  # Quadratic Mean / Root Mean Square

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.

*Note: This is different from the root mean square error (RMSE), which is a value used in regression analysis to describe how spread out data is around a regression line.

## Formula

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): References:
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

------------------------------------------------------------------------------

Need help with a homework or test question? With Chegg Study, you can get step-by-step solutions to your questions from an expert in the field. Your first 30 minutes with a Chegg tutor is free!

Statistical concepts explained visually - Includes many concepts such as sample size, hypothesis tests, or logistic regression, explained by Stephanie Glen, founder of StatisticsHowTo.