MATH1280 Statistics 1 Discussion forum UNIT8
Grades 9.67/0-10
In past courses, some students have had trouble with the main topics of Chapter 7, so let's review it here.
Imagine that you had to explain the law of large numbers and the central limit theorem to a person who has never heard of these things. Write an explanation to help this person understand these concepts. If you use a technical term, be sure to explain it.
Do not cut and paste anything from the Internet, but if you get ideas from a book or Internet source, be sure to cite it in the text and add a reference entry at the end (and put the ideas into your own words).
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1. Imagine that you had to explain the law of large numbers and the central limit theorem to a person who has never heard of these things. Write an explanation to help this person understand these concepts. If you use a technical term, be sure to explain it.
The law of large numbers
The Law of Large Numbers is "a mathematical theorem that describes the sampling distribution of the average for large samples," and "as the sample size becomes larger, the sampling distribution of the sample average becomes more and more concentrated about the expectation" (Yakir, 2011, p. 115). For example, when the same experiment is repeated many times, the mean of the results will be close to the mean of the entire population.
The central limit theorem
The central limit theorem describes the error between the sample mean and the population means when the sample size increases (Yakir, 2011). For example, the sample means distribution obtained by randomly selecting n samples from the population approaches the normal distribution as n increases. That is, regardless of the probability distribution of the population, it matches the normal distribution represented by the same mean and variance.
References
Yakir. B, (2011). Introduction to Statistical Thinking (With R, Without Calculus). Retrieved from https://my.uopeople.edu/pluginfile.php/1097279/mod_book/chapter/267923/MATH1280RInstall Notes. pdf
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