Geometric Mean
When to use the geometric mean
The geometric mean is useful to determine "average factors". For example, if a stock rose 10% in the first year, 20% in the second year and fell 15% in the third year, then we compute the geometric mean of the factors 1.10, 1.20 and 0.85 as (1.10 × 1.20 × 0.85)1/3 = 1.0391... and we conclude that the stock rose 3.91 percent per year, on average.
Put another way...
The arithmetic mean is relevant any time several quantities add together to produce a total. The arithmetic mean answers the question, "if all the quantities had the same value, what would that value have to be in order to achieve the same total?"
In the same way, the geometric mean is relevant any time several quantities multiply together to produce a product. The geometric mean answers the question, "if all the quantities had the same value, what would that value have to be in order to achieve the same product?"
For example, suppose you have an investment which earns 10% the first year, 50% the second year, and 30% the third year. What is its average rate of return? It is not the arithmetic mean, because what these numbers signify is that on the first year your investment was multiplied (not added to) by 1.10, on the second year it was multiplied by 1.50, and the third year it was multiplied by 1.30. The relevant quantity is the geometric mean of these three numbers, which is about 1.28966 or about 29% annual interest.
In the scientific community, when reporting experimental results, it is also important to know whether arithmetic mean or geometric mean should be used. If, for example, you are averaging ratios (i.e. ratio = new method/old method) over many experiments, geometric mean should be used. This becomes evident when considering the two extremes. If one experiment yields a ratio of 10,000 and the next yields a ratio of 0.0001, an arithmetic mean would misleadingly report that the average ratio was near 5000. Taking a geometric mean will more honestly represent the fact that the average ratio was 1.
for more: http://en.wikipedia.org/wiki/Geometric_mean
See also
arithmetic mean
External links
[Category:Means]
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