Difference between revisions of "Arithmetic mean"
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For example, if I wanted to find the average of the numbers 3, 1, 4, 1, and 5, I would compute: | For example, if I wanted to find the average of the numbers 3, 1, 4, 1, and 5, I would compute: | ||
<center><math> \frac{3+1+4+1+5}{5} = \frac{14}{5}.</math></center> | <center><math> \frac{3+1+4+1+5}{5} = \frac{14}{5}.</math></center> | ||
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Arithmetic means show up frequently in contest problems, often in the [[AM-GM]] [[inequality]] or its variant, the [[RMS-AM-GM-HM]] inequality. | Arithmetic means show up frequently in contest problems, often in the [[AM-GM]] [[inequality]] or its variant, the [[RMS-AM-GM-HM]] inequality. | ||
Revision as of 16:04, 22 June 2006
Arithmetic Mean
The arithmetic mean of a set of numbers (or variables) is the sum of all the numbers, divided by the number of numbers - the average of the set. If we let 
denote Arithmetic Mean,
is the arithmetic mean of the 
numbers 
.
For example, if I wanted to find the average of the numbers 3, 1, 4, 1, and 5, I would compute:
Arithmetic means show up frequently in contest problems, often in the AM-GM inequality or its variant, the RMS-AM-GM-HM inequality.
