Differences between revisions 4 and 6 (spanning 2 versions)
Revision 4 as of 2005-06-28 02:43:53
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Editor: yakko
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Revision 6 as of 2020-01-23 23:16:12
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Editor: scot
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Deletions are marked like this. Additions are marked like this.
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[[latex2($$Geometric~Mean = \sqrt[n]{\prod_{i=1}^{n} Normalized(P_i)}$$)]] $$$Geometric~Mean = \sqrt[n]{\prod_{i=1}^{n} Normalized(P_i)}$$$
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where [[latex2($$Normalized(P_i) = \frac{P_i}{Pn}$$)]] where n is the referenced execution time. Obviously the geometic mean of the referenced machine is 1. where $$$Normalized(P_i) = \frac{P_i}{Pn}$$$ where n is the referenced execution time. Obviously the geometic mean of the referenced machine is 1.
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[[latex2($$GeometricMean\left(\frac{X_i}{Y_i}\right) = \frac{GeometricMean(X_i)}{GeometricMean(Y_i)}$$)]] $$$GeometricMean\left(\frac{X_i}{Y_i}\right) = \frac{GeometricMean(X_i)}{GeometricMean(Y_i)}$$$

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The geometric mean of P1,..,Pn is

$$$Geometric~Mean = \sqrt[n]{\prod_{i=1}^{n} Normalized(P_i)}$$$

where $$$Normalized(P_i) = \frac{P_i}{Pn}$$$ where n is the referenced execution time. Obviously the geometic mean of the referenced machine is 1.

One of the nice features of Geometric means is that the following property holds:

$$$GeometricMean\left(\frac{X_i}{Y_i}\right) = \frac{GeometricMean(X_i)}{GeometricMean(Y_i)}$$$

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GeometricMean (last edited 2020-01-23 23:16:12 by scot)