## Related questions with answers

In the 2008 baseball season, first baseman Ryan Howard of the Philadelphia Phillies led the Major Leagues with 48 home runs (HR) and 146 runs batted in (RBI). Overall, using all players with at least 300 plate appearances, the mean number of HR was $14.9$ with a standard deviation of $9.8$, whereas the mean number of RBI was $62.5$ with a standard deviation of $25.5$. Which was the more impressive PERFORMANCE? Explain, using the methods of this chapter.

Solution

VerifiedWe want to determine the MORE impressive performance.

We will compare home runs and runs batted in deviations from the mean to the standard deviation of each distribution. This will tell us how far each performance is above the mean, relative to the performances of the other eligible players in the distribution. (basically we will calculate $z$-scores for both home runs and runs batted in).

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