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

Calling Sequence


stats[describe, quadraticmean](data)
describe[quadraticmean](data)


Description


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

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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.

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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.

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

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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.
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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
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 (1) 
The RMSvelocity is
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 (2) 
The energy associated with the 2 particles of mass M and velocity Rv is
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 (3) 
Note that the arithmetic average is not suitable here:
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 (4) 
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 (5) 


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