Relationship To The Arithmetic Mean and The Standard Deviation
If is the arithmetic mean and is the standard deviation of a population or a waveform then:
From this it is clear that the RMS value is always greater than or equal to the average, in that the RMS includes the "error" / square deviation as well.
Physical scientists often use the term "root mean square" as a synonym for standard deviation when referring to the square root of the mean squared deviation of a signal from a given baseline or fit. This is useful for electrical engineers in calculating the "AC only" RMS of a signal. Standard deviation being the root mean square of a signal's variation about the mean, rather than about 0, the DC component is removed (i.e. RMS(signal) = Stdev(signal) if the mean signal is 0).
Read more about this topic: Root Mean Square
Famous quotes containing the words relationship to the, relationship to, relationship, arithmetic and/or standard:
“Whatever may be our just grievances in the southern states, it is fitting that we acknowledge that, considering their poverty and past relationship to the Negro race, they have done remarkably well for the cause of education among us. That the whole South should commit itself to the principle that the colored people have a right to be educated is an immense acquisition to the cause of popular education.”
—Fannie Barrier Williams (1855–1944)
“Film music should have the same relationship to the film drama that somebody’s piano playing in my living room has to the book I am reading.”
—Igor Stravinsky (1882–1971)
“Christianity as an organized religion has not always had a harmonious relationship with the family. Unlike Judaism, it kept almost no rituals that took place in private homes. The esteem that monasticism and priestly celibacy enjoyed implied a denigration of marriage and parenthood.”
—Beatrice Gottlieb, U.S. historian. The Family in the Western World from the Black Death to the Industrial Age, ch. 12, Oxford University Press (1993)
“Under the dominion of an idea, which possesses the minds of multitudes, as civil freedom, or the religious sentiment, the power of persons are no longer subjects of calculation. A nation of men unanimously bent on freedom, or conquest, can easily confound the arithmetic of statists, and achieve extravagant actions, out of all proportion to their means; as, the Greeks, the Saracens, the Swiss, the Americans, and the French have done.”
—Ralph Waldo Emerson (1803–1882)
“An indirect quotation we can usually expect to rate only as better or worse, more or less faithful, and we cannot even hope for a strict standard of more and less; what is involved is evaluation, relative to special purposes, of an essentially dramatic act.”
—Willard Van Orman Quine (b. 1908)