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The Arithmetic Mean Standard Deviation Distribution: A Geometrical Framework

DOI: 10.4236/am.2013.411A4001, PP. 1-10

Keywords: Standard Deviation, n-Spaces, Direction Cosines, Quadrics

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Abstract:

The current attempt is aimed to outline the geometrical framework of a well known statistical problem, concerning the explicit expression of the arithmetic mean standard deviation distribution. To this respect, after a short exposition, three steps are performed as 1) formulation of the arithmetic mean standard deviation, \"\", as a function of the errors, \"\", which, by themselves, are statistically independent; 2) formulation of the arithmetic mean standard deviation distribution, \"\", as a function of the errors, \"\"; 3) formulation of the arithmetic mean standard deviation distribution, \"\", as a function of the arithmetic mean standard deviation, \"\", and the arithmetic mean rms error, \"\". The integration domain can be expressed in canonical form after a change of reference frame in the n-space, which is recognized as an infinitely thin n-cylindrical corona where the symmetry axis coincides with a coordinate axis. Finally, the solution is presented and a number of (well known) related parameters are inferred for sake of completeness.

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