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Teaching univariate measures of location‐using loss functions
Author(s) -
Paolino JonPaul
Publication year - 2017
Publication title -
teaching statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.425
H-Index - 13
eISSN - 1467-9639
pISSN - 0141-982X
DOI - 10.1111/test.12144
Subject(s) - univariate , curriculum , mathematics education , statistical analysis , computer science , sample size determination , statistical software , software , sample (material) , statistics , descriptive statistics , calculus (dental) , mathematics , psychology , machine learning , multivariate statistics , medicine , programming language , pedagogy , chemistry , chromatography , dentistry
Summary This article presents a new method for introductory teaching of the sample mean, median and mode(s) from a univariate dataset. These basic statistical concepts are taught at various levels of education from elementary school curriculums to courses at the tertiary level. These descriptive measures of location can be taught as optimized solutions to certain loss functions. Although proving these require some understanding of derivatives as used in a first year calculus course, the attained insight is valuable for higher level statistical thinking. Using the statistical computing software R, we visually illustrate the minimization of these loss functions using some example datasets.