Editing Root mean square (section)

==Relationship to other statistics==
{{see also|Accuracy}}
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The [[standard deviation]] <math>\sigma_x=(x-\overline{x})_\text{rms}</math> of a [[statistical population|population]] or a [[waveform]] <math>x</math> is the RMS deviation of <math>x</math> from its [[arithmetic mean]] <math>\bar{x}</math>.  They are related to the RMS value of <math>x</math> by <ref>
{{cite book
| title=Digital signal transmission
| edition=2nd
| author1=Chris C. Bissell
| author2=David A. Chapman
| publisher=Cambridge University Press
| year=1992
| isbn=978-0-521-42557-5
| page=64
}}</ref>
:<math>\sigma_x^2 = \overline{(x-\overline{x})^2} = x_\text{rms}^2 - \overline{x}^2 </math>.  

From this it is clear that the RMS value is always greater than or equal to the average, in that the RMS includes the squared deviation (error) as well.

Physical scientists often use the term ''root mean square'' as a synonym for [[standard deviation]] when it can be assumed the input signal has zero mean, that is, referring to the square root of the mean squared deviation of a signal from a given baseline or fit.<ref>
{{cite encyclopedia
| title=Root-Mean-Square
| url=https://mathworld.wolfram.com/Root-Mean-Square.html
| last=Weisstein|first=Eric W.
| encyclopedia=[[MathWorld]]
}}</ref><ref>{{cite web
| title=ROOT, TH1:GetRMS
| url=http://root.cern.ch/root/html/TH1.html#TH1:GetRMS
| access-date=2013-07-18
| archive-date=2017-06-30
| archive-url=https://web.archive.org/web/20170630033713/http://root.cern.ch/root/html/TH1.html#TH1:GetRMS
| url-status=dead
}}</ref> This is useful for electrical engineers in calculating the "AC only" RMS of a signal. Standard deviation being the RMS of a signal's variation about the mean, rather than about 0, the [[DC component]] is removed (that is, RMS(signal) = stdev(signal) if the mean signal is 0).