Based on these facts, would you expect batting averages above .350 to be more or less common today than in the past? A. Because the mean is unchanged, batting averages above .350 are less common today because the standard deviation is lower, thus it is less probable to have such a high batting average. B. Because the mean is unchanged, batting averages above .350 are more common today because the standard deviation is higher, thus it is less probable to have such a high batting average. C. Because the mean is unchanged, batting averages above .350 are less common today because the standard deviation is higher, thus it is more probable to have such a high batting average. D. Because the mean is unchanged, batting averages above 350 are more common today because the standard deviation is lower, thus it is less probable to have such a high batting average.
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Bonus Knowledge
In the realm of baseball statistics, batting averages are influenced by various factors, including player skill, pitching quality, and even the type of ball being used. Historically, we saw peaks in batting averages during different eras, but as training, analytics, and game strategies have evolved, we've seen shifts in performance metrics. The lower standard deviations in recent years suggest that the top players are more consistently excellent, making those lofty averages rarer. So, if the mean hasn't changed while the standard deviation has decreased, it indeed makes it statistically less likely for players to reach those elite .350 averages, as they have less room to diverge from that central average. In essence, today's baseball landscape has shaped a new normal for batting averages!
