Editing Root mean square (section)

{{Short description|Square root of the mean square}}
In [[mathematics]], the '''root mean square''' (abbrev. '''RMS''', '''{{sc|rms}}''' or '''rms''') of a [[set (mathematics)|set]] of values is the [[square root]] of the set's [[mean square]].<ref name=dicphys>{{cite book
|title=A Dictionary of Physics (6 ed.)
|chapter=Root-mean-square value
|publisher=Oxford University Press
|year=2009
|isbn=9780199233991
|url=https://www.oxfordreference.com/view/10.1093/acref/9780199233991.001.0001/acref-9780199233991-e-2676
}}</ref>
Given a set <math>x_i</math>, its RMS is denoted as either <math>x_\mathrm{RMS}</math> or <math>\mathrm{RMS}_x</math>. The RMS is also known as the '''quadratic mean''' (denoted <math>M_2</math>),<ref>{{cite book |last1=Thompson |first1=Sylvanus P. |title=Calculus Made Easy |date=1965 |publisher=Macmillan International Higher Education |isbn=9781349004874 |page=185 |url=https://books.google.com/books?id=6VJdDwAAQBAJ&pg=PA185 |access-date=5 July 2020 }}{{Dead link|date=August 2023 |bot=InternetArchiveBot |fix-attempted=yes }}</ref><ref>{{cite book |last1=Jones |first1=Alan R. |title=Probability, Statistics and Other Frightening Stuff |date=2018 |publisher=Routledge |isbn=9781351661386 |page=48 |url=https://books.google.com/books?id=OvtsDwAAQBAJ&pg=PA48 |access-date=5 July 2020}}</ref> a special case of the [[generalized mean#Quadratic|generalized mean]]. The RMS of a continuous [[function (mathematics)|function]] is denoted <math>f_\mathrm{RMS}</math> and can be defined in terms of an [[integral]] of the square of the function.
In [[estimation theory]], the [[root-mean-square deviation]] of an estimator measures how far the estimator strays from the data.