See geometric mean on Wiktionary
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In symbols: if A(x,y)#x3D;#x7B;x#x2B;y#x5C;over 2#x7D;, H(x,y)#x3D;#x7B;2xy#x5C;overx#x2B;y#x7D;, and G(x,y)#x3D;#x5C;sqrt#x7B;xy#x7D;, then G(A(x,y),H(x,y))#x3D;#x5C;sqrt#x3A;Template#x3A;x#x2B;y#x5C;over 2#x7D;#x5C;cdot#x7B;2xy#x5C;overx#x2B;y#x3D;#x5C;sqrt#x7B;xy#x7D;#x3D;G(x,y).", "type": "example" } ], "glosses": [ "A measure of central tendency of a set of n values computed by extracting the nth root of the product of the values." ], "hypernyms": [ { "word": "measure of central tendency" }, { "word": "Pythagorean mean" } ], "id": "en-geometric_mean-en-noun-aTD8R0BL", "links": [ [ "mathematics", "mathematics" ], [ "measure of central tendency", "measure of central tendency" ] ], "raw_glosses": [ "(mathematics) A measure of central tendency of a set of n values computed by extracting the nth root of the product of the values." ], "topics": [ "mathematics", "sciences" ], "translations": [ { "code": "hy", "lang": "Armenian", "roman": "erkračʻapʻakan miǰin", "sense": "measure of central tendency", "word": "երկրաչափական միջին" }, { "code": "cmn", "lang": "Chinese Mandarin", "sense": "measure of central tendency", "word": "幾何平均數" }, { "code": "cmn", "lang": "Chinese Mandarin", "roman": "jǐhé píngjūnshù", "sense": "measure of central tendency", "word": "几何平均数" }, { "code": "cmn", "lang": "Chinese Mandarin", "sense": "measure of central tendency", "word": "几何中项" }, { "code": "cs", "lang": "Czech", "sense": "measure of central tendency", "tags": [ "masculine" ], "word": "geometrický průměr" }, { "code": "et", "lang": "Estonian", "sense": "measure of central tendency", "word": "geomeetriline keskmine" }, { "code": "fi", "lang": "Finnish", "sense": "measure of central tendency", "word": "geometrinen keskiarvo" }, { "code": "fi", "lang": "Finnish", "sense": "measure of central tendency", "word": "keskiverto" }, { "code": "fr", "lang": "French", "sense": "measure of central tendency", "word": "moyenne géométrique" }, { "code": "de", "lang": "German", "sense": "measure of central tendency", "tags": [ "neuter" ], "word": "geometrisches Mittel" }, { "code": "hu", "lang": "Hungarian", "sense": "measure of central tendency", "word": "mértani közép" }, { "code": "ja", "lang": "Japanese", "sense": "measure of central tendency", "word": "幾何平均" }, { "code": "ko", "lang": "Korean", "roman": "giha pyeonggyun", "sense": "measure of central tendency", "word": "기하 평균" }, { "code": "pl", "lang": "Polish", "sense": "measure of central tendency", "tags": [ "feminine" ], "word": "średnia geometryczna" }, { "code": "ro", "lang": "Romanian", "sense": "measure of central tendency", "tags": [ "feminine" ], "word": "medie geometrică" }, { "code": "ru", "lang": "Russian", "roman": "srédneje geometríčeskoje", "sense": "measure of central tendency", "tags": [ "neuter" ], "word": "сре́днее геометри́ческое" }, { "code": "sh", "lang": "Serbo-Croatian", "sense": "measure of central tendency", "tags": [ "feminine" ], "word": "geometrijska sredina" }, { "code": "es", "lang": "Spanish", "sense": "measure of central tendency", "tags": [ "feminine" ], "word": "media geométrica" }, { "code": "tl", "lang": "Tagalog", "sense": "measure of central tendency", "word": "sukgising tamtaman" } ], "wikipedia": [ "geometric mean" ] } ], "word": "geometric mean" }
{ "coordinate_terms": [ { "word": "arithmetic mean" }, { "word": "harmonic mean" }, { "word": "quadratic mean" } ], "forms": [ { "form": "geometric means", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "geometric mean (plural geometric means)", "name": "en-noun" } ], "hypernyms": [ { "word": "measure of central tendency" }, { "word": "Pythagorean mean" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ "English countable nouns", "English entries with incorrect language header", "English lemmas", "English multiword terms", "English nouns", "English terms with usage examples", "Entries with translation boxes", "Mandarin terms with redundant transliterations", "Pages with 1 entry", "Pages with entries", "Terms with Armenian translations", "Terms with Czech translations", "Terms with Estonian translations", "Terms with Finnish translations", "Terms with French translations", "Terms with German translations", "Terms with Hungarian translations", "Terms with Japanese translations", "Terms with Korean translations", "Terms with Mandarin translations", "Terms with Polish translations", "Terms with Romanian translations", "Terms with Russian translations", "Terms with Serbo-Croatian translations", "Terms with Spanish translations", "Terms with Tagalog translations", "en:Mathematics" ], "examples": [ { "text": "The geometric mean of 2, 4 and 1 is √ = 2" }, { "text": "The geometric mean of the arithmetic mean and the harmonic mean is the geometric mean. In symbols: if A(x,y)#x3D;#x7B;x#x2B;y#x5C;over 2#x7D;, H(x,y)#x3D;#x7B;2xy#x5C;overx#x2B;y#x7D;, and G(x,y)#x3D;#x5C;sqrt#x7B;xy#x7D;, then G(A(x,y),H(x,y))#x3D;#x5C;sqrt#x3A;Template#x3A;x#x2B;y#x5C;over 2#x7D;#x5C;cdot#x7B;2xy#x5C;overx#x2B;y#x3D;#x5C;sqrt#x7B;xy#x7D;#x3D;G(x,y).", "type": "example" } ], "glosses": [ "A measure of central tendency of a set of n values computed by extracting the nth root of the product of the values." ], "links": [ [ "mathematics", "mathematics" ], [ "measure of central tendency", "measure of central tendency" ] ], "raw_glosses": [ "(mathematics) A measure of central tendency of a set of n values computed by extracting the nth root of the product of the values." ], "topics": [ "mathematics", "sciences" ], "wikipedia": [ "geometric mean" ] } ], "translations": [ { "code": "hy", "lang": "Armenian", "roman": "erkračʻapʻakan miǰin", "sense": "measure of central tendency", "word": "երկրաչափական միջին" }, { "code": "cmn", "lang": "Chinese Mandarin", "sense": "measure of central tendency", "word": "幾何平均數" }, { "code": "cmn", "lang": "Chinese Mandarin", "roman": "jǐhé píngjūnshù", "sense": "measure of central tendency", "word": "几何平均数" }, { "code": "cmn", "lang": "Chinese Mandarin", "sense": "measure of central tendency", "word": "几何中项" }, { "code": "cs", "lang": "Czech", "sense": "measure of central tendency", "tags": [ "masculine" ], "word": "geometrický průměr" }, { "code": "et", "lang": "Estonian", "sense": "measure of central tendency", "word": "geomeetriline keskmine" }, { "code": "fi", "lang": "Finnish", "sense": "measure of central tendency", "word": "geometrinen keskiarvo" }, { "code": "fi", "lang": "Finnish", "sense": "measure of central tendency", "word": "keskiverto" }, { "code": "fr", "lang": "French", "sense": "measure of central tendency", "word": "moyenne géométrique" }, { "code": "de", "lang": "German", "sense": "measure of central tendency", "tags": [ "neuter" ], "word": "geometrisches Mittel" }, { "code": "hu", "lang": "Hungarian", "sense": "measure of central tendency", "word": "mértani közép" }, { "code": "ja", "lang": "Japanese", "sense": "measure of central tendency", "word": "幾何平均" }, { "code": "ko", "lang": "Korean", "roman": "giha pyeonggyun", "sense": "measure of central tendency", "word": "기하 평균" }, { "code": "pl", "lang": "Polish", "sense": "measure of central tendency", "tags": [ "feminine" ], "word": "średnia geometryczna" }, { "code": "ro", "lang": "Romanian", "sense": "measure of central tendency", "tags": [ "feminine" ], "word": "medie geometrică" }, { "code": "ru", "lang": "Russian", "roman": "srédneje geometríčeskoje", "sense": "measure of central tendency", "tags": [ "neuter" ], "word": "сре́днее геометри́ческое" }, { "code": "sh", "lang": "Serbo-Croatian", "sense": "measure of central tendency", "tags": [ "feminine" ], "word": "geometrijska sredina" }, { "code": "es", "lang": "Spanish", "sense": "measure of central tendency", "tags": [ "feminine" ], "word": "media geométrica" }, { "code": "tl", "lang": "Tagalog", "sense": "measure of central tendency", "word": "sukgising tamtaman" } ], "word": "geometric mean" }
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