# Tagged Questions

The median is the value below which half the data or probability distribution lies - when the sample size is odd, the median is the 'middle' value of an ordered sample.

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### When to use sample median as an estimator for the median of a lognormal distribution?

I myself would always use geometric mean to estimate a lognormal median. However, in the industry world, sometimes using the sample median gives better results. The question thus is, is there a cutoff ...
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### How to estimate errors on a sample with very few data points

I have a very simple question to ask, but I can't figure this on my own. I have two samples: sample A with only three data points, and sample B with hundreds of points. For each sample I measure the ...
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### Does a median-unbiased estimator minimize mean absolute deviance?

This is a follow-up but also a different question of my previous one. I read on wikipedia that " A median-unbiased estimator minimizes the risk with respect to the absolute-deviation loss function, ...
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### Expression for the median of a sum of half-Cauchy random variables

This is a technical problem I encountered in research. Sorry if it reads simple for professional statisticians. Let $X_1, \cdots, X_n$ be iid standard Cauchy random variables. What estimate or exact ...
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### Median bootstrap

I ran a data set containing ages through SAS npar1way first, but a reviewer wanted standard errors, so that motivated a smooth bootstrap. Since I could not use survyselect, I had to code a data step. ...
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### Mean or median as the measure of central tendency for data spanning three orders of magnitude

Here is a data set I am working with. I basically have a total of 1082 different data segments of $y$ vs. $x$ all plotted here on a log scale in bright blue in the background. Now what I need to do ...
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### How does one derive the Fisher-consistency correction factor for Rousseeuw and Croux's $S_n$ (and $Q_n$)?

In "Alternatives to the Median Absolute Deviation" (Rousseeuw and Croux, J. Amer. Statistical Assoc, 88(424), 1993, pp.1273–1283) and a few other papers from the same authors published in ...
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### Nonintegral (and not half-integral) median

I was recently looking at the National Survey of Family Growth (US Census Bureau) and noticed that the numbers on the median column were not whole numbers, but rather numbers like 5.1 and 4.6. (Not ...
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### Breakdown point of weighted median

I posted the same question on math.stackexchange, but haven't got any reply. So I will try my luck here: In the context of robust statistics, there is the concept of breakdown point, which basically ...
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### Length weighted median

In the field of genome assemblies in biology (the problem being reconstructing the genome from many, short random pieces of it, where a genome is one or more long strings of a limited alphabet), there ...
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### Mean and median in Zipf's distribution

I have a collection of $10^5$ essays, each of which on average contains $10^3$ distinct words. There are $10^6$ distinct words in the entire collection. If I index every word what is the mean and ...
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### How to split up variable equally (50/50) above and below the median in Stata?

So I am trying to assign 1 to numbers above the median and 0 to those below the median using the generate command. The problem is that I have a bunch of numbers ...
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### Inferring low p values and medians

For my set of data, I have a very low p-value (< 2.2 e-16) and a median of -1. I'm new to statistics and I really am not sure what to make of this data and how to interpret it. Note: The p-value ...
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### How to report results from Friedman's test including post-hoc results

I have performed comparison of repeated measures for a group using Friedmanâ€™s test (K-related-samples test) and additional post-hoc analysis with Wilcoxon signed-rank test and Bonferroni correction. I ...
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### Machine learning Jaakkola different sized data

I have an assignment for a machine learning problem and requires me to to compute $G=\{\|X_i-X_j\| \mid (X_i,Y_i),(X_j,Y_j)\, \text{that belong to training data}\, S\, \text{and} Y_i\neq Y_j\}$. In my ...