Editing Mathematics (section)

=== Statistics and other decision sciences ===
{{Main|Statistics|Probability theory}}
[[File:IllustrationCentralTheorem.png|upright=1.5|thumb|right|Whatever the form of a random population [[Probability distribution|distribution]] (μ), the sampling [[mean]] (x̄) tends to a [[Gaussian distribution]] and its [[variance]] (σ) is given by the [[central limit theorem]] of probability theory.<ref>{{cite book |last=Rouaud |first=Mathieu |date=April 2017 |orig-date=First published July 2013 |title=Probability, Statistics and Estimation |page=10 |url=http://www.incertitudes.fr/book.pdf |url-status=live |archive-url=https://ghostarchive.org/archive/20221009/http://www.incertitudes.fr/book.pdf |archive-date=October 9, 2022 |access-date=February 13, 2024}}</ref>|class=skin-invert-image]]

The field of statistics is a mathematical application that is employed for the collection and processing of data samples, using procedures based on mathematical methods especially [[probability theory]]. Statisticians generate data with [[random sampling]] or randomized [[design of experiments|experiments]].<ref>{{cite book |last=Rao |first=C. Radhakrishna |author-link=C. R. Rao |year=1997 |orig-date=1989 |title=Statistics and Truth: Putting Chance to Work |edition=2nd |pages=3–17, 63–70 |publisher=World Scientific |isbn=981-02-3111-3 |lccn=97010349 |mr=1474730 |oclc=36597731}}</ref>

[[Statistical theory]] studies [[statistical decision theory|decision problems]] such as minimizing the [[risk]] ([[expected loss]]) of a statistical action, such as using a [[statistical method|procedure]] in, for example, [[parameter estimation]], [[hypothesis testing]], and [[selection algorithm|selecting the best]]. In these traditional areas of [[mathematical statistics]], a statistical-decision problem is formulated by minimizing an [[objective function]], like expected loss or [[cost]], under specific constraints. For example, designing a survey often involves minimizing the cost of estimating a population mean with a given level of confidence.<ref name="RaoOpt">{{cite book |last=Rao |first=C. Radhakrishna |author-link=C.R. Rao |editor1-last=Arthanari |editor1-first=T.S. |editor2-last=Dodge |editor2-first=Yadolah |editor2-link=Yadolah Dodge |chapter=Foreword |title=Mathematical programming in statistics |series=Wiley Series in Probability and Mathematical Statistics |publisher=Wiley |location=New York |year=1981 |pages=vii–viii |isbn=978-0-471-08073-2 |lccn=80021637 |mr=607328 |oclc=6707805}}</ref> Because of its use of [[optimization]], the mathematical theory of statistics overlaps with other [[decision science]]s, such as [[operations research]], [[control theory]], and [[mathematical economics]].{{sfn|Whittle|1994|pp=10–11, 14–18}}