Difference between revisions of "SOCR EduMaterials Activities GeneralCentralLimitTheorem"
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== [[SOCR_EduMaterials_Activities | SOCR Educational Materials - Activities ]] - SOCR General Central Limit Theorem (CLT) Activity == | == [[SOCR_EduMaterials_Activities | SOCR Educational Materials - Activities ]] - SOCR General Central Limit Theorem (CLT) Activity == | ||
| − | === This activity represents a very general demonstration of the effects of the [http://en.wikipedia.org/wiki/Central_limit_theorem Central Limit Theorem (CLT)]. The activity is based on the [[About_pages_for_SOCR_Experiments | SOCR Sampling Distribution CLT Experiment]]. This experiment builds upon a [http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/ RVLS CLT applet] by extending the applet functionality and providing the capability of sampling from any [[About_pages_for_SOCR_Distributions | SOCR | + | === This activity represents a very general demonstration of the effects of the [http://en.wikipedia.org/wiki/Central_limit_theorem Central Limit Theorem (CLT)]. The activity is based on the [[About_pages_for_SOCR_Experiments | SOCR Sampling Distribution CLT Experiment]]. This experiment builds upon a [http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/ RVLS CLT applet] by extending the applet functionality and providing the capability of sampling from any [[About_pages_for_SOCR_Distributions | SOCR Distribution]].=== |
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** show that the variation of the sample average rapidly decreases as the sample size increases (<math> ~1\over{\sqrt(n)}</math>). | ** show that the variation of the sample average rapidly decreases as the sample size increases (<math> ~1\over{\sqrt(n)}</math>). | ||
| − | <center>[[Image: | + | * The '''SOCR CLT Experiment''': To start the this Experiment, go to [http://www.socr.ucla.edu/htmls/SOCR_Experiments.html SOCR Experiments] and select the SOCR Sampling Distribution CLT Experiment from the drop-down list of experiments in the left panel. |
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| + | <center>[[Image:SOCR_Activities_General_CLT_Dinov_012207_Fig1.jpg|400px]]</center> | ||
Revision as of 16:14, 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 Distribution.
- 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 (\( ~1\over{\sqrt(n)}\)).
- The SOCR CLT Experiment: To start the this Experiment, go to SOCR Experiments and select the SOCR Sampling Distribution CLT Experiment from the drop-down list of experiments in the left panel.
- SOCR Home page: http://www.socr.ucla.edu
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