See Chebyshev's inequality in All languages combined, or Wiktionary
Download JSON data for Chebyshev's inequality meaning in English (4.2kB)
{
"etymology_text": "From the surname of Russian mathematician Pafnuty Chebyshev (1821–1894), the discoverer.",
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"orig": "en:Probability theory",
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"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:",
"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-P1WVI6I2",
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"variance",
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"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"
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],
"synonyms": [
{
"word": "Chebyshev inequality"
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{
"word": "Tchebycheff inequality"
},
{
"word": "Tchebycheff's inequality"
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"topics": [
"mathematics",
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"statistics"
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"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.",
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"examples": [
{
"text": "Pr (|X-μ|≥kσ)≤1/(k²)"
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"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:",
"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"
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"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": [
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"wikipedia": [
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"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": [
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],
"word": "нера́венство Чебышёва"
},
{
"code": "es",
"lang": "Spanish",
"sense": "theorem",
"tags": [
"feminine"
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"word": "desigualdad de Chebyshov"
}
],
"word": "Chebyshev's inequality"
}
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