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stats[describe, quadraticmean] - Quadratic Mean of a Statistical List

Calling Sequence

stats[describe, quadraticmean](data)

describe[quadraticmean](data)

Parameters

data

-

statistical list

Description

• 

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.

Examples

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

withstats:

If V is the velocity of a particle of mass M, then its kinetic energy is defined to be 1/2*M*V^2. If we have two particles, one with velocity 3 and the other with velocity 4, the total kinematic energy is given by

Tot_Kinetic:=1M322+1M422

Tot_Kinetic:=252M

(1)

The RMS-velocity is

Rv:=describequadraticmean3,4

Rv:=522

(2)

The energy associated with the 2 particles of mass M and velocity Rv is

21MRv22=Tot_Kinetic

252M=252M

(3)

Note that the arithmetic average is not suitable here:

Av:=describemean3,4

Av:=72

(4)

21MAv22Tot_Kinetic

494M252M

(5)

See Also

describe(deprecated)[geometricmean], describe(deprecated)[harmonicmean], describe(deprecated)[mean], Statistics, Statistics[QuadraticMean], stats(deprecated)[data], transform(deprecated)[classmark]


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