contraharmonic mean

plural contraharmonic means

1. mathematicsA type of average calculated as the arithmetic mean of the squares of the values divided by the arithmetic mean of the values, i.e. C=(x_1²+x_2²+...+x_n²)/n/(x_1+x_2+...+x_n)/norC(x_1,x_2,...,x_n)=x_1²+x_2²+...+x_n²/x_1+x_2+...+x_n

   1 more example

   The contraharmonic mean of two numbers a and c is the number b such that #123;a-b#92;overc#125;#61;#123;b-c#92;overa#125;. Combining the two ratios: #123;b-c#92;overa#125;#61;#123;(a-b)#43;(b-c)#92;overc#43;a#125;#61;#123;a-c#92;overa#43;c#125;. Rotating the proportion 90° clockwise: #123;a#92;overa#43;c#125;#61;#123;b-c#92;overa-c#125;; transposing twice to isolate the b: b#61;c#43;a#92;left(#123;a-c#92;overa#43;c#125;#92;right). Likewise b#61;a-c#92;left(#123;a-c#92;overa#43;c#125;#92;right); these are both equivalent to the more symmetrical b#61;#123;a²#43;c²#92;overa#43;c#125;.