See harmonic mean on Wiktionary
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"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.}}",
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"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."
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{
"topics": [
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"word": "measure of central tendency"
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{
"word": "Pythagorean mean"
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"(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."
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"word": "arithmetic mean"
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"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",
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"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": "hi",
"lang": "Hindi",
"roman": "harātmak mādhya",
"sense": "type of average",
"word": "हरात्मक माध्य"
},
{
"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"
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}
],
"word": "harmonic mean"
}
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"examples": [
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"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.}}",
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"(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."
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"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": "hi",
"lang": "Hindi",
"roman": "harātmak mādhya",
"sense": "type of average",
"word": "हरात्मक माध्य"
},
{
"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"
}
Download raw JSONL data for harmonic mean meaning in All languages combined (4.9kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.