Root-mean-square

In statistics and its applications, the root mean square (abbreviated RMS or rms) is defined as the square root of mean square (the arithmetic mean of the squares of a set of numbers). The RMS is also known as the quadratic mean and is a particular case of the generalized mean with exponent 2. RMS can also be defined for a continuously varying function in terms of an integral of the squares of the instantaneous values during a cycle.

For a cyclically alternating electric current, RMS is equal to the value of the direct current that would produce the same average power dissipation in a resistive load. In Estimation theory the root mean square error of an estimator is a measure of the imperfection of the fit of the estimator to the data.

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 Physics, the RMS current is the "value of the direct current that dissipates power in a resistor."

In the case of a set of n values ${\displaystyle \{x_{1},x_{2},\dots ,x_{n}\}}$, the RMS

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