Gaussian Distributions©
Kevin Lehmann
Department of Chemistry
Princeton University
Princeton, NJ 08544
United States
mail to: Lehmann@princeton.edu



Abstract
In this document the author presents a broad treatment of the properties of Gaussian distributions. In a systematic development of the topic the author generates a set of data from a Gaussian distribution and then analyzes the distribution using standard statistical methods to illustrate the properties of the distribution. The document proceeds to include an analysis of the mean of a set of laboratory measurements and the confidence level for the mean of the data with respect to the assumption that the set of data is from a Gaussian parent distribution. The chi-squared function is introduced to show that for a sample of modest size the estimate of the standard deviation calculated from the computed variance can be quite different from the true value for the distribution. This leads to the Student t Distribution. The document concludes with a discussion of the mean absolute deviation and a survey of the Moments of a distribution and how the mean absolute deviation and the moments are used to characterize the shape of the distribution. Variance, skew, and kurtosis are the three moments discussed in this document. This document would be valuable for anyone wishing to learn more about Gaussian distributions and their properties. This document is suitable for advanced undergraduates and graduate students. Sixteen exercises at the end of the document permit the learner to use the concepts and test their mastery of these concepts. Other Mathcad documents by this author in this collection will address other aspects of numerical methods in chemistry.
Keywords
Audiences: Upper-Division Undergraduate, Graduate Education / Research
Pedagogies: Computer-Based Learning
Domains: Analytical Chemistry, Laboratory Instruction, Physical Chemistry
Topics: Chemometrics, Mathematics / Symbolic Mathematics
Documents
File NameDescriptionSoftware TypeSoftware Version
GaussianDistribution.mcd Mathcad Computational Document Mathcad
GaussianDistribution.pdf Read-Only Document
Comments to: Kevin Lehmann at Lehman@princeton.edu.
©Copyright Kevin Lehmann, 1997. All rights reserved. You are welcome to use this document in your own classes but commercial use is not allowed without the permission of the author.