Difference between revisions of "SOCR EduMaterials Activities GeneralCentralLimitTheorem"
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** emperacally demonstrate that the ''sample-average'' is special and other sample statistics (e.g., median, variance, range, etc.) generally do not have distributions that are normal | ** emperacally demonstrate that the ''sample-average'' is special and other sample statistics (e.g., median, variance, range, etc.) generally do not have distributions that are normal | ||
** illustrate that the expectation of the sample-average equals the population mean (and the sample-average is typically a good measure of centrality for a population/process) | ** illustrate that the expectation of the sample-average equals the population mean (and the sample-average is typically a good measure of centrality for a population/process) | ||
| − | ** show that the variation of the sample average rapidly decreases | + | ** show that the variation of the sample average rapidly decreases as the sample size increases <math>\left ( ~1\over{\sqrt(n)} \right)</math>. |
<center>[[Image:SOCR_Activities_CardCoinSampling_Dinov_092206_Fig1.jpg|300px]]</center> | <center>[[Image:SOCR_Activities_CardCoinSampling_Dinov_092206_Fig1.jpg|300px]]</center> | ||
Revision as of 15:50, 22 January 2007
SOCR Educational Materials - Activities - SOCR General Central Limit Theorem (CLT) Activity
This activity represents a very general demonstration of the effects of the Central Limit Theorem (CLT). The activity is based on the SOCR Sampling Distribution CLT Experiment. This experiment builds upon a RVLS CLT applet by extending the applet functionality and providing the capability of sampling from any SOCR Distribuion.
- Goals: The aims of this activity are to
- provide intuitive notion of sampling from any process with a well-defined distribution
- motivate and facilitate learning of the central limit theorem
- emperically validate that sample-averages of random observations (most processes) follow approximately normal distribution
- emperacally demonstrate that the sample-average is special and other sample statistics (e.g., median, variance, range, etc.) generally do not have distributions that are normal
- illustrate that the expectation of the sample-average equals the population mean (and the sample-average is typically a good measure of centrality for a population/process)
- show that the variation of the sample average rapidly decreases as the sample size increases \(\left ( ~1\over{\sqrt(n)} \right)\).
- SOCR Home page: http://www.socr.ucla.edu
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