Which player had the higher batting average in both 1995 and 1996? Compute the batting average for each player for the two years combined. Which player had the higher combined batting average for 1995 and 1996? Briefly explain why the results might seem surprising or paradoxical.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The following table shows the number of hits (H), number of at-bats (AB), and batting average (AVG=H/AB)(AVG=H/AB) for Major Leaguers Derek Jeter and David Justice in 1995 and 1996.
| 1995 | 1996 | |
|---|---|---|
| Jeter |
12 H 48 AB AVG=250AVG=250 |
183 H 582 AB AVG=314AVG=314 |
| Justice |
104 H 411 AB AVG=253AVG=253 |
45 H 140 AB AVG=321AVG=321 |
Source: Based on Ken Ross, A Mathematician at the Ballpark: Odds and Probabilities for Baseball Fans, Pi Press, 2004.
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Which player had the higher batting average in both 1995 and 1996?
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Compute the batting average for each player for the two years combined.
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Which player had the higher combined batting average for 1995 and 1996?
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Briefly explain why the results might seem surprising or paradoxical.
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