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.” ยง4.15 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

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