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 denote Arithmetic Mean,
![$AM=\frac{x_1+x_2+\cdots+x_n}{n}$](http://latex.artofproblemsolving.com/a/b/6/ab63d60096a5f74caf6e4653660c7733013a1c18.png)
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:
![$\frac{3+1+4+1+5}{5} = \frac{14}{5}.$](http://latex.artofproblemsolving.com/c/6/c/c6ce6f84dbe450a1e81b0ab8633e0eda1ad28b44.png)
Arithmetic means show up frequently in contest problems, often in the AM-GM inequality or its variant, the RMS-AM-GM-HM inequality.