harmonic mean

Definitions

A type of measure of central tendency calculated as the reciprocal of the mean of the reciprocals, i.e., H=n/1/x_1+1/x_2+⋯+1/x_n.

Equivalents

Examples

“The harmonic mean⟳ of two numbers a and c is the number⟳ b such that #123;a-b#92;overa#125;#61;#123;b-c#92;overc#125;. Combining the two ratios: #123;b-c#92;overc#125;#61;#123;(a-b)#43;(b-c)#92;overa#43;c#125;#61;#123;a-c#92;overa#43;c#125;. Rotating the proportion 90° clockwise: #123;c#92;overa#43;c#125;#61;#123;b-c#92;overa-c#125;; transposing twice to isolate the b: b#61;c#43;c#92;left(#123;a-c#92;overa#43;c#125;#92;right). Likewise b#61;a-a#92;left(#123;a-c#92;overa#43;c#125;#92;right); these are both equivalent to the more typical, symmetrical equations: b#61;#123;2ac#92;overa#43;c#125;#61;#123;2#92;over#123;1#92;overa#125;#43;#123;1#92;overc”

CEFR level