Difference between revisions of "Root-mean-square"
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| − | The '''root-mean square''' | + | The '''root-mean-square''' or ''quadratic mean'' of a collection of [[real number]]s <math>x_1,\dots , x_n</math> is defined to be <math>\sqrt{\frac{x^2_1+x^2_2+\dots+x^2_n}{n}}</math>. This is the second [[power mean]] of the <math>x_i</math>. |
| − | <math> | + | It is so-named because it is the square root of the mean of the squares of the <math>x_i</math>. |
| + | |||
| + | It is also part of the well-known [[Root-Mean Square-Arithmetic Mean-Geometric Mean-Harmonic mean Inequality]] | ||
| + | |||
| + | == See Also == | ||
| + | * [[RMS-AM-GM-HM]] [[inequality]] | ||
| + | * [[Power Mean Inequality]] | ||
| + | |||
| + | {{stub}} | ||
Latest revision as of 12:41, 8 May 2013
The root-mean-square or quadratic mean of a collection of real numbers 
is defined to be 
. This is the second power mean of the 
.
It is so-named because it is the square root of the mean of the squares of the .
It is also part of the well-known Root-Mean Square-Arithmetic Mean-Geometric Mean-Harmonic mean Inequality
See Also
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