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An Upper Bound on Standard Deviation as a Function of Range
Author(s) -
Petocz Peter
Publication year - 2005
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/j.1467-9639.2005.00206.x
Subject(s) - standard deviation , range (aeronautics) , function (biology) , mathematics , studentized range , statistics , geometric standard deviation , conjecture , relative standard deviation , set (abstract data type) , upper and lower bounds , econometrics , mathematical analysis , computer science , combinatorics , materials science , evolutionary biology , composite material , biology , detection limit , programming language
Summary This article disproves a conjecture that the ratio of the maximum standard deviation to the range of a set of data decreases as the number of data points increases. It also provides an alternative and more general approach for examining the standard deviation as a function of the range.