Descriptive Statistics > Quadratic Mean / Root Mean Square
What is the Quadratic Mean / Root Mean Square?
The quadratic mean (also called the root mean square*) is a type of average.
Sometimes the quadratic mean is referred to as being “the same as” the standard deviation. This isn’t strictly true: standard deviation is actually equal to the quadratic deviations from the mean of the data set. For example, quadratic mean is used in the physical sciences as a synonym for standard deviation when referencing the “square root of the mean squared deviation of a signal from a given baseline or fit”(Wolfram).
The quadratic mean is also called the root mean square because it is the square root of the mean of the squares of the numbers in the set.
The quadratic mean is equal to the square root of the mean of the squared values. The formula is:
An equivalent formula has a summation sign (summation means “to add up”, so it’s telling you here to add all of the squared x-values up):
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.
Wolfram. Root Mean Square. Available at: http://mathworld.wolfram.com/Root-Mean-Square.html
Stephanie Glen. "Quadratic Mean / Root Mean Square" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/quadratic-mean/
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