"contraharmonic mean" meaning in English

{
  "etymology_text": "The contraharmonic mean of two variables is at the same distance from their arithmetic mean as their harmonic mean but on the opposite side.",
  "forms": [
    {
      "form": "contraharmonic means",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "contraharmonic mean (plural contraharmonic means)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "The contraharmonic mean of two numbers a and c is the number b such that #x7B;a-b#x5C;overc#x7D;#x3D;#x7B;b-c#x5C;overa#x7D;. Combining the two ratios: #x7B;b-c#x5C;overa#x7D;#x3D;#x7B;(a-b)#x2B;(b-c)#x5C;overc#x2B;a#x7D;#x3D;#x7B;a-c#x5C;overa#x2B;c#x7D;. Rotating the proportion 90° clockwise: #x7B;a#x5C;overa#x2B;c#x7D;#x3D;#x7B;b-c#x5C;overa-c#x7D;; transposing twice to isolate the b: b#x3D;c#x2B;a#x5C;left(#x7B;a-c#x5C;overa#x2B;c#x7D;#x5C;right). Likewise b#x3D;a-c#x5C;left(#x7B;a-c#x5C;overa#x2B;c#x7D;#x5C;right); these are both equivalent to the more symmetrical b#x3D;#x7B;a²#x2B;c²#x5C;overa#x2B;c#x7D;.",
          "type": "example"
        }
      ],
      "glosses": [
        "A type of average calculated as the arithmetic mean of the squares of the values divided by the arithmetic mean of the values, ie. 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"
      ],
      "id": "en-contraharmonic_mean-en-noun-tMbUDyvB",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "average",
          "average"
        ],
        [
          "arithmetic mean",
          "arithmetic mean"
        ],
        [
          "square",
          "square"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A type of average calculated as the arithmetic mean of the squares of the values divided by the arithmetic mean of the values, ie. 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"
      ],
      "related": [
        {
          "word": "arithmetic mean"
        },
        {
          "word": "centroidal mean"
        },
        {
          "word": "harmonic mean"
        },
        {
          "word": "heronian mean"
        },
        {
          "word": "geometric mean"
        },
        {
          "word": "quadratic mean"
        }
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "type of average",
          "word": "kontraharmoninen keskiarvo"
        },
        {
          "code": "sh",
          "lang": "Serbo-Croatian",
          "sense": "type of average",
          "tags": [
            "feminine"
          ],
          "word": "kontraharmonijska sredina"
        }
      ]
    }
  ],
  "word": "contraharmonic mean"
}

{
  "etymology_text": "The contraharmonic mean of two variables is at the same distance from their arithmetic mean as their harmonic mean but on the opposite side.",
  "forms": [
    {
      "form": "contraharmonic means",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "contraharmonic mean (plural contraharmonic means)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "arithmetic mean"
    },
    {
      "word": "centroidal mean"
    },
    {
      "word": "harmonic mean"
    },
    {
      "word": "heronian mean"
    },
    {
      "word": "geometric mean"
    },
    {
      "word": "quadratic mean"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with usage examples",
        "en:Mathematics"
      ],
      "examples": [
        {
          "text": "The contraharmonic mean of two numbers a and c is the number b such that #x7B;a-b#x5C;overc#x7D;#x3D;#x7B;b-c#x5C;overa#x7D;. Combining the two ratios: #x7B;b-c#x5C;overa#x7D;#x3D;#x7B;(a-b)#x2B;(b-c)#x5C;overc#x2B;a#x7D;#x3D;#x7B;a-c#x5C;overa#x2B;c#x7D;. Rotating the proportion 90° clockwise: #x7B;a#x5C;overa#x2B;c#x7D;#x3D;#x7B;b-c#x5C;overa-c#x7D;; transposing twice to isolate the b: b#x3D;c#x2B;a#x5C;left(#x7B;a-c#x5C;overa#x2B;c#x7D;#x5C;right). Likewise b#x3D;a-c#x5C;left(#x7B;a-c#x5C;overa#x2B;c#x7D;#x5C;right); these are both equivalent to the more symmetrical b#x3D;#x7B;a²#x2B;c²#x5C;overa#x2B;c#x7D;.",
          "type": "example"
        }
      ],
      "glosses": [
        "A type of average calculated as the arithmetic mean of the squares of the values divided by the arithmetic mean of the values, ie. 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"
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "average",
          "average"
        ],
        [
          "arithmetic mean",
          "arithmetic mean"
        ],
        [
          "square",
          "square"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A type of average calculated as the arithmetic mean of the squares of the values divided by the arithmetic mean of the values, ie. 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"
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "type of average",
      "word": "kontraharmoninen keskiarvo"
    },
    {
      "code": "sh",
      "lang": "Serbo-Croatian",
      "sense": "type of average",
      "tags": [
        "feminine"
      ],
      "word": "kontraharmonijska sredina"
    }
  ],
  "word": "contraharmonic mean"
}