Talk:Interquartile range

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This article was the subject of a Wiki Education Foundation-supported course assignment, between 27 August 2021 and 19 December 2021. Further details are available on the course page. Student editor(s): Pinkfrog22. Peer reviewers: Ziyanggod, GeorgePan1012, Jiang1725.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 00:42, 17 January 2022 (UTC)

Q4?

What Q4 stands for in this article? --Piecu 09:41, 7 August 2007 (UTC)

The 4th quartile, the maximum.

Merge?

Should midhinge be merged into this? And all of the synonyms redirected here? —Preceding unsigned comment added by Belg4mit (talk • contribs) 18:48, 24 October 2007 (UTC)

Eeep, according to its article, the midhinge is the mean of the quartiles, a measure of location, while the IQR is their difference, a measure of scale. That article needs fixing... But yes, after things are set right, it would seem some consolidation here would be a good thing. Baccyak4H (Yak!) 19:01, 24 October 2007 (UTC)

Data in table

There is something strange with this table

3	105	Q1
4	107
5	108
6	109
7	110	Q2 (median)
8	112
9	115	Q3
10	116
11	118

While the median is the 7the value, the number of data should be 13. Apparently some data are not shown, but with 13 data Q1 is the the mean of the 3rd and 4th, and Q3 the mean of the 10th and 11th value in the ordering. Nijdam (talk) 19:58, 16 May 2010 (UTC)

I found the original table and restored it. Nijdam (talk) 06:59, 17 May 2010 (UTC)

Somehow the data table has become incomprehensible. The values x[i] are no longer sorted and the quartiles no longer ordered, in particular Q1 > Q3. Therefore, the IQR makes no more sense either. 129.69.210.11 (talk) 12:18, 14 December 2016 (UTC)

Interquartile range of distributions

In the table, what is phi^-1? Also, under 'Interquartile range test for normality', is there a reference, or more importantly, is there an objective way to define "differ substantially", i.e. is there a proper test rule for this that gives probability values? Moo (talk) 16:02, 10 May 2012 (UTC)

Φ⁻¹ is the quantile function (inverse of the cumulative distribution function) of the standard normal distribution. I have found a table for the distribution of the studentized range, but not the studentized interquantile range. For the studentized range, the test is not described as a test of normality, but rather as an indicator of outliers or data problems. The only hits on google for "Interquartile range test for normality" seem to be copies of this article. Melcombe (talk) 20:34, 10 May 2012 (UTC)

Interquartile range test for normality of distribution

This lsection is incomprehensive. Anyone understanding it, anyone to improve it?? Nijdam (talk) 11:25, 8 April 2013 (UTC)

The middle 50%

I'm not a big stats guy by any means, but is there any good reason for not simply saying that the interquartile range is the middle 50% of a collection of rank ordered data? That's basically the easiest way to explain it - and how most of us initially understood it - yet instead of writing that here we have a fairly confusing (if technically accurate) description in this article. Namely that it's the "difference between the upper and lower quartiles" or the "25% trimmed mid-range" (which, to my eyes, are simply phrases that say "middle 50%" in a somewhat confusing way).

I ask because not being a big stats guy maybe I've overlooked something. However if not, and it is always the middle 50%, then I think this should be changed for clarity. There's no point in having a technically accurate description if it confuses lay readers. Bandanamerchant (talk) 01:00, 6 January 2014 (UTC)

"the middle 50%" would be ambiguous. I don't know your understanding of this term, but for me it would be the set of values between the 1st and 3rd quartile, not the difference between the smallest and largest of this set. In my opinion it is more confusing if everyone immediately understands what is meant by it, but ends up at a different answer. For instance, some journal in medicine caused me to come here because it states that the interquartile range is the pair of Q1 and Q3 values, not their absolute difference. (Search for https://www.google.de/search?q=interquartile+range+nejm if you don't believe me.) --Johannes Hüsing (talk) 07:53, 17 November 2015 (UTC)

"figure 3" caption incorrect?

hello everybody,
is it me, or is the caption to "figure 3" incorrect on several levels?
firstly, there are two figures on that page, and the first one is not referred to as "figure 1",
and secondly, the caption says "Box-and-whisker plot with [...] extreme values, defined as outliers above Q3 + 1.5(IQR) and Q3 + 3(IQR), respectively.", whereas the actual image description says they're standard Q1-1.5(IQR) and Q3+1.5(IQR) whiskers.

--Mnolf (talk) 11:59, 27 January 2014 (UTC)

Algorithm Section appears to be out of date

The "Algorithm" section appears to me to be out of date, with its citation of a 1988 German-language textbook. I found this Quartile page which outlines the various methods in use, and Method 2 seems to be the one presented on this page as definitive, but as we can see on the Quartile page it is by no means definitive, and the dataset presented below is misleading as it gives the same answer regardless of which method you use. Could we replace this "Algorithm" section by a link to the Quartile page? I'm new at this, not sure how to do so. — Preceding unsigned comment added by Bellastrange (talk • contribs) 21:14, 14 December 2017 (UTC)

Looking for citations

For this content Interquartile range test for normality of distribution

The IQR, mean, and standard deviation of a population P can be used in a simple test of whether or not P is normally distributed, or Gaussian. If P is normally distributed, then the standard score of the first quartile, z1, is −0.67, and the standard score of the third quartile, z3, is +0.67. Given mean =  {\displaystyle {\bar {P}}}

and standard deviation = σ for P, if P is normally distributed, the first quartile

{\displaystyle Q_{1}=(\sigma \,z_{1})+{\bar {P}}}

and the third quartile

{\displaystyle Q_{3}=(\sigma \,z_{3})+{\bar {P}}}

If the actual values of the first or third quartiles differ substantially [clarification needed] from the calculated values, P is not normally distributed. However, a normal distribution can be trivially perturbed to maintain its Q1 and Q2 std. scores at 0.67 and −0.67 and not be normally distributed (so the above test would produce a false positive). A better test of normality, such as Q–Q plot would be indicated here. — Preceding unsigned comment added by Pinkfrog22 (talk • contribs) 18:56, 14 December 2021 (UTC)