query: Show that $|\operatorname{median}(X) - \operatorname{mean}(x)| \leq \sigma_X$
positive_passages.docid: 12669
positive_passages.text: Distance between mean and median
negative_passages.docid: 47644
negative_passages.text: Inequality involving rearrangement: $ \sum_{i=1}^n |x_i - y_{\sigma(i)}| \ge \sum_{i=1}^n |x_i - y_i|. $
negative_passages.docid: 115352
negative_passages.text: C++: Mean Median and Mode
negative_passages.docid: 139537
negative_passages.text: Show that $x\subseteq y \Leftrightarrow \mathcal{P}(x)\subseteq\mathcal{P}(y)$.
negative_passages.docid: 120624
negative_passages.text: Weighted median of a portfolio
negative_passages.docid: 30386
negative_passages.text: Showing the inequality $|\alpha + \beta|^p \leq 2^{p-1}(|\alpha|^p + |\beta|^p)$
negative_passages.docid: 78754
negative_passages.text: Showing that $E[X|X<x]$ is smaller or equal than $E[X]$ for all x
negative_passages.docid: 52618
negative_passages.text: AM-GM inequality basic
negative_passages.docid: 20040
negative_passages.text: shorter proof of generalized mediant inequality?
negative_passages.docid: 28822
negative_passages.text: $|x| - |y| \leq |x-y|?$
negative_passages.docid: 69082
negative_passages.text: Show that $\frac{X}{X+Y}\sim Beta(\alpha,\beta)$
negative_passages.docid: 131626
negative_passages.text: Finding the distribution of $\|X-\mu \|_\Sigma^2$ with $X \sim N(\mu,\Sigma)$
negative_passages.docid: 106979
negative_passages.text: Prove the inequality and limitation
negative_passages.docid: 4064
negative_passages.text: An equality involving the mean value property
negative_passages.docid: 9938
negative_passages.text: Proof of upper-tail inequality for standard normal distribution
negative_passages.docid: 116689
negative_passages.text: Joint distribution of range $(R=X_n-X_1)$ and mid-range $(V=\frac{1}{2}(X_1+X_n)$order statistics
negative_passages.docid: 117417
negative_passages.text: Prove that the standard deviation is less than half the range