COMPSCI C8 Lecture Notes - Lecture 26: Central Limit Theorem, Standard Deviation
14 Mar 2018
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The central limit theorem describes scenarios in which the normal distribution (a bell- shaped curve) arises. Most distributions we observed were not bell-shaped, but empirical distributions of sa(cid:373)ple a(cid:448)erages (cid:449)ere : sample averages estimate population averages, a proportion within a sample is a sample average. If the sample is: large, drawn at random with replacement. Then, regardless of the distribution of the population: the probability distribution of the sample average (or sample sum) is roughly bell-shaped. Every bell-shaped (cid:272)ur(cid:448)e is (cid:272)alled (cid:862)the (cid:374)or(cid:373)al distri(cid:271)utio(cid:374)(cid:863: the average (center) could be different, the standard deviation (spread) could be different, these two numbers alone determine the whole shape. The purpose of repeated sampling is to under how a statistic could have been different. If he statistic is an average of a large random sample, then we know the statistic is drawn from a bell curve. Draw all possible random samples of that size. You"ll e(cid:374)d up (cid:449)ith a lot of (cid:373)ea(cid:374)s.
