Last Updated
：2025/11/21
Chebyshev's inequality
Proper noun
Japanese Meaning
有限分散を持つ任意のデータサンプルにおいて、平均μからk倍以上の標準偏差σ離れた位置にある任意の確率変数Xの出現確率が、1/k²以下となることを保証する統計学の定理。
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(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:
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Chebyshev's inequality
Chebyshev's inequality shows that, for any distribution with finite variance, the probability that a random variable lies at least k standard deviations from the mean is at most 1/k2.
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Chebyshev's inequality shows that, for any distribution with finite variance, the probability that a random variable lies at least k standard deviations from the mean is at most 1/k2.
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