Talk:Quartile

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The article says:

Example 2:
Ordered Data Set: 7, 15, 36, 39, 40, 41
Q1 = (36+15)/2 = 25.5
Q2 = (39+36)/2 = 37.5
Q3 = (40+39)/2 = 39.5

Now unless I've misunderstood, shouldn't Q1 be 15 and Q3 be 40? The median cuts the 6 member data set into two 3 member data sets. The median of a 3 member data set is the item in the middle. 80.177.129.251 11:33, 11 September 2006 (UTC)

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[edit] Example 1

This is flat out wrong. Q1=15, the median is 40, and Q3=43. How could they see the correct median (Q2), but screw up the other quartiles? The number of variable is either odd or even: if it's an odd number, there is no need to do any averaging to find the quartiles. If it's even, you need the averages of three sets of two numbers. I could see this error happening if we were dealing with say 117 variables but 11? Sheesh.

[edit] Examples, discrete case

As the article stands now, the above posts have been taken into account. However, the two examples in the article - and also the 2nd post above - seem to indicate there are two cases, n odd and n even. I believe there are four cases (depending on n modulus 4):

  • 2, 6, 10, 14, ... observations:
Example with 10 observations: 11,13,16,17,19 ; 22,23,27,28,30: Q1=16, M=(19+22)/2, Q3=27 (mean involved in median only)
  • 3, 7, 11, 15, ... observations:
Example with 7 observations: 11,13,16,17,19,22,23: Q1=13, M=17, Q3=22 (no means involved)
  • 4, 8, 12, 16, ... observations:
Example with 8 observations: 11,13 ; 16,17 ; 19,22 ; 23,27: Q1=(13+16)/2, M=(17+19)/2, Q3=(22+23)/2 (all means!)
  • 5, 9, 13, 17, ... observations:
Example with 9 observations: 11,13 ; 16,17,19,22,23 ; 27,28: Q1=(13+16)/2, M=19, Q3=(23+27)/2 (means involved in quartiles only)

In other words:

  • With an odd number of observations, the median is the middle observation, and the quartiles are the medians of the lower resp. upper half of the observations, omitting the middle one.
  • With an even number of observations, the median is the mean of the two middle observations, and the quartiles are the medians of the lower resp. upper half of the observations.

Finding the median of half the observations, one may again have to consider either an odd or an even number of observations; hence the four cases above.

[edit] Grouped data

Honestly I do not understand everything in the article; the answer to the following question may be hidden in there. But how do you find quartiles for grouped data? (I know the answer, I think, involving a cumulative frequency graph, but I have discovered that some advocate strange variants of "my" methods, and I donøt understand why.)--Niels Ø 22:44, 27 November 2006 (UTC)


[edit] Explicit rule

I added an example of an explicit rule for computing quartile values (there is no uniform agreement on this). I this way the reader can work out the examples for himself. I also added an example where the quartile values are not data points. 84.196.107.235 07:13, 10 March 2007 (UTC)

[edit] Invalid Example That doesn't follow the rule

I think the title is enough to explain everything, not to mention all the discussions above. The first example is clearly inconsistent with what is mentioned to be the rule of finding quartiles (lower and upper). Please resolve this. --Freiddie 12:56, 1 April 2007 (UTC)

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