re: "Half the schools are below average" - not always true

quote:

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However, it has been shown that in large enough sample sizes, and when averaging the scores of the students (i.e., the mean of means) that we come to be able to use something called the Central Limit Theorem.

Dont worry, your 7005 class will cover this in November.

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Your understanding of the central limit theorem is flawed.

The central limit theorem means that if we take a large enough population of Presidential polls - the results of those polls will be normally distributed.

It doesn't mean if we sample a large enough population, the result of the poll will always tend towards 50/50.


So in this context - it would mean if we created samples of schools by random selection - the distribution of scores among those samples is normally distributed - it doesn't mean the scores themselves are normally distributed. If that's the case - it means there can be no skewed distributions in nature - which is kinda absurd as they are observed all the time.