Difference between revisions of "Arithmetic mean"

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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 <math>{AM}</math> denote 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 <math>{AM}</math> denote Arithmetic Mean,  
 
<center><math>AM=\frac{x_1+x_2+\cdots+x_n}{n}</math></center>
 
<center><math>AM=\frac{x_1+x_2+\cdots+x_n}{n}</math></center>
is the arithmetic mean of the <math>\displaystyle {n}</math> numbers <math>\displaystyle x_1,x_2,\ldots,x_n</math>.
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is the arithmetic mean of the <math>{n}</math> numbers <math>x_1,x_2,\ldots,x_n</math>.
  
 
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:  
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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.
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[[Category:Statistics]]

Latest revision as of 12:44, 20 September 2015

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 ${n}$ numbers $x_1,x_2,\ldots,x_n$.

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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