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, arithmetic and/or standard:
“... the Wall became a magnet for citizens of every generation, class, race, and relationship to the war perhaps because it is the only great public monument that allows the anesthetized holes in the heart to fill with a truly national grief.”
—Adrienne Rich (b. 1929)
“We must introduce a new balance in the relationship between the individual and the government—a balance that favors greater individual freedom and self-reliance.”
—Gerald R. Ford (b. 1913)
“O! O! another stroke! that makes the third.
He stabs me to the heart against my wish.
If that be so, thy state of health is poor;
But thine arithmetic is quite correct.”
—A.E. (Alfred Edward)
“[The Declaration of Independence] meant to set up a standard maxim for free society, which should be familiar to all, and revered by all; constantly looked to, constantly labored for, and even though never perfectly attained, constantly approximated, and thereby constantly spreading and deepening its influence, and augmenting the happiness and value of life to all people of all colors everywhere.”
—Abraham Lincoln (1809–1865)