Phrase guide

contraharmonic mean

noun · 1 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

Each Play button uses your device's default local English voice, or a natural local fallback. The selected voice name appears after playback. This is synthesized speech, not a source recording.

No pronunciation record was provided for this word.

1

noun

Meaning 1

A 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

Definition source: English Wiktionary via Wiktextract

Topics: mathematics, sciences

Examples

  • 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;.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

History

Etymology

The contraharmonic mean of two variables is at the same distance from their arithmetic mean as their harmonic mean but on the opposite side.

Across languages

Translations

2 source translations are retained for this English entry.

  • Finnish: kontraharmoninen keskiarvo — type of average
  • Serbo-Croatian: kontraharmonijska sredina — type of average