Central Limit Theorem
The central limit theorem (CLT) establishes that (under certain conditions) the properly normalized sum of independent random variables tends toward a normal distribution even if the original variables themselves are not normally distributed. This result is incredibly important in Statistics.
Resources
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The Central Limit Theorem for means:
Central Limit Theorem for Means
This Shiny app allows users to choose from several different population distributions, and to drag sliders to change the population parameters, sample size and number of samples. The resulting sampling distribution illustrates the effect of the Central Limit Theorem.
Author: OpenIntro.
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Sample means from a non-normally distributed population:
Sampling from a Non-Normally Distributed Population
This wonderfully animated applet helps users understand the sample mean's properties, under various simulated situations. Users can choose from four different population distributions (each accompanied by an illustrated fictional application), and set the sample size. The applet animates how the sample is obtained, and calculates the resulting sample mean. After multiple sample means have been calculated, the sampling distribution of the sample means is shown.
This applet also includes a convenient tutorial for users.
Author: Mike Whitlock and others, The University of British Columbia.
License: CC0.
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The Central Limit Theorem for proportions:
Central Limit Theorem for Proportions
This Shiny app allows users to drag sliders to change the population proportion, sample size and number of samples. The resulting sampling distribution illustrates the effect of the Central Limit Theorem for proportions.
Author: OpenIntro.