Difference between revisions of "Arithmetic mean"
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=== Arithmetic Mean === | === 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. 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>{n}</math> numbers <math>x_1,x_2,\ldots,x_n</math>. | + | is the arithmetic mean of the <math>\displaystyle {n}</math> numbers <math>\displaystyle 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: | ||
<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> | ||
| − | + | 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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Revision as of 16:59, 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.
