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  "body": "\n## Definition\n\nLet $X_1, \\dots, X_n$ be random variables with values in a measurable space $(E, \\mathcal{E})$. For example, they can be a random sample from a law with an unknown parameter $\\theta$.\nA statistic is a random variable of the form $T = g(X_1, \\dots, X_n)$, where $g \\colon E^n \\to \\mathbb{R}^k$ is a measurable function that does not depend on $\\theta$.\n\n## Remarks\n\nExamples are the sample mean $\\bar{X}_n = (X_1 + \\dots + X_n)/n$, the sample variance, the sample maximum $\\max_i X_i$ and the order statistics.\nA statistic is a random variable, so it has a law: the sampling distribution of the statistic.\nA statistic that one uses to estimate a parameter is an [[estimator|0TTNRP5PFQ]]. A statistic that one uses to decide a hypothesis test is a test statistic.\n\n## Explanations\n\n### L1 human\n\nA statistic is a number that you can compute from your data alone, such as the average of the measurements.\nIt must not contain the unknown quantity that you want to learn about.\n",
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