In the idealized normal distribution, the mean score is identical to the median score (i.e., the “middle” score), which is also identical to the mode (the most frequent score). One common, well-documented shape is the so-called normal distribution. We can also describe a distribution by its shape. Similarly, some people are tall, while others are short. On an exam, this means that some people did well, while others did worse. Most distributions have some amount of variance. So is the set of all heights in a population. For example, the set of all scores on an exam is a kind of distribution. In statistics, we often think of phenomena in terms of distributions: a set of scores or values. ![]() Regression to the mean Understanding distributions But in both cases, there’s an alternative explanation that’s both much more banal and much less intuitive. That explanation could very well be true. And maybe doing really poorly pushes you into action, so you study harder (or practice more, etc.) and thus improve your grade (or batting average). Maybe doing really well makes you complacent, so you don’t try as hard in the future. One intuitive explanation might chalk both findings up to something like motivation. Often, the students who performed the very best on the first exam perform slightly worse on the second exam (but still quite well)––and the students who performed the very worse now perform slightly better. Longtime teachers may have noticed a similar phenomenon. So it’s not as though these players were suddenly performing poorly, but all seven experienced a systematic decrease in performance. 313 in 2015––a score that would’ve ranked him at about 7, if he’d batted that way in 2014. ![]() The magnitude of this decrease varied across players, but in some cases was pretty substantial: the top hitter went from. Here’s a fact that may surprise you: the top seven hitters in 2014 all had worse batting averages in 2015.
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