Background

Batting averages tend to be normally distributed over a season and the sports gurus have kept track of batting averages for over 100 years. Here are the league batting averages since 1901. While the standard deviation of the batting averages has fluctuated over time, we are going to assume a standard deviation of \(0.0375\). We will also be using the individual batter data from 2009.

If baseball isn’t your sport, here is the definition of batting average.

Your Task

Our challenge is to check the normality of batting averages and compare some of the best hitters from 2009 to a few of the greats from history.

  1. Create two histograms and compute the mean and standard deviation of each histogram. You can use the QuantitativeDescriptiveStatistics.xlsx or the histogram tools in Excel 2016 or later. A. First, the batting averages of the National League. B. Second, the batting averages of the American League.

  2. Assess the normality of each histogram using Q-Q Plots. (Review the Reading)
  3. Select two players from each league. Use z-scores and the Normal Applet to show the percentile of each player within their respective leagues. (Review the Reading)
  4. Compare the z-score of the player with the best batting average from 2009 to the following players.1
    A. 2004 Ichiro Suzuki with a batting average of \(0.372\)
    B. 2002 Barry Bonds with a batting average of \(0.370\)

  5. Type a three to five sentence paragraph that shows your understanding of how z-scores, percentiles, and probabilities can be used to show how individuals compare to a normally distributed population.

  1. See here for the z-score leaders - http://archive.alexreisner.com/baseball/stats/leaders?s=AVG↩