query: Infimum of the sum of absolute differences from $x$ occurs when $x$ is the median
positive_passages.docid: 7740
positive_passages.text: The median minimizes the sum of absolute deviations (the $ {\ell}_{1} $ norm)
negative_passages.docid: 105768
negative_passages.text: Proof involving absolute value and maximums
negative_passages.docid: 7945
negative_passages.text: Approximate $|x|$ with a smooth function
negative_passages.docid: 156663
negative_passages.text: Interchanging limit with infimum/supremum
negative_passages.docid: 45361
negative_passages.text: Checking the consistency and Bias of $\frac{\sum X_i +\sqrt{n}/2}{n+\sqrt{n}}$
negative_passages.docid: 12669
negative_passages.text: Distance between mean and median
negative_passages.docid: 76290
negative_passages.text: arithmetic mean of a sequence converges
negative_passages.docid: 85614
negative_passages.text: Do inequalities hold under differentiation?
negative_passages.docid: 106816
negative_passages.text: Medians of a triangle and similar triangle properties
negative_passages.docid: 114786
negative_passages.text: Question about Infimum. (conclusion about intersection)
negative_passages.docid: 78463
negative_passages.text: Prove that $\sup \{-x \mid x \in A\} = -\inf\{x\mid x \in A\}$
negative_passages.docid: 130996
negative_passages.text: Find the median of an array
negative_passages.docid: 119558
negative_passages.text: A basic question on convergence in prob. and a.s. convergence
negative_passages.docid: 13750
negative_passages.text: Position the limits of Sum
negative_passages.docid: 96931
negative_passages.text: Supremum and infimum of $\{\frac{1}{n}-\frac{1}{m}:m, n \in \mathbb{N}\}$
negative_passages.docid: 155415
negative_passages.text: Minimax problem for optimization $\inf \sup \frac{x f(x)}{\int_0^1 f(t) dt}$
negative_passages.docid: 10079
negative_passages.text: Standard error of the median