Root Mean Square
In mathematics, the root mean square (abbrev. RMS, RMS or rms) of a set of numbers is the square root of the set's mean square.
Given a set
x
i
{\displaystyle x_{i}}
, its RMS is denoted as either
x
R
M
S
{\displaystyle x_{\mathrm {RMS} }}
or
R
M
S
x
{\displaystyle \mathrm {RMS} _{x}}
. The RMS is also known as the quadratic mean (denoted
M
2
{\displaystyle M_{2}}
), a special case of the generalized mean. The RMS of a continuous function is denoted
f
R
M
S
{\displaystyle f_{\mathrm {RMS} }}
and can be defined in terms of an integral of the square of the function.
The RMS of an alternating electric current equals the value of constant direct current that would dissipate the same power in a resistive load.
In estimation theory, the root-mean-square deviation of an estimator measures how far the estimator strays from the data.
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