Is Root Mean Square The Same As Standard Error
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be challenged and removed. (March 2010) (Learn how and when to remove this template message) 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 root mean square calculator squares of a set of numbers).[1] The RMS is also known as the quadratic root mean square velocity mean and is a particular case of the generalized mean with exponent 2. RMS can also be defined for a continuously varying function
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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
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power dissipation in a resistive load.[1] In econometrics the root mean square error of an estimator is a measure of the imperfection of the fit of the estimator to the data. Contents 1 Definition 2 RMS of common waveforms 2.1 RMS of waveform combinations 3 Uses 3.1 In electrical engineering 3.1.1 Root-mean-square voltage 3.1.2 Average electrical power 3.2 Root-mean-square speed 3.3 Root-mean-square error 4 RMS in frequency domain 5 Relationship to other statistics 6 rms matlab See also 7 References 8 External links Definition[edit] 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 the case of a set of n values { x 1 , x 2 , … , x n } {\displaystyle \{x_{1},x_{2},\dots ,x_{n}\}} , the RMS x r m s = 1 n ( x 1 2 + x 2 2 + ⋯ + x n 2 ) . {\displaystyle x_{\mathrm {rms} }={\sqrt {{\frac {1}{n}}\left(x_{1}^{2}+x_{2}^{2}+\cdots +x_{n}^{2}\right)}}.} The corresponding formula for a continuous function (or waveform) f(t) defined over the interval T 1 ≤ t ≤ T 2 {\displaystyle T_{1}\leq t\leq T_{2}} is f r m s = 1 T 2 − T 1 ∫ T 1 T 2 [ f ( t ) ] 2 d t , {\displaystyle f_{\mathrm {rms} }={\sqrt {{1 \over {T_{2}-T_{1}}}{\int _{T_{1}}^{T_{2}}{[f(t)]}^{2}\,dt}}},} and the RMS for a function over all time is f r m s = lim T → ∞ 1 T ∫ 0 T [ f ( t ) ] 2 d t . {\displaystyle f_{\mathrm {rms} }=\lim _{T\rightarrow \infty }{\sqrt {{1 \over {T}}{\int _{0}^{T}{[f(t)]}^{2}\,dt}}}.} The RMS over all time of a periodic function is equal to t
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Root Mean Square Error Matlab
nurturedbyEricWeisstein at WolframResearch Probability and Statistics>Moments> Calculus and Analysis>Special Functions>Means> Interactive Entries>Interactive root mean square error excel Demonstrations> Root-Mean-Square For a set of numbers or values of a discrete distribution , ..., , the root-mean-square rms in excel (abbreviated "RMS" and sometimes called the quadratic mean), is the square root of mean of the values , namely (1) (2) (3) where denotes the mean of the values . https://en.wikipedia.org/wiki/Root_mean_square For a variate from a continuous distribution , (4) where the integrals are taken over the domain of the distribution. Similarly, for a function periodic over the interval ], the root-mean-square is defined as (5) The root-mean-square is the special case of the power mean. Hoehn and Niven (1985) show that (6) for any positive constant . Physical scientists often use http://mathworld.wolfram.com/Root-Mean-Square.html the term root-mean-square as a synonym for standard deviation when they refer to the square root of the mean squared deviation of a signal from a given baseline or fit. SEE ALSO: Arithmetic-Geometric Mean, Arithmetic-Harmonic Mean, Geometric Mean, Harmonic Mean, Harmonic-Geometric Mean, Mean, Mean Square Displacement, Power Mean, Pythagorean Means, Standard Deviation, Statistical Median, Variance REFERENCES: Hoehn, L. and Niven, I. "Averages on the Move." Math. Mag. 58, 151-156, 1985. Kenney, J.F. and Keeping, E.S. "Root Mean Square." §4.15 in Mathematics of Statistics, Pt.1, 3rd ed. Princeton, NJ: Van Nostrand, pp.59-60, 1962. Referenced on Wolfram|Alpha: Root-Mean-Square CITE THIS AS: Weisstein, Eric W. "Root-Mean-Square." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/Root-Mean-Square.html Wolfram Web Resources Mathematica» The #1 tool for creating Demonstrations and anything technical. Wolfram|Alpha» Explore anything with the first computational knowledge engine. Wolfram Demonstrations Project» Explore thousands of free applications across science, mathematics, engineering, technology, business, art, finance, social sciences, and more. Computerbasedmath.org» Join the initiative for modernizing math education. Online Integral Calculator» Solve integrals with Wolfram|Alpha. Step-by-step Solutions» Walk through homework problems step-by-step from beginning to end. Hints
Why is standard deviation the root mean square? (merged) For the discussion of math. Duh. Moderators: gmalivuk, Moderators General, Prelates Post Reply Print view Search Advanced search 18 posts • Page 1 of 1 Vhailor Posts: 18 Joined: Sat Aug 04, http://echochamber.me/viewtopic.php?t=44935 2007 2:32 pm UTC Why is standard deviation the root mean square? (merged) Quote Postby Vhailor » Wed Sep 09, 2009 12:06 am UTC I have been wondering about this question for a very long time and never had a very much satisfactory answer...In statistics, why is the standard deviation the most used measure of dispersion, when its definition is definitely not intuitive, and its interpretation isn't either? Why square the values before root mean summing them and then take the square root?A much easier to understand and natural measure of dispersion is the mean absolute deviation, it is interpreted as the mean of the distances to the mean, which is pretty simple and natural to me.The best answer I could get from a teacher was that originally in ancient times, the square root of the square was easier to compute (say on a computer) because there is no root mean square need of a 'if' statement like there is for the absolute value... but I find this very unsatisfactory, anyone has a better explanation?I have thought that the use might come from the normal distribution because the st. dev. is a parameter for it, but I believe that the standard deviation must have been used before the normal distribution... Top Token Posts: 1481 Joined: Fri Dec 01, 2006 5:07 pm UTC Location: London Re: Basic statistics question Quote Postby Token » Wed Sep 09, 2009 1:51 am UTC Vhailor wrote:I have thought that the use might come from the normal distribution because the st. dev. is a parameter for itThat's it right there. The standard deviation is useful because it crops up in a bunch of general theorems and formulas (e.g. Chebyshev), and this is largely because the normal distribution crops up so much.As to providing a more intuitive example of why it's useful, consider this thought experiment. Say you have a set of data points (each a real number) that have been produced by some probability distribution, and you want to make a guess at the mean of the probability distribution. The obvious thing to do is to take the mean of the data points, and this is indeed the sensible guess. But let's say that for some reason