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 ${AM}$ denote Arithmetic Mean,

$AM=\frac{x_1+x_2+\cdots+x_n}{n}$

is the arithmetic mean of the $\displaystyle {n}$ numbers $\displaystyle x_1,x_2,\ldots,x_n$.

For example, if I wanted to find the average of the numbers 3, 1, 4, 1, and 5, I would compute:

$\frac{3+1+4+1+5}{5} = \frac{14}{5}.$


Arithmetic means show up frequently in contest problems, often in the AM-GM inequality or its variant, the RMS-AM-GM-HM inequality.

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