See harmonic mean in All languages combined, or Wiktionary
Download JSON data for harmonic mean meaning in English (4.5kB)
{
"forms": [
{
"form": "harmonic means",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "harmonic mean (plural harmonic 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": "other",
"name": "Japanese terms with redundant script codes",
"parents": [
"Terms with redundant script codes",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "Mandarin terms with redundant transliterations",
"parents": [
"Terms with redundant transliterations",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"derived": [
{
"word": "contraharmonic mean"
}
],
"examples": [
{
"text": "The harmonic mean of two numbers a and c is the number b such that #x7B;a-b#x5C;overa#x7D;#x3D;#x7B;b-c#x5C;overc#x7D;. Combining the two ratios: #x7B;b-c#x5C;overc#x7D;#x3D;#x7B;(a-b)#x2B;(b-c)#x5C;overa#x2B;c#x7D;#x3D;#x7B;a-c#x5C;overa#x2B;c#x7D;. Rotating the proportion 90° clockwise: #x7B;c#x5C;overa#x2B;c#x7D;#x3D;#x7B;b-c#x5C;overa-c#x7D;; transposing twice to isolate the b: b#x3D;c#x2B;c#x5C;left(#x7B;a-c#x5C;overa#x2B;c#x7D;#x5C;right). Likewise b#x3D;a-a#x5C;left(#x7B;a-c#x5C;overa#x2B;c#x7D;#x5C;right); these are both equivalent to the more typical, symmetrical equations: b#x3D;#x7B;2ac#x5C;overa#x2B;c#x7D;#x3D;#x7B;2#x5C;over#x7B;1#x5C;overa#x7D;#x2B;#x7B;1#x5C;overc.}}",
"type": "example"
}
],
"glosses": [
"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."
],
"hypernyms": [
{
"topics": [
"statistics",
"mathematics",
"sciences"
],
"word": "measure of central tendency"
},
{
"word": "Pythagorean mean"
}
],
"id": "en-harmonic_mean-en-noun-m0fexaff",
"links": [
[
"mathematics",
"mathematics"
],
[
"measure of central tendency",
"measure of central tendency"
],
[
"reciprocal",
"reciprocal"
]
],
"raw_glosses": [
"(mathematics) 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."
],
"related": [
{
"word": "arithmetic mean"
},
{
"word": "geometric mean"
},
{
"word": "quadratic mean"
}
],
"topics": [
"mathematics",
"sciences"
],
"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "type of average",
"word": "調和平均數"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "tiáohé píngjūnshù",
"sense": "type of average",
"word": "调和平均数"
},
{
"code": "cs",
"lang": "Czech",
"sense": "type of average",
"tags": [
"masculine"
],
"word": "harmonický průměr"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "type of average",
"word": "harmoninen keskiarvo"
},
{
"code": "fr",
"lang": "French",
"sense": "type of average",
"word": "moyenne harmonique"
},
{
"code": "de",
"lang": "German",
"sense": "type of average",
"tags": [
"neuter"
],
"word": "harmonisches Mittel"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "type of average",
"word": "harmonikus közép"
},
{
"code": "id",
"lang": "Indonesian",
"sense": "type of average",
"word": "rerata harmonik"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "chōwaheikin",
"sense": "type of average",
"word": "調和平均"
},
{
"code": "ko",
"lang": "Korean",
"roman": "johwa pyeonggyun",
"sense": "type of average",
"word": "조화 평균"
},
{
"code": "pl",
"lang": "Polish",
"sense": "type of average",
"tags": [
"feminine"
],
"word": "średnia harmoniczna"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "type of average",
"tags": [
"Portugal",
"feminine"
],
"word": "média harmónica"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "type of average",
"tags": [
"Brazil",
"feminine"
],
"word": "média harmônica"
},
{
"code": "ru",
"lang": "Russian",
"roman": "srédneje garmoníčeskoje",
"sense": "type of average",
"tags": [
"neuter"
],
"word": "сре́днее гармони́ческое"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "type of average",
"tags": [
"feminine"
],
"word": "harmonijska sredina"
},
{
"code": "es",
"lang": "Spanish",
"sense": "type of average",
"tags": [
"feminine"
],
"word": "media armónica"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "type of average",
"tags": [
"neuter"
],
"word": "harmoniskt medelvärde"
},
{
"code": "tl",
"lang": "Tagalog",
"sense": "type of average",
"word": "suwatuhing tamtaman"
}
],
"wikipedia": [
"harmonic mean"
]
}
],
"word": "harmonic mean"
}
{
"derived": [
{
"word": "contraharmonic mean"
}
],
"forms": [
{
"form": "harmonic means",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "harmonic mean (plural harmonic means)",
"name": "en-noun"
}
],
"hypernyms": [
{
"topics": [
"statistics",
"mathematics",
"sciences"
],
"word": "measure of central tendency"
},
{
"word": "Pythagorean mean"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "arithmetic 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",
"Japanese terms with redundant script codes",
"Mandarin terms with redundant transliterations",
"en:Mathematics"
],
"examples": [
{
"text": "The harmonic mean of two numbers a and c is the number b such that #x7B;a-b#x5C;overa#x7D;#x3D;#x7B;b-c#x5C;overc#x7D;. Combining the two ratios: #x7B;b-c#x5C;overc#x7D;#x3D;#x7B;(a-b)#x2B;(b-c)#x5C;overa#x2B;c#x7D;#x3D;#x7B;a-c#x5C;overa#x2B;c#x7D;. Rotating the proportion 90° clockwise: #x7B;c#x5C;overa#x2B;c#x7D;#x3D;#x7B;b-c#x5C;overa-c#x7D;; transposing twice to isolate the b: b#x3D;c#x2B;c#x5C;left(#x7B;a-c#x5C;overa#x2B;c#x7D;#x5C;right). Likewise b#x3D;a-a#x5C;left(#x7B;a-c#x5C;overa#x2B;c#x7D;#x5C;right); these are both equivalent to the more typical, symmetrical equations: b#x3D;#x7B;2ac#x5C;overa#x2B;c#x7D;#x3D;#x7B;2#x5C;over#x7B;1#x5C;overa#x7D;#x2B;#x7B;1#x5C;overc.}}",
"type": "example"
}
],
"glosses": [
"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."
],
"links": [
[
"mathematics",
"mathematics"
],
[
"measure of central tendency",
"measure of central tendency"
],
[
"reciprocal",
"reciprocal"
]
],
"raw_glosses": [
"(mathematics) 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."
],
"topics": [
"mathematics",
"sciences"
],
"wikipedia": [
"harmonic mean"
]
}
],
"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "type of average",
"word": "調和平均數"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "tiáohé píngjūnshù",
"sense": "type of average",
"word": "调和平均数"
},
{
"code": "cs",
"lang": "Czech",
"sense": "type of average",
"tags": [
"masculine"
],
"word": "harmonický průměr"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "type of average",
"word": "harmoninen keskiarvo"
},
{
"code": "fr",
"lang": "French",
"sense": "type of average",
"word": "moyenne harmonique"
},
{
"code": "de",
"lang": "German",
"sense": "type of average",
"tags": [
"neuter"
],
"word": "harmonisches Mittel"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "type of average",
"word": "harmonikus közép"
},
{
"code": "id",
"lang": "Indonesian",
"sense": "type of average",
"word": "rerata harmonik"
},
{
"code": "ja",
"lang": "Japanese",
"roman": "chōwaheikin",
"sense": "type of average",
"word": "調和平均"
},
{
"code": "ko",
"lang": "Korean",
"roman": "johwa pyeonggyun",
"sense": "type of average",
"word": "조화 평균"
},
{
"code": "pl",
"lang": "Polish",
"sense": "type of average",
"tags": [
"feminine"
],
"word": "średnia harmoniczna"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "type of average",
"tags": [
"Portugal",
"feminine"
],
"word": "média harmónica"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "type of average",
"tags": [
"Brazil",
"feminine"
],
"word": "média harmônica"
},
{
"code": "ru",
"lang": "Russian",
"roman": "srédneje garmoníčeskoje",
"sense": "type of average",
"tags": [
"neuter"
],
"word": "сре́днее гармони́ческое"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "type of average",
"tags": [
"feminine"
],
"word": "harmonijska sredina"
},
{
"code": "es",
"lang": "Spanish",
"sense": "type of average",
"tags": [
"feminine"
],
"word": "media armónica"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "type of average",
"tags": [
"neuter"
],
"word": "harmoniskt medelvärde"
},
{
"code": "tl",
"lang": "Tagalog",
"sense": "type of average",
"word": "suwatuhing tamtaman"
}
],
"word": "harmonic mean"
}
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