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Module by: Paul E Pfeiffer. E-mail the author

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 Name: Variance ID: m23441 Language: English (en) Summary: The mean value locates the center of the probability mass distribution induced by X on the real line. In this unit, we examine how expectation may be used for further characterization of the distribution for X. In particular, we deal with the variance and its square root the standard deviation. We identify some important properties of variance and identify the concept covariance. The variance is calculated for several distributions, comparing analytical and Matlab results. Subject: Mathematics and Statistics Keywords: Basic patterns for variance, Calculating formula, Chebyshev inequality, Matlab examples, Spread of probability mass, Standard deviation, Uncorrelated random variables, Variance, Various examples License: Creative Commons Attribution License CC-BY 3.0 Authors: Copyright Holders: Maintainers: Latest version: 1.7 (history) First publication date: Apr 17, 2009 12:07 pm -0500 Last revision to module: Sep 18, 2009 2:03 pm -0500

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## Version History

 Version: 1.7 Sep 18, 2009 2:03 pm -0500 by Changes: `added google analytics tracking code` Version: 1.6 Jul 28, 2009 2:00 pm -0500 by Changes: `Summary added` Version: 1.5 Jul 27, 2009 12:19 pm -0500 by Changes: `disjoint union fix` Version: 1.4 Jun 19, 2009 11:30 am -0500 by Changes: `m-file fixes, supplemental links, metadata updated` Version: 1.3 Jun 9, 2009 5:31 pm -0500 by Changes: `updated links, images and accessibility` Version: 1.2 May 26, 2009 4:47 pm -0500 by Changes: `fixed module names, and updated content structure` Version: 1.1 May 18, 2009 5:00 pm -0500 by Changes: `Content`

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## How to Cite and Attribute This Content

The following citation styles comply with the attribution requirements for the license (CC-BY 3.0) of this work:

### American Chemical Society (ACS) Style Guide:

Pfeiffer, P. Variance, Connexions Web site. http://cnx.org/content/m23441/1.7/, Sep 18, 2009.

### American Medical Assocation (AMA) Manual of Style:

Pfeiffer P. Variance [Connexions Web site]. September 18, 2009. Available at: http://cnx.org/content/m23441/1.7/.

### American Psychological Assocation (APA) Publication Manual:

Pfeiffer, P. (2009, September 18). Variance. Retrieved from the Connexions Web site: http://cnx.org/content/m23441/1.7/

### Chicago Manual of Style (Bibliography):

Pfeiffer, Paul. "Variance." Connexions. September 18, 2009. http://cnx.org/content/m23441/1.7/.

### Chicago Manual of Style (Note):

Paul Pfeiffer, "Variance," Connexions, September 18, 2009, http://cnx.org/content/m23441/1.7/.

### Chicago Manual of Style (Reference, in Author-Date style):

Pfeiffer, P. 2009. Variance. Connexions, September 18, 2009. http://cnx.org/content/m23441/1.7/.

### Modern Languages Association (MLA) Style Manual:

Pfeiffer, Paul. Variance. Connexions. 18 Sep. 2009 <http://cnx.org/content/m23441/1.7/>.