# Root-Mean-Square Deviation

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## root-mean-square deviation

[¦rüt ¦mēn ¦skwer ‚der·ə′vā·shən]
(statistics)
The square root of the sum of squared deviations from the mean divided by the number of observations in the sample.

## Root-Mean-Square Deviation

The root-mean-square (rms) deviation of the quantities x1, x2, …, xn from a is the square root of the expression The rms deviation has its least value when a = , where is the arithmetic mean of the quantities x1, x2, … xn In this case the rms deviation may serve as a measure of the dispersion of the system of quantities x1, x2, … xn. The more general concept of weighted rms deviation is also used; p1, … pn in this case are called the weights corresponding to the quantities x1, … xn. The weighted rms deviation attains its least value when a is equal to the weighted mean:

(p1x1 + ..... + pnxn)/(p1 + ... + pn)

In probability theory the weighted rms deviation σx of a random variable X (from its mathe matical expectation) is the square root of the variance , and is called the standard deviation of X.

The standard deviation is used as a measure of the quality of statistical estimates and in this case is called the standard error.

References in periodicals archive ?
First of all, purposefulness of the compensation of those errors was determined by comparing the mean error, the difference of maximum [[delta].sub.imax] and minimum [[delta].sub.imin] values with root-mean-square deviation [S.sub.PV] of error values
The following values of root-mean-square deviation were obtained after calculation:
The root-mean-square deviation of the module's random angular fluctuations resulting from the above variations is [S.sub.a] = 0.069".
5 illustrates that the estimate of the root-mean-square deviation of the spread of measurement results of the carriage's angular fluctuations on the vertical plane is dependent on the carriage's distance from the laser interferometer q calculated in accordance with the results of six realizations presented in Fig.
While the carriage is sliding from the minimum to the maximum 3500 mm distance from the laser interferometer, the mean value of root-mean-square deviation [S.sub.PV] of the spread of measurement results varies from 0.113" to 0.215".
The estimate of root-mean-square deviation of those vibrations is [S.sub.x] =1.7*[10.sup.-2] [micro]m.

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