Editing Root mean square (section)

==Definition==
The RMS value of a set of values (or a [[continuous-time]] [[waveform]]) is the square root of the arithmetic mean of the squares of the values, or the square of the function that defines the continuous waveform. 

In the case of a set of ''n'' values <math>\{x_1,x_2,\dots,x_n\}</math>, the RMS is
:<math>
x_\text{RMS} = \sqrt{ \frac{1}{n} \left( {x_1}^2 + {x_2}^2 + \cdots + {x_n}^2 \right) }.
</math>

The corresponding formula for a continuous function (or waveform) ''f''(''t'') defined over the interval <math>T_1 \le t \le T_2</math> is
:<math>
f_\text{RMS} = \sqrt {{1 \over {T_2-T_1}} {\int_{T_1}^{T_2} {[f(t)]}^2\, {\rm d}t}},
</math>

and the RMS for a function over all time is
:<math>
f_\text{RMS} = \lim_{T\rightarrow \infty} \sqrt {{1 \over {2T}} {\int_{-T}^{T} {[f(t)]}^2\, {\rm d}t}}.
</math>

The RMS over all time of a [[periodic function]] is equal to the RMS of one period of the function. The RMS value of a continuous function or signal can be approximated by taking the RMS of a sample consisting of equally spaced observations. Additionally, the RMS value of various waveforms can also be determined without [[Calculus#Integral calculus|calculus]], as shown by Cartwright.<ref>{{cite journal |last=Cartwright|first=Kenneth V|title=Determining the Effective or RMS Voltage of Various Waveforms without Calculus|journal=Technology Interface|volume=8|issue=1|pages=20 pages|date=Fall 2007|url=http://tiij.org/issues/issues/fall2007/30_Cartwright/Cartwright-Waveforms.pdf}}</ref>

In the case of the RMS statistic of a [[random process]], the [[expected value]] is used instead of the mean.