.}}$, where $x = 6350000$.

Step4: Interpret results

Percentile shows position in data set. Z - score shows std. dev. from mean.

Answer:

(a) First, count salaries less than 6350000 to find percentile.
(b) $z=\frac{6350000 - 3388617}{3767484}$, interpret z - score meaning.