Diff for "GeometricMean"

Differences between revisions 3 and 6 (spanning 3 versions)

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:

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

-  ⇤ ← Revision 3 as of 2004-02-18 00:05:51 → 
  Size: 646
  Editor: yakko
  Comment:
+   ← Revision 6 as of 2020-01-23 23:16:12 → ⇥
  Size: 491
  Editor: scot
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
 Line 5:
-{{{
                        _____________ 
                       / n 
Geometric Mean =    n / __ 
                     /  ||  Normalized(Pi) 
                   \/   i=1
+$$$Geometric~Mean = \sqrt[n]{\prod_{i=1}^{n} Normalized(P_i)}$$$
-Line 12:
+Line 7:
-     where Normalized(Pi) = Pi / 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.
-Line 15:
+Line 9:
-}}}
-Line 19:
+Line 13:
-{{{
                        GeometricMean(Xi)
GeometricMean(Xi/Yi) = ------------------
                        GeometricMean(Yi)
}}}
+$$$GeometricMean\left(\frac{X_i}{Y_i}\right) = \frac{GeometricMean(X_i)}{GeometricMean(Y_i)}$$$