Talk:Median

message: Does someone know how to demonstrate this optimality property ?
REPLY: This is a typical homework problem, whose solution can be found by visiting standard intermediate textbooks (only some of which have the solution). Kiefer.Wolfowitz (talk) 18:17, 3 June 2009 (UTC)
thread_title:  Optimality property 

message: Part 2 about the nonuniqueness is directly contradicted by the first external link at the bottom. Unless someone can find some documentation supporting not interpolating the median then this section needs to be removed. —Preceding unsigned comment added by Jdparker28 (talk • contribs) 
:Sorry, you fail to make your case.  That particular external link is not cogent unless perhaps it's an instructor telling students how he wished exercises done, or otherwise there for some extraneous reason.  The basic definition of "median" given in that same external link logically entails that what this article says is right.  So do innumerable books.  Certainly in some situations it makes sense to interpolate like that, but that doesn't mean the article is wrong to point out non-uniqueness of the median in certain cases. Michael Hardy 19:43, 17 October 2006 (UTC)
thread_title:  The posted definition is partly wrong!! 

message: Completed the example for an even number of observations as defined for a sample median. If there is a question regarding the uniqueness of a sample median for an even number of observations, please discuss first before changing the information. JackOL31 (talk) 01:55, 22 November 2009 (UTC)
thread_title:  The sample median  

message: : I've heard of a "smoothed weighted median", defined something like this.  Given a list of numbers xi for i = 1, ..., n, first consider a bell-shaped curve centered at each one.  Take a weighted average of those bell-shaped functions, getting a probability density.  Finally, take the median of that distribution.  The bell curves are the "smoothing".
: But here's my guess as to the general meaning of "weighted median".  Assign weights, i.e., non-negative numbers whose sum is 1, to all the numbers in your list; different numbers may carry different weights.  Take the median of the resulting discrete probablity distribution. Michael Hardy 21:52, 5 Jan 2005 (UTC)
thread_title:  Does anyone know what a "weighted median" is? 

message: Do you mean that although sorting time is O(nlogn) the median can be found in O(1) time if the list is sorted? Or does it mean that for an unsorted list the median can be found in O(n) time? I feel this needs clarification in the article 203.33.164.42 02:26, 2 April 2006 (UTC)
replies: text: This is Wikipedia. The selection algorithm is desribed in a linked, separate article. Note that Wikipedia does not mean to include pseudocode for all possible algorithms, this is still a dictionary, not a programming book --87.174.120.8 (talk) 08:22, 21 January 2011 (UTC)
replies: text:  Thanks, I understand now. I think it might preferable to move the "Efficient computation" part below the "Easy explanation" part. The way it is now is confusing. Roerd (talk) 23:50, 22 January 2011 (UTC)
thread_title:  Efficient Computation 

message: I think the relation between the median and mode is missing. The 'popular explanation' might actually be misunderstood to describe the mode, and the difference between the two concept is not given. Junuxx 03:35, 1 November 2006 (UTC)
thread_title:  Mode 

message: http://en.wikipedia.org/wiki/Median#Theoretical_properties says "Note, however, that c is not always unique, and therefore not well defined in general." Can someone give me an example where c is not unique? -72.221.120.191 (talk) 10:04, 15 June 2008 (UTC)
thread_title:  Note, however, that c is not always unique, and therefore not well defined in general. 

message: I recently rewrote the Computer Science median section. The original contribution strayed from the referenced article. The referenced article did not specifically deal with the "even case," and the original editor incorrectly used the term underflow.
The overall implementation of a median in Computer Science still needs a good source. Much appreciation to anyone who can find a good link.
Also, the even/odd cases are not currently dealt with (they weren't explained properly in the original section either).
JoshuaSchaeffer (talk) 23:24, 28 November 2008 (UTC)
thread_title:  Medians in Computer Science 

message: The article says For continuous probability distributions, the difference between the median and the mean is less than or equal to one standard deviation. However, I think this holds for any distribution, not just continuous one.  —Preceding unsigned comment added by Matumba (talk • contribs) 14:22, 19 January 2009 (UTC)
thread_title:  An inequality relating means and medians 

message: I quote 
==== History ====
Gustav Fechner introduced the median into the formal analysis of data.Keynes, John Maynard; A Treatise on Probability (1921), Pt II Ch XVII §5 (p 201).
Laplace was older then Fechner and used the median frequently. Therefore, I suggest using the alternative wording
Laplace used the sample median (to estimate the population median). Gustav Fechner further popularized the median for the statistical analysis of data.Keynes, John Maynard; A Treatise on Probability (1921), Pt II Ch XVII §5 (p 201).
or deleting this section, since I added a short discussion of median-unbiased estimators and the absolute-value loss function (again following the ideas of Laplace).Kiefer.Wolfowitz (talk) 18:22, 3 June 2009 (UTC)
thread_title:  History?? Laplace versus Fechner 

message: Gustav Fechner introduced the median into the formal analysis of data.Keynes, John Maynard; A Treatise on Probability (1921), Pt II Ch XVII §5 (p 201).
</blockquote>
Laplace was older then Fechner and used the median frequently. Therefore, I suggest using the alternative wording
Laplace used the sample median (to estimate the population median). Gustav Fechner further popularized the median for the statistical analysis of data.Keynes, John Maynard; A Treatise on Probability (1921), Pt II Ch XVII §5 (p 201).
or deleting this section, since I added a short discussion of median-unbiased estimators and the absolute-value loss function (again following the ideas of Laplace).Kiefer.Wolfowitz (talk) 18:22, 3 June 2009 (UTC)
thread_title:  History 

message: "Median is the middle value after arranging data by any order[citation needed]."
This obviously follows from the definition, does a definitive source have to be cited in this case? --99.39.111.144 (talk) 23:07, 25 October 2009 (UTC)
replies: text: Hmm... I'd say "no". To me, the concept of the median is an axiom, so a source is not needed. You don't see citations in the "addition" article neither. But if a source could be provided, it wouldn't hurt.--Nwinther (talk) 09:37, 14 January 2010 (UTC)
thread_title:  Citation Needed for obvious fact 

message: Who can tell me ?
i do not know how to find it.  —Preceding unsigned comment added by 219.76.99.194 (talk) 09:15, 3 November 2009 (UTC)
thread_title:  Find Mean,Median,Mode in Grouped data 

message: The first and second paragraphs are mostly incorrect. First, one must understand the difference between the median of a population and the median of a set of observations (aka sample median). This is similar to knowing the difference between the mean of a population [aka Expected value or µ = E(X)] and the mean of a sample [x-bar = Σ(i)/n]. Median of a population is not the same as the median of a sample. The median of a population is given in the section "Medians of probability distributions" and the median need not be unique. However, given an ordered sample of n observations where n is odd, the sample median is defined as the [(n+1)/2]th observation. If n is even, then the sample median is the arithmetic mean of the (n/2)th and [(n/2)+1]th observations. The median of a sample is unique (by definition). Also, the statement, "...The median may not be unique, as there may be a number of observations with the same value occupying the middle range of a distribution" mixes terminology of observations used in samples with members used in distributions. In other words, observations is to sample as members is to distribution. A sample has observations and a population has members. Starting at the second sentence thru the end of the second paragraph, the article needs to have the word distribution changed to sample and population changed to observations. None of it is referring to a distribution (population). The above definitions need to be included in the "Medians in descriptive statistics" with the correct definition of a unique median. I will make the appropriate changes after after discussion and concurrence. JackOL31 (talk) 21:24, 24 November 2009 (UTC)
replies: text: So much wrong, I got distracted. The statement, "...The median may not be unique, as there may be a number of observations with the same value occupying the middle range of a "distribution" (sic). First, "distribution" should be written as "sample" and the sample median is unique by definition. Secondly, the median will be unique when there are observations of the same value, for example {1, 4, 4, 5} yields a sample median of 4. Maybe I don't know what is being said here. JackOL31 (talk) 11:42, 22 November 2009 (UTC)

text: Corrected terminology in the "Easy explanation of the sample median" section. The is no "distribution" given nor are we working with numbers. We are working with (sample) observations with measured values, i.e. length of growth, scores for a quiz, etc.  —Preceding unsigned comment added by JackOL31 (talk • contribs) 00:35, 22 November 2009 (UTC)
replies: text: Melcombe did a fantastic job of cleaning this up. JackOL31 (talk) 21:37, 24 November 2009 (UTC)
thread_title: Definition (Nov 2009)

message: Should mention that U.S. census reports make very extensive use of medians where  people might expect averages to be used... AnonMoos (talk) 20:18, 1 November 2010 (UTC)
replies: text: This is a nice illustration of the 2-dimensional marginal median, in which the median is taken by components. (The marginal median should generally be avoided when the number of observations exceeds the dimension squared, as a rule of thumb). This application is discussed in recent papers on the multivariate median. Just search for "spatial median" and "United States" and "population center".  Kiefer.Wolfowitz 21:48, 7 May 2012 (UTC)
thread_title: U.S. Census use

message: I vaguely recall that a running median or median filter was included by Tukey et al. as part of "exploratory data analysis". Can anyone contribute text and reference for this? The present content covers image processing only, but this would have been for a time-series context. I see that there is an article on median polish, which is somewhat different it seems, and I suppose something on this might also be included here. Melcombe (talk) 13:03, 7 May 2012 (UTC)
replies: text: Look in 2004(?) Statistical Science, which had a special issue on nonparametric statistics. The last article was on nonparametric multivariate time series. There are some nice articles using spatial medians in chemometrics and image processing, for example.  Kiefer.Wolfowitz 21:52, 7 May 2012 (UTC)
replies: text: I have found (via google) Evans pdf (1981) on seismology which at least confirms Tukey as a basic origin for running medians and it has a range of interesting results. But I expect there are better sources. Melcombe (talk) 23:22, 7 May 2012 (UTC)
thread_title:  Running median or median filter 

message: Until recent edits, the text in this article was very similar to that in Bias_of_an_estimator#Median_unbiased_estimators, and that here has now been improved. I haven't looked to see what was copied where,  but I would suggest that that other aricle is the better place to have a longer outline of median-unbiasedness, with perhaps a reduction in the present article concentrating on whether/why the sample median is median-unbiased rather than median-unbiasedness itself. Melcombe (talk) 09:06, 9 May 2012 (UTC)
thread_title:  Median-unbiased 

message: I wonder if it would be appropriate to add a couple ways of determining the median (in nonproblematical cases).  For example, in an unordered and uncounted list, start with the largest and smallest numbers, and then the next pairs etc.  OR, in a spread sheet, take the number of entries, divide by two.... 211.225.33.104 (talk) 01:42, 16 January 2014 (UTC)
thread_title:  Calculating by hand etc. 

message: Just looked at the entry to learn more but found the piece a bit hard going with a liberal arts education.
Isn't it part of Wikipedia's mission to make information more accessible? An easier to read introduction would help a lot here.
Petercascio (talk) 20:45, 5 April 2014 (UTC)
thread_title:  Creating a section that is more readable for the mathematically challenged 

message: The page says, "In statistics and probability theory, the median is the numerical value separating the higher half of a data sample, a population, or a probability distribution, from the lower half." Numerical value is defined as the absolute value of a number, and as far as I know, the median need not be above zero, so I've changed numerical value to number. I'm not an expert, so make sure to change it back if I'm wrong.  — Preceding unsigned comment added by Y2N1-09631 (talk • contribs) 23:37, 5 March 2015 (UTC)
replies: text: "Numerical value", according to the source linked by you, means not always "absolute value"; sometimes also "definite quantity". But anyway, I agree: just "number" is better. Boris Tsirelson (talk) 05:48, 6 March 2015 (UTC)
thread_title:  Number, not numerical value 

message: I see what you did there...
149.71.132.107 (talk) 19:19, 27 May 2015 (UTC)
thread_title:  "The median is of central importance" 

message: I've was looking at this article and wondering if there's any sense in adding a basic illustration of the median concept at the top of the article, and if so how people think this could be done - any thoughts? I feel it would be nice to have a basic illustration of how you take the median (maybe from an odd-numbered dataset, then an even one), and a graphic showing how the mean can be skewed by outliers - essentially a representation of the median as it is taught on an average high-school course (which most people initially reading the article will be looking for). Blythwood (talk) 04:23, 16 June 2016 (UTC)
replies: text: What I've decided to do instead is give the article a reorganisation. I've written an introduction that's a lot more non-technical and really aimed for people with no more than basic maths if that. Then I've emphasised the basic procedure (which most people will be coming to this article for) by giving it its own section. Then moved most of the more technical material into a "discussion" section. In places where it makes sense to introduce technical material early I've cordoned it off at the end of a paragraph by using words like "in more technical terms" at the start of a sentence. And everywhere tried to deduplicate and reduce sentence and paragraph length. Let me know if you have any thoughts on this. Blythwood (talk) 21:09, 18 July 2016 (UTC)
thread_title:  Graphical representation 

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thread_title:  External links modified (January 2018) 

message: Recent changes to this article suggested that reordering data elements changes the median - that is simply incorrect. To arrive at the median, one finds the value such that at least half the set is less than or equal to the proposed value and half is greater than or equal (this is a paraphrase of the formal definition section) - that condition is clearly independent of the order of the data elements. MrOllie (talk) 03:03, 10 January 2024 (UTC)
thread_title:  Order of the data set