The Essentials ofComputer(computer) 476

The Essentials ofComputer(computer) 476 - are comparing the...

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TABLE 10.3 The Weighted Average Running Times for System A Using a Revised Execution Mix Program Weighted Average 2817.5 seconds Execution Time Execution Frequency v w x y z 50 200 250 400 5000 25% 5% 10% 5% 55% are certain to be at a loss to explain why their brand new system is suddenly offering such poor performance. The Geometric Mean We know from the previous discussion that we cannot use the arithmetic mean if our measurements exhibit a great deal of variability. Further, unless we have a clear view of a static and representative workload, the weighted arithmetic mean is of no help either. The geometric mean gives us a consistent number with which to perform comparisons regardless of the distribution of the data. Formally, the geometric mean is defined as the n th root of the product of the n measurements. It is represented by the following formula: G = x 1 × x 2 × x 3 × . . . × x n n The geometric mean is more helpful to us than the arithmetic average when we
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Unformatted text preview: are comparing the relative performance of two systems. Performance results are easy to compare when they are stated in relation to the performance of a common machine used only as a reference. We say that the systems under evaluation are normalized to the reference machine when we take the ratio of the run time of a program on the reference machine to the run time of the same program on the system being evaluated. To find the geometric mean of the normalized ratios we take the n th root of the product of the n ratios. The geometric means for System A and System C nor-malized to System B are calculated as follows: Geometric Mean for A = (100/50 ± 400/200 ± 500/250 ± 800/400 ± 4100/5000)/5 ± 1.6733 Geometric Mean for C = (100/500 ± 400/600 ± 500/500 ± 800/800 ± 4100/3500)/5 ± 0.6898...
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