See Chebyshev's inequality on Wiktionary
{ "etymology_text": "From the surname of Russian mathematician Pafnuty Chebyshev (1821–1894), the discoverer.", "head_templates": [ { "args": { "head": "Chebyshev's inequality" }, "expansion": "Chebyshev's inequality", "name": "en-proper noun" } ], "lang": "English", "lang_code": "en", "pos": "name", "senses": [ { "categories": [ { "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w" }, { "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w" }, { "kind": "other", "name": "Pages with entries", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Catalan translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Czech translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Finnish translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with French translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with German translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Italian translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Mandarin translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Portuguese translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Russian translations", "parents": [], "source": "w" }, { "kind": "other", "name": "Terms with Spanish translations", "parents": [], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Probability theory", "orig": "en:Probability theory", "parents": [ "Mathematical analysis", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Statistics", "orig": "en:Statistics", "parents": [ "Formal sciences", "Mathematics", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "examples": [ { "text": "Pr (|X-μ|≥kσ)≤1/(k²)" } ], "glosses": [ "The theorem that in any data sample with finite variance, the probability of any random variable X that lies k or more standard deviations away from the mean is no more than 1/k², i.e. assuming mean μ and standard deviation σ, the probability is" ], "id": "en-Chebyshev's_inequality-en-name-BhYNRifH", "links": [ [ "statistics", "statistics" ], [ "sample", "sample" ], [ "finite", "finite" ], [ "variance", "variance" ], [ "random variable", "random variable" ], [ "standard deviation", "standard deviation" ], [ "mean", "mean" ] ], "raw_glosses": [ "(statistics) The theorem that in any data sample with finite variance, the probability of any random variable X that lies k or more standard deviations away from the mean is no more than 1/k², i.e. assuming mean μ and standard deviation σ, the probability is:" ], "related": [ { "word": "Chebyshev's sum inequality" } ], "synonyms": [ { "word": "Chebyshev inequality" }, { "word": "Tchebycheff inequality" }, { "word": "Tchebycheff's inequality" } ], "topics": [ "mathematics", "sciences", "statistics" ], "translations": [ { "code": "ca", "lang": "Catalan", "sense": "theorem", "tags": [ "feminine" ], "word": "desigualtat de Txebixov" }, { "code": "cmn", "lang": "Chinese Mandarin", "roman": "Qièbǐxuěfū bùděngshì", "sense": "theorem", "word": "切比雪夫不等式" }, { "code": "cs", "lang": "Czech", "sense": "theorem", "tags": [ "feminine" ], "word": "Čebyševova nerovnost" }, { "code": "fi", "lang": "Finnish", "sense": "theorem", "word": "Tšebyšovin epäyhtälö" }, { "code": "fr", "lang": "French", "sense": "theorem", "tags": [ "feminine" ], "word": "inégalité de Tchebychev" }, { "code": "de", "lang": "German", "sense": "theorem", "tags": [ "feminine" ], "word": "tschebyscheffsche Ungleichung" }, { "code": "de", "lang": "German", "sense": "theorem", "tags": [ "feminine" ], "word": "Tschebyscheff-Ungleichung" }, { "code": "it", "lang": "Italian", "sense": "theorem", "tags": [ "feminine" ], "word": "disuguaglianza di Čebyšëv" }, { "code": "pt", "lang": "Portuguese", "sense": "theorem", "tags": [ "feminine" ], "word": "desigualdade de Chebyshev" }, { "code": "ru", "lang": "Russian", "roman": "nerávenstvo Čebyšóva", "sense": "theorem", "tags": [ "neuter" ], "word": "нера́венство Чебышёва" }, { "code": "es", "lang": "Spanish", "sense": "theorem", "tags": [ "feminine" ], "word": "desigualdad de Chebyshov" } ], "wikipedia": [ "Chebyshev's inequality", "Pafnuty Chebyshev" ] } ], "word": "Chebyshev's inequality" }
{ "etymology_text": "From the surname of Russian mathematician Pafnuty Chebyshev (1821–1894), the discoverer.", "head_templates": [ { "args": { "head": "Chebyshev's inequality" }, "expansion": "Chebyshev's inequality", "name": "en-proper noun" } ], "lang": "English", "lang_code": "en", "pos": "name", "related": [ { "word": "Chebyshev's sum inequality" } ], "senses": [ { "categories": [ "English entries with incorrect language header", "English eponyms", "English lemmas", "English multiword terms", "English proper nouns", "English uncountable nouns", "Entries with translation boxes", "Pages with 1 entry", "Pages with entries", "Terms with Catalan translations", "Terms with Czech translations", "Terms with Finnish translations", "Terms with French translations", "Terms with German translations", "Terms with Italian translations", "Terms with Mandarin translations", "Terms with Portuguese translations", "Terms with Russian translations", "Terms with Spanish translations", "en:Probability theory", "en:Statistics" ], "examples": [ { "text": "Pr (|X-μ|≥kσ)≤1/(k²)" } ], "glosses": [ "The theorem that in any data sample with finite variance, the probability of any random variable X that lies k or more standard deviations away from the mean is no more than 1/k², i.e. assuming mean μ and standard deviation σ, the probability is" ], "links": [ [ "statistics", "statistics" ], [ "sample", "sample" ], [ "finite", "finite" ], [ "variance", "variance" ], [ "random variable", "random variable" ], [ "standard deviation", "standard deviation" ], [ "mean", "mean" ] ], "raw_glosses": [ "(statistics) The theorem that in any data sample with finite variance, the probability of any random variable X that lies k or more standard deviations away from the mean is no more than 1/k², i.e. assuming mean μ and standard deviation σ, the probability is:" ], "topics": [ "mathematics", "sciences", "statistics" ], "wikipedia": [ "Chebyshev's inequality", "Pafnuty Chebyshev" ] } ], "synonyms": [ { "word": "Chebyshev inequality" }, { "word": "Tchebycheff inequality" }, { "word": "Tchebycheff's inequality" } ], "translations": [ { "code": "ca", "lang": "Catalan", "sense": "theorem", "tags": [ "feminine" ], "word": "desigualtat de Txebixov" }, { "code": "cmn", "lang": "Chinese Mandarin", "roman": "Qièbǐxuěfū bùděngshì", "sense": "theorem", "word": "切比雪夫不等式" }, { "code": "cs", "lang": "Czech", "sense": "theorem", "tags": [ "feminine" ], "word": "Čebyševova nerovnost" }, { "code": "fi", "lang": "Finnish", "sense": "theorem", "word": "Tšebyšovin epäyhtälö" }, { "code": "fr", "lang": "French", "sense": "theorem", "tags": [ "feminine" ], "word": "inégalité de Tchebychev" }, { "code": "de", "lang": "German", "sense": "theorem", "tags": [ "feminine" ], "word": "tschebyscheffsche Ungleichung" }, { "code": "de", "lang": "German", "sense": "theorem", "tags": [ "feminine" ], "word": "Tschebyscheff-Ungleichung" }, { "code": "it", "lang": "Italian", "sense": "theorem", "tags": [ "feminine" ], "word": "disuguaglianza di Čebyšëv" }, { "code": "pt", "lang": "Portuguese", "sense": "theorem", "tags": [ "feminine" ], "word": "desigualdade de Chebyshev" }, { "code": "ru", "lang": "Russian", "roman": "nerávenstvo Čebyšóva", "sense": "theorem", "tags": [ "neuter" ], "word": "нера́венство Чебышёва" }, { "code": "es", "lang": "Spanish", "sense": "theorem", "tags": [ "feminine" ], "word": "desigualdad de Chebyshov" } ], "word": "Chebyshev's inequality" }
Download raw JSONL data for Chebyshev's inequality meaning in All languages combined (3.3kB)
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.