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Square root of the mean square
In mathematics, the root mean square (abbrev. RMS, rms or rms) of a set of values is the square root of the set's mean square. Given a set x i {\displaystyle
Root_mean_square
Statistical measure
The root mean square deviation (RMSD) or root mean square error (RMSE) is a frequently used measure of the distances between actual observed values and
Root_mean_square_deviation
Measure of the error of an estimator
square of the quantity being estimated. In an analogy to standard deviation, taking the square root of MSE yields the root-mean-square error or root-mean-square
Mean_squared_error
Average of squared values of a sample
{\displaystyle E(X^{2})} 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
Mean_square
Specific probability distribution function, important in physics
The mean square speed ⟨ v 2 ⟩ {\displaystyle \langle v^{2}\rangle } is the second-order raw moment of the speed distribution. The "root mean square speed"
Maxwell–Boltzmann distribution
Maxwell–Boltzmann_distribution
Measure of change in a periodic variable
spectroscopy). Root mean square (RMS) amplitude is used especially in electrical engineering: the RMS is defined as the square root of the mean over time of
Amplitude
Statistical error measure
related to the mean squared error, the equivalent for mean absolute error is least absolute deviations. MAE is not identical to root-mean square error (RMSE)
Mean_absolute_error
Measure of the deviation of position over time
statistical mechanics, the mean squared displacement (MSD), also called mean square displacement, average squared displacement, or mean square fluctuation, is a
Mean_squared_displacement
Form of statistical factor analysis
acceptable model fit. The root mean square residual (RMR) and standardized root mean square residual (SRMR) are the square root of the discrepancy between
Confirmatory_factor_analysis
Statistical model validation technique
value being predicted is continuously distributed, the mean squared error, root mean squared error or median absolute deviation could be used to summarize
Cross-validation_(statistics)
Electric current that periodically reverses direction
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
Alternating_current
Concept in signal processing
_{n=0}^{N-1}\left|x[m,n]\right|^{2}}}} Root-mean-square deviation is derived from MSE by taking the square root of the MSE. It downscale the MSE, providing
Similarity (signal processing)
Similarity_(signal_processing)
Machine learning technique
^{(t)})^{2}={\frac {1}{D}}\sum _{i=1}^{D}(x_{i}^{(t)}-\mu ^{(t)})^{2}} Root mean square layer normalization (RMSNorm): x i ^ = x i 1 D ∑ j = 1 D x j 2 , y
Normalization (machine learning)
Normalization_(machine_learning)
Measure of distance between atoms of superimposed proteins
In bioinformatics, the root mean square deviation of atomic positions, or simply root mean square deviation (RMSD), is the measure of the average distance
Root mean square deviation of atomic positions
Root_mean_square_deviation_of_atomic_positions
Statistical measure of the magnitude of a phenomenon
effect size estimator for multiple comparisons (e.g., ANOVA) is the Ψ root-mean-square standardized effect: Ψ = 1 k − 1 ⋅ ∑ j = 1 k ( μ j − μ σ ) 2 {\displaystyle
Effect_size
Quantity derived from seismic data
computes the square root of the sum of squared amplitudes divided by the number of samples within the specified window used. With this root mean square amplitude
Seismic_attribute
Mathematical relationships
(GM), arithmetic mean (AM), and quadratic mean (QM; also known as root mean square). Suppose that x 1 , x 2 , … , x n {\displaystyle x_{1},x_{2},\ldots
QM–AM–GM–HM_inequalities
Ballistics measure of a weapon system's precision
An associated concept, the DRMS (distance root mean square), calculates the square root of the average squared distance error, a form of the standard deviation
Circular_error_probable
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
statistics, the coefficient of variation (CV), also known as normalized root-mean-square deviation (NRMSD), and relative standard deviation (RSD), is a standardized
Coefficient_of_variation
Number taken as representative of a list of numbers
mean Logarithmic mean Moving average Neuman–Sándor mean Quasi-arithmetic mean Root mean square (quadratic mean) Rényi's entropy (a generalized f-mean)
Average
Measure of forecasting quality
The mean absolute scaled error has favorable properties when compared to other methods for calculating forecast errors, such as root-mean-square-deviation
Mean_absolute_scaled_error
Type of algorithm
calculating the optimal rotation matrix that minimizes the RMSD (root mean squared deviation) between two paired sets of points. It is useful for point-set
Kabsch_algorithm
N-th root of the arithmetic mean of the given numbers raised to the power n
Minkowski distance Quasi-arithmetic mean – another name for the generalized f-mean mentioned above Root mean square If NM = a and PM = b. AM = AM of a
Generalized_mean
Unit of measurement for amplitude levels in digital systems
of −6 dBFS, which is 6 dB below full scale. Conventions differ for root mean square (RMS) measurements, but all peak measurements smaller than the maximum
DBFS
Dataflow programming language
sqroot(avg(square(a))) where square(x) = x*x; avg(y) = mean where n = 1 fby n+1; mean = first y fby mean + d; d = (next y - mean)/(n+1); end; sqroot(z)
Lucid_(programming_language)
Type of average of a collection of numbers
{x}})^{2}} . The sample mean is also the best single predictor because it has the lowest root mean squared error. If the arithmetic mean of a population of
Arithmetic_mean
harmonic mean, G is geometric mean, L is the logarithmic mean, A is the arithmetic mean, R is the root mean square and C is the contraharmonic mean. Unless
Contraharmonic_mean
N-th root of the product of n numbers
numbers is the square root of their product, for example with numbers 2 {\displaystyle 2} and 8 {\displaystyle 8} the geometric mean is 2 ⋅ 8 = {\displaystyle
Geometric_mean
Measurement of the harmonic distortion present in a signal
These can be distinguished as THDF (for "fundamental"), and THDR (for "root mean square"). THDR cannot exceed 100%. At low distortion levels, the difference
Total_harmonic_distortion
SI unit of apparent power in an electrical circuit
electrical circuit. It is the product of the root mean square voltage (in volts) and the root mean square current (in amperes). Volt-amperes are usually
Volt-ampere
Distance from center of mass to axis of rotation
by the SI unit metre. Mathematically the radius of gyration is the root mean square distance of the object's parts from either its center of mass or a
Radius_of_gyration
Physical constant relating particle kinetic energy with temperature
the root-mean-square speed of the atoms, which turns out to be inversely proportional to the square root of the atomic mass. The root mean square speeds
Boltzmann_constant
Statistics concept
root mean square error (RMSE) is the square root of MSE. The sum of squares of errors (SSE) is the MSE multiplied by the sample size. Sum of squares of
Errors_and_residuals
Formula for the average value of a function over its domain
notions of the mean of a function. There is also a harmonic average of functions and a quadratic average (or root mean square) of functions. Mean Dougherty
Mean_of_a_function
Audible vibration that travels via pressure waves in matter
usually averaged over time and/or space, and a square root of this average provides a root mean square (RMS) value. For example, 1 Pa RMS sound pressure (94
Sound
Algorithm in numerical analysis
worst-case error that grows proportional to n {\displaystyle n} , and a root mean square error that grows as n {\displaystyle {\sqrt {n}}} for random inputs
Kahan_summation_algorithm
Hypotenuse of right triangle from its sides
quadrature. A scaled version of this operation gives the quadratic mean or root mean square. It is available in many programming libraries as the hypot function
Pythagorean_addition
Electronic circuit
is often converted into a direct current of equivalent value, the root mean square (RMS). Simple instrumentation and signal converters carry out this
True_RMS_converter
Ratio of active power to apparent power
electricity for performing work. Apparent power is the product of root mean square (RMS) current and voltage. Apparent power is often higher than real
Power_factor
Classical averages studied in ancient Greece
classical Pythagorean means are the arithmetic mean (AM), the geometric mean (GM), and the harmonic mean (HM). These means were studied with proportions
Pythagorean_means
Number whose square is a given number
mathematics, a square root of a number x is a number y such that y 2 = x {\displaystyle y^{2}=x} ; in other words, a number y whose square (the result of
Square_root
waveform (signal) is the ratio of the RMS (root mean square) value to the average value (mathematical mean of absolute values of all points on the waveform)
Form_factor_(electronics)
Logarithmic unit expressing the ratio of physical quantities
where Vout is the root-mean-square (rms) output voltage, Vin is the rms input voltage. A similar formula holds for current. The term root-power quantity
Decibel
Performance measure of a digital radio
difference between actual received symbols and ideal symbols. The root mean square (RMS) average amplitude of the error vector, normalized to ideal signal
Error_vector_magnitude
Positive real number which when multiplied by itself gives 6
product of 2 and 3, the square root of 6 is the geometric mean of 2 and 3, and is the product of the square root of 2 and the square root of 3, both of which
Square_root_of_6
Measure of variation in statistics
probability distribution is the square root of its variance (the variance being the average of the squared deviations from the mean). A useful property of the
Standard_deviation
Measure of surface finish or texture
peak. The average wavelength λ {\displaystyle \lambda } a and the root mean square wavelength λ {\displaystyle \lambda } q are derived from Δ {\displaystyle
Surface_roughness
Typical velocity of the thermal motion of particles
velocities: If v th {\displaystyle v_{\text{th}}} is defined as the root mean square of the velocity in any one dimension (i.e. any single direction), then
Thermal_velocity
Variation in the time intervals between heartbeats
longer than 5 minutes. RMSSD (root mean square of successive differences), the square root of the mean of the squares of the successive differences between
Heart_rate_variability
Device for acoustic measurements
distinguishable by the voltage value produced when a known, constant root mean square sound pressure is applied. This is known as microphone sensitivity
Sound_level_meter
Type of motion in mechanical engineering
the usual ways to specify random vibrations. The root mean square acceleration (Grms) is the square root of the area under the ASD curve in the frequency
Random_vibration
Mathematics and basic principles of three-phase electric power
generators and motors running smoothly. Notice also that using the root mean square voltage V = V p 2 {\displaystyle V={\frac {V_{p}}{\sqrt {2}}}} , the
Mathematics of three-phase electric power
Mathematics_of_three-phase_electric_power
log-spectral distance (LSD), also referred to as log-spectral distortion or root mean square log-spectral distance, is a distance measure between two spectra. The
Log-spectral_distance
Mathematical diagram
terms of three statistics: the Pearson correlation coefficient, the root-mean-square error (RMSE) error, and the standard deviation. Although Taylor diagrams
Taylor_diagram
Clock deviation from perfect periodicity
be quantified in the same terms as all time-varying signals, e.g., root mean square (RMS), or peak-to-peak displacement. Also, like other time-varying
Jitter
Indicator for how well data points fit a line or curve
coefficient Proportional reduction in loss Regression model validation Root mean square deviation Stepwise regression Steel, R. G. D.; Torrie, J. H. (14 July
Coefficient_of_determination
Arithmetic mean is greater than or equal to geometric mean
The geometric mean is similar, except that it is only defined for a list of nonnegative real numbers, and uses multiplication and a root in place of addition
AM–GM_inequality
Form of causal modeling that fit networks of constructs to data
for some common indices: the RMSEA (Root Mean Square Error of Approximation), SRMR (Standardized Root Mean Squared Residual), CFI (Confirmatory Fit Index)
Structural_equation_modeling
Test statistic
dating and variance of unit weight in the context of weighted least squares. Its square root is called regression standard error, standard error of the regression
Reduced_chi-squared_statistic
Geometric condition for workpieces and tools
several flatness measures: least squares reference plane minimum zone reference planes local flatness deviation root-mean-square flatness deviation The two-dimensional
Flatness_(manufacturing)
Algorithms for calculating square roots
Square root algorithms compute the non-negative square root S {\displaystyle {\sqrt {S}}} of a positive real number S {\displaystyle S} . Since all square
Square_root_algorithms
Large language model by Meta AI
arXiv:1607.06450 [stat.ML]. Zhang, Biao; Sennrich, Rico (2019-10-01). "Root Mean Square Layer Normalization". arXiv:1910.07467 [cs.LG]. Goldman, Sharon (2023-04-18)
Llama_(language_model)
Calculations in probability theory
Squared deviations from the mean (SDM) result from squaring deviations. In probability theory and statistics, the definition of variance is either the
Squared deviations from the mean
Squared_deviations_from_the_mean
one full period of the waveform. While conceptually similar to the root mean square (RMS), ARV will differ from it whenever a function's absolute value
Average_rectified_value
Mean kinetic energy per unit mass of eddies in turbulent flow
Physically, the turbulence kinetic energy is characterized by measured root-mean-square (RMS) velocity fluctuations. In the Reynolds-averaged Navier Stokes
Turbulence_kinetic_energy
Artificial intelligence program by DeepMind
2 achieved a median score of 87.[citation needed] Measured by the root-mean-square deviation (RMS-D) of the placement of the alpha-carbon atoms of the
AlphaFold
Peak divided by the Root mean square (RMS) of the waveform
Noise - "The standard deviation of a Gaussian noise voltage is the root-mean-square or rms value of the voltage." Noise: Frequently Asked Questions - "Noise
Crest_factor
Measure of the size of atomic nuclei
which a mean can be taken. The qualification of "rms" (root mean square) arises because it is the nuclear cross-section, proportional to the square of the
Charge_radius
Measure of directional electromagnetic energy flux
}}={\frac {\mathsf {E_{\text{rms}}^{2}}}{\eta }},} where Erms is the root mean square (RMS) electric field amplitude. In the important case that E(t) is
Poynting_vector
Electronic measuring instrument that combines several measurement functions in one unit
Since the rectified average value and the root mean square (RMS) value of a waveform are only the same for a square wave, simple rectifier-type circuits can
Multimeter
Optimization algorithm
introduced with AdaGrad (for "Adaptive Gradient") in 2011 and RMSprop (for "Root Mean Square Propagation") in 2012. In 2014, Adam (for "Adaptive Moment Estimation")
Stochastic_gradient_descent
Process of a gas escaping through a small hole
pressure and temperature, the root-mean-square speed and therefore the effusion rate are inversely proportional to the square root of the molecular weight.
Effusion
Understanding of gas properties in terms of molecular motion
of speeds). See: Average, Root-mean-square speed Arithmetic mean Mean Mode (statistics) In kinetic theory of gases, the mean free path is the average distance
Kinetic_theory_of_gases
Mean amplitude of a waveform in the time domain
JPEG. Electronics portal Energy portal Phantom power Root-mean-square amplitude Root-mean-square voltage Kees Schouhamer Immink (March 1997). "Performance
DC_bias
Rate at which electrical energy is transferred by an electric circuit
is the peak current in amperes Vrms is the root-mean-square voltage in volts Irms is the root-mean-square current in amperes θ = θv − θi is the phase
Electric_power
Random fluctuation in an electrical signal
relatively constant, but the individual raindrops arrive discretely. The root-mean-square value of the shot noise current in is given by the Schottky formula
Noise_(electronics)
Topics referred to by the same term
known as ARMS Alveolar rhabdomyosarcoma, a form of cancer Arms, Amps root mean square, seen in electrical specifications often as the unit of current Search
Arms
Process forming a path from many random steps
any distribution with zero mean and a finite variance (not necessarily just a normal distribution), the root mean square translation distance after n
Random_walk
Unique positive real number which when multiplied by itself gives 2
The square root of 2 (approximately 1.4142) is the positive real number that, when multiplied by itself or squared, equals the number 2. It may be written
Square_root_of_2
Type of lower-voltage electricity most commonly provided by utilities
voltages are generally in the range 100–240 V (always expressed as root-mean-square voltage). The two commonly used frequencies are 50 Hz and 60 Hz. Single-phase
Mains_electricity
Ratio of the desired signal to the background noise
{A_{\mathrm {signal} }}{A_{\mathrm {noise} }}}\right)^{2},} where A is root mean square (RMS) amplitude (for example, RMS voltage). Because many signals have
Signal-to-noise_ratio
Electrical standard designed to protect against electric shock
exceed 120 volts (V) for ripple-free direct current (DC) or 50 VRMS (root mean square volts) for alternating current (AC). The IEC and IET go on to define
Extra-low_voltage
Study of the separation, identification, and quantification of matter
spectral density is constant throughout the frequency spectrum. The root mean square value of the thermal noise in a resistor is given by v R M S = 4 k
Analytical_chemistry
Measure of statistical error
Minimum mean-square error Squared deviations Peak signal-to-noise ratio Root mean square deviation Errors and residuals in statistics Khan, Aman U.; Hildreth
Mean_percentage_error
Unit for the arithmetic difference of two percentages
related descriptive statistics, including the standard deviation and root-mean-square error, the result should be expressed in units of percentage points
Percentage_point
Maximum range of an indicator
assessment of the magnitude of roughness. Statistical methods such as root mean square (RMS) duly address the "total" idea in this respect. The newer name
Total_indicator_reading
Region in space
than the average CMB temperature (approximately 2.7 K), whereas the root mean square of typical temperature variations is only 18 μK. At some points, the
CMB_cold_spot
Mathematical operation that predicts future values of a discrete-time signal
the root mean square criterion which is also called the autocorrelation criterion. In this method we minimize the expected value of the squared error
Linear_prediction
Measurement in communication theory
Another method of specifying spectral width is a special case of root-mean-square deviation where the independent variable is wavelength, λ, and f (λ)
Spectral_width
Solid (crystalline) phase of electrons
critical rs. The criterion states that the crystal melts when the root-mean-square displacement of the electrons ⟨ r 2 ⟩ {\displaystyle {\sqrt {\langle
Wigner_crystal
Statistics concept
is called sum squared prediction error. The root mean squared prediction error is the square root of MSPE: RMSPE=√MSPE. The mean squared prediction error
Mean_squared_prediction_error
Discrete Fourier transform algorithm
𝜀 is the machine floating-point relative precision. In fact, the root mean square (rms) errors are much better than these upper bounds, being only O
Fast_Fourier_transform
Ruze's equation is an equation relating the gain of an antenna to the root mean square (RMS) of the antenna's random surface errors. The equation was originally
Ruze's_equation
Length scale at which eddy currents are significantly affected by viscosity
{1}{\sqrt {3}}}{\sqrt {(v'_{1})^{2}+(v'_{2})^{2}+(v'_{3})^{2}}}} is the root mean square of the velocity fluctuations. The Taylor microscale is given as λ =
Taylor_microscale
is the root mean square (rms) delay spread. Denoting the power delay profile of the channel by A c ( τ ) {\displaystyle A_{c}(\tau )} , the mean delay
Delay_spread
Approximation method in statistics
Least-squares spectral analysis Measurement uncertainty Orthogonal projection Proximal gradient methods for learning Quadratic loss function Root mean square
Least_squares
Electrical noise due to thermal vibration within a conductor
approximately 13 nV/√Hz at room temperature. The square root of the mean square voltage yields the root mean square (RMS) voltage observed over the bandwidth
Johnson–Nyquist_noise
Type of amplifier that emphasizes a specific frequency in a noisy signal
than the signal. In the simplest case of white noise, even if the root mean square of noise is 103 times as large as the signal to be recovered, if the
Lock-in_amplifier
Property of a charged particle beam
distribution, the emittance of the beam may be specified in terms of the root mean square value of x {\displaystyle x} and the fraction of the beam to be included
Beam_emittance
Measure of similarity between two protein structures
program. It is intended as a more accurate measurement than the common root-mean-square deviation (RMSD) metric - which is sensitive to outlier regions created
Global_distance_test
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