Important: The stats package has been deprecated. Use the superseding package Statistics instead.

The function quadraticmean of the subpackage stats[describe, ...] computes the quadratic mean of the given data.

The quadratic mean, also known as the root mean square, is the square root of the mean of the squares of the observations. It is a measure of central tendency. For more information about such measures, see the help for the (arithmetic) mean.

This type of mean is used in some physical applications. For example, it gives the ``average'' speed of particles of the same mass, where average is defined in such a way as to give each particle the same kinetic energy.

Classes are assumed to be represented by the class mark, for example 10..12 has the value 11. Missing data are ignored.

The command with(stats[describe],quadraticmean) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{stats}\right)\:$

$\mathrm{Tot\_Kinetic}≔\frac{1}{2}M{3}^2+\frac{1}{2}M{4}^2$

$\mathrm{Tot\_Kinetic}≔\frac{25M}{2}$

$\mathrm{Rv}≔\mathrm{describe}\left[\mathrm{quadraticmean}\right]\left(\left[3\,4\right]\right)$

$\mathrm{Rv}≔\frac{5\sqrt{2}}{2}$

$2\frac{1}{2}M{\mathrm{Rv}}^2=\mathrm{Tot\_Kinetic}$

$\frac{25M}{2}=\frac{25M}{2}$

$\mathrm{Av}≔\mathrm{describe}\left[\mathrm{mean}\right]\left(\left[3\,4\right]\right)$

$\mathrm{Av}≔\frac{7}{2}$

$2\frac{1}{2}M{\mathrm{Av}}^2\ne \mathrm{Tot\_Kinetic}$

$\frac{49M}{4}\ne \frac{25M}{2}$