In mathematics and its applications, the mean square is normally defined as the arithmetic mean of the squares of a set of numbers or of a random variable.[1]
It may also be defined as the arithmetic mean of the squares of the deviations between a set of numbers and a reference value (e.g., may be a mean or an assumed mean of the data),[2] in which case it may be known as mean square deviation.
When the reference value is the assumed true value, the result is known as mean squared error.
A typical estimate for the sample variance from a set of sample values uses a divisor of the number of values minus one, n-1, rather than n as in a simple quadratic mean, and this is still called the "mean square" (e.g. in analysis of variance):
The second moment of a random variable, is also called the mean square.
The square root of a mean square is known as the root mean square (RMS or rms), and can be used as an estimate of the standard deviation of a random variable.
^"Noise and Noise Rejection" (PDF). engineering.purdue.edu/ME365/Textbook/chapter11. Retrieved 6 January 2020.
^"OECD Glossary of Statistical Terms". oecd.org. Retrieved 6 January 2020.
In mathematics, the root meansquare (abbrev. RMS, RMS or rms) of a set of numbers is the square root of the set's meansquare. Given a set x i {\displaystyle...
In mathematics and its applications, the meansquare is normally defined as the arithmetic mean of the squares of a set of numbers or of a random variable...
In statistics, the meansquared error (MSE) or meansquared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures...
The root meansquare deviation (RMSD) or root meansquare error (RMSE) is either one of two closely related and frequently used measures of the differences...
meansquare (RMS) amplitude is used especially in electrical engineering: the RMS is defined as the square root of the mean over time of the square of...
Least meansquares (LMS) algorithms are a class of adaptive filter used to mimic a desired filter by finding the filter coefficients that relate to producing...
with unknown mean and unknown variance. No correction is necessary if the population mean is known. It is remarkable that the sum of squares of the residuals...
In bioinformatics, the root meansquare deviation of atomic positions, or simply root meansquare deviation (RMSD), is the measure of the average distance...
signal processing, a minimum meansquare error (MMSE) estimator is an estimation method which minimizes the meansquare error (MSE), which is a common...
Heronian mean Identric mean Lehmer mean Logarithmic mean Moving average Neuman–Sándor mean Quasi-arithmetic mean Root meansquare (quadratic mean) Rényi's...
statistical mechanics, the meansquared displacement (MSD, also meansquare displacement, average squared displacement, or meansquare fluctuation) is a measure...
≥ 1, convergence in r-th mean implies convergence in s-th mean. Hence, convergence in meansquare implies convergence in mean. Additionally, X n → L r...
DC component) is assumed. The RMS voltage is the square root of the mean over one cycle of the square of the instantaneous voltage. For an arbitrary periodic...
In statistics, the phi coefficient (or meansquare contingency coefficient and denoted by φ or rφ) is a measure of association for two binary variables...
In statistics the meansquared prediction error (MSPE), also known as meansquared error of the predictions, of a smoothing, curve fitting, or regression...
related to the meansquared error, the equivalent for mean absolute error is least absolute deviations. MAE is not identical to root-meansquare error (RMSE)...
acceptable model fit. The root meansquare residual (RMR) and standardized root meansquare residual (SRMR) are the square root of the discrepancy between...
{x}})^{2}} . The sample mean is also the best single predictor because it has the lowest root meansquared error. If the arithmetic mean of a population of...
and computing a mean for each sample. The mean's standard error turns out to equal the population standard deviation divided by the square root of the sample...
are common: Window design method Frequency sampling method Least MSE (meansquare error) method Parks–McClellan method (also known as the equiripple, optimal...
Squared deviations from the mean (SDM) result from squaring deviations. In probability theory and statistics, the definition of variance is either the...
statistics, expected meansquares (EMS) are the expected values of certain statistics arising in partitions of sums of squares in the analysis of variance...
In mathematics, the geometric mean is a mean or average which indicates a central tendency of a finite set of real numbers by using the product of their...
n]-x[m,n]\right|)} Measuring the average squared difference between two signals. Unlike the maximum error, meansquared error takes into account the overall...
can be judged by looking at their properties, such as unbiasedness, meansquare error, consistency, asymptotic distribution, etc. The construction and...
In mathematics, the harmonic mean is one of several kinds of average, and in particular, one of the Pythagorean means. It is sometimes appropriate for...
Global Information
