Question

Let $s^2=\frac{1}{n}\sum_1^n( X_i-\bar{X})^2$ and $\widetilde{X}$ denote the sample median. Is $s^2\leq \widetilde{X}(1-\widetilde{X})$ true

score 36 · Answer 1 · 2026-04-17 05:11:06

36

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Let $s^2=\frac{1}{n}\sum_1^n( X_i-\bar{X})^2$ and $\widetilde{X}$ denote the sample median. Is $s^2\leq \widetilde{X}(1-\widetilde{X})$ true

Published on 17 Apr 2026 - 5:11

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804

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30

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314

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126

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score 66 · Answer 7 · 2026-04-15 00:22:22

66

Views

How to show that the $\sum_{i=1}^{n}|A[i]-x|$ is minimal for $x=m$ with median $m$?

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score 192 · Answer 8 · 2026-04-16 06:34:52

192

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94

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score 58 · Answer 11 · 2026-04-17 09:02:56

58

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score 62 · Answer 12 · 2026-04-15 09:49:14

62

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69

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score 94 · Answer 14 · 2026-04-12 23:49:23

94

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score 152 · Answer 15 · 2026-04-15 07:16:33

152

Views

Sample $k$ of $n$ numbers (with replacement), what is the probability for a certain from the $n$ numbers to be the median of the $k$ numbers

Published on 15 Apr 2026 - 7:16

List Question

Let $s^2=\frac{1}{n}\sum_1^n( X_i-\bar{X})^2$ and $\widetilde{X}$ denote the sample median. Is $s^2\leq \widetilde{X}(1-\widetilde{X})$ true

Median Calculation on Grouped Interval Data

Inequality of difference of medians of two datasets.

What Can Median Tell Me About my Data?

Find a number having minimum sum of distances between a set of numbers

Property of median of probability distributiom

How to show that the $\sum_{i=1}^{n}|A[i]-x|$ is minimal for $x=m$ with median $m$?

Sample-quartile

Mean concentration implies median concentration

Is there a way to find $\min\{m(|X-c|), \:c \in \mathbb{R}\}$?

Distance to median vs average intra-distances

LP where I need to take medians of multiple sets of variables

Writing median rather than mean

Proving the median is less than the mean

Sample $k$ of $n$ numbers (with replacement), what is the probability for a certain from the $n$ numbers to be the median of the $k$ numbers

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