Root mean square

<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the root mean square (abbrev. RMS, RMS or rms) of a <a href="/facts/Set_(mathematics)/BfucfHMq">set</a> of values is the <a href="/facts/Square_root/AfrzfBdQ">square root</a> of the set's <a href="/facts/Mean_square/CYKUw0yI">mean square</a>.
Given a set 
  
    
      
        
          x
          
            i
          
        
      
    
    {\displaystyle x_{i}}
  
, its RMS is denoted as either 
  
    
      
        
          x
          
            
              R
              M
              S
            
          
        
      
    
    {\displaystyle x_{\mathrm {RMS} }}
  
 or 
  
    
      
        
          
            R
            M
            S
          
          
            x
          
        
      
    
    {\displaystyle \mathrm {RMS} _{x}}
  
. The RMS is also known as the quadratic mean (denoted 
  
    
      
        
          M
          
            2
          
        
      
    
    {\displaystyle M_{2}}
  
), a special case of the <a href="/facts/Generalized_mean/Xhqjzhnc">generalized mean</a>. The RMS of a continuous <a href="/facts/Function_(mathematics)/CdReEKCh">function</a> is denoted 
  
    
      
        
          f
          
            
              R
              M
              S
            
          
        
      
    
    {\displaystyle f_{\mathrm {RMS} }}
  
 and can be defined in terms of an <a href="/facts/Integral/4PeM0mJc">integral</a> of the square of the function.
In <a href="/facts/Estimation_theory/4nbgFDec">estimation theory</a>, the <a href="/facts/Root-mean-square_deviation/MlQVhebp">root-mean-square deviation</a> of an estimator measures how far the estimator strays from the data.
</p>

Root mean square open-in-new

Root mean square