Talk:Median

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Contents

[edit] Optimality property

Does someone know how to demonstrate this optimality property ?

[edit] The posted definition is partly wrong!!

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)

Okay, I will show you mine, and you show me yours

Biometry by Sokal and Rolf, 3rd edition, pages 44 to 46, specifically box 4.1

Statisitics Explained by Mckillup 2006, page 74 and 75.

You are correct that I am an instructor telling students how to do exercises and it is very confusing when the posting emphasizes this nonstandard, and as far as I can tell unaccepted interpretation of the definition. Are there two definitions of median?? The middle variable(s) and the middle of the distribution? Even if section 2 of the article does follow logically, I have never seen anyone defy convention and state that there are two medians and to not interpolate. Can you please provide some sort of citaion where this nonuniqueness of the median idea is presented? If not, it might be good to pull it infavour of the interpolating definition to avoid confusing students. If you are correct and there are solid sources then we should add a bit on the interpolating convention in section 2 as a warning.

The best precise definition of "the median" of an even-cardinality multiset is not easy to discern. I have seen several good discussions and I'll try to find some references. The bottom line is that it seems not many practitioners care; but it can matter in automated software -- see the penultimate edition of Numerical Recipes versus the latest edition. I have a quibble about the definition in the Preamble where it says "If there are an even number of observations, one often takes the mean of the two middle values.” – but this last is ambiguous: Is the median of {0,1,1,2,2,2} 1.5, the average of numbers 1 & 2, or, rather and perhaps better, 1.6, the weighted mean of the sub-multiset formed of the two middle values {1,1,2,2,2}? The Preamble perhaps means (sorry!) to say "one often takes the average of the values of the two middle observations". But I like the subtlety of the other definition a little better, somehow; and it ought not to be too hard to construct an example of a discrete distribution limiting to a continuous one, in which the first definition behaves, in the limit, worse than the second. 75.36.232.78 11:19, 11 December 2006 (UTC)


For some discussions of this issue you might want to read: Hyndman, R. J. and Fan, Y. (1996) Sample quantiles in statistical packages, _American Statistician_, *50*, 361-365. Hadleywickham 03:30, 6 March 2007 (UTC)

[edit] Does anyone know what a "weighted median" is?

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)

[edit] Median = 50th percentile

I just wanted to check, the median's equal to the 50th percentile, right? I think this would be helpful to have in the defintion of median (assuming it's right).

Correct. Michael Hardy 23:04, 20 Apr 2005 (UTC)
I think the page currently incorrectly says that median is 50% percentile, rather than 50th percentile. I'm not an expert in statistics, so this is really just a question: Isn't this equivalent to 0.5-quantile (50%-quantile)? -- JKľ 2006-04-24

[edit] Efficient Computation

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)

[edit] Mode

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)


does somebody have a picture? Andries (talk) 19:13, 9 December 2007 (UTC) can you please include and intermediate definition of this. from and inteermidiate student!