R help - Sep 2009 - strange results in summary and IQR functions

Dear R users,
Something is strange in summary and IQR. Suppose, I have a data set and I
would like to find the Q1, Q2, Q3 and IQR.  
 
x<-c(2,4,11,12,13,15,31,31,37,47)
> summary(x)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   2.00   11.25   14.00   20.30   31.00   47.00 
> IQR(x)
[1] 19.75
However, I test the same data set in SAS "proc univariate", and SAS
shows
that Q1=11, Q2=14 and Q3=31. I think most of us agree that Q1 is 11 not
11.25. 

Could someone please explain to me why R shows Q1=11.25 not 11?

Many Thanks
Tu


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It's all simply a matter of definitions, and there are many who disagree.
See ?quantile , specifically the "type" argument.  Since IQR does not
appear to have a type argument, you could easily write your own versions of
these that do what SAS does (assuming that is your goal).

With x defined as you have it, look at the results of this function call, which
shows the different values for quantile that you get by using different
"type" arguments.
> sapply(1:9, function(y) quantile(x, type = y))
     [,1] [,2] [,3] [,4] [,5]  [,6]  [,7]     [,8]    [,9]
0%      2    2    2  2.0    2  2.00  2.00  2.00000  2.0000
25%    11   11    4  7.5   11  9.25 11.25 10.41667 10.5625
50%    13   14   13 13.0   14 14.00 14.00 14.00000 14.0000
75%    31   31   31 31.0   31 32.50 31.00 31.50000 31.3750
100%   47   47   47 47.0   47 47.00 47.00 47.00000 47.0000


Best,
Erik Iverson 


-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On Behalf Of Chunhao Tu
Sent: Tuesday, September 08, 2009 10:09 AM
To: r-help at r-project.org
Subject: [R] strange results in summary and IQR functions


Dear R users,
Something is strange in summary and IQR. Suppose, I have a data set and I
would like to find the Q1, Q2, Q3 and IQR.  
 
x<-c(2,4,11,12,13,15,31,31,37,47)
> summary(x)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   2.00   11.25   14.00   20.30   31.00   47.00 
> IQR(x)
[1] 19.75
However, I test the same data set in SAS "proc univariate", and SAS
shows
that Q1=11, Q2=14 and Q3=31. I think most of us agree that Q1 is 11 not
11.25. 

Could someone please explain to me why R shows Q1=11.25 not 11?

Many Thanks
Tu


-- 
View this message in context:
http://www.nabble.com/strange-results-in-summary-and-IQR-functions-tp25348079p25348079.html
Sent from the R help mailing list archive at Nabble.com.

______________________________________________
R-help at r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.

Have a look at ?IQR
  "Note that this function computes the quartiles using the quantile
function rather than following Tukey's recommendations, i.e., IQR(x) =
quantile(x,3/4) - quantile(x,1/4)."

It looks like boxplot() gives the results you expect.  

tt <- boxplot(x)
tt







--- On Tue, 9/8/09, Chunhao Tu <tu_chunhao at yahoo.com> wrote:
> From: Chunhao Tu <tu_chunhao at yahoo.com>
> Subject: [R]  strange results in summary and IQR functions
> To: r-help at r-project.org
> Received: Tuesday, September 8, 2009, 11:09 AM
> 
> Dear R users,
> Something is strange in summary and IQR. Suppose, I have a
> data set and I
> would like to find the Q1, Q2, Q3 and IQR.? 
>  
> x<-c(2,4,11,12,13,15,31,31,37,47)
> > summary(x)
> ???Min. 1st Qu.? Median? ?
> Mean 3rd Qu.? ? Max. 
> ???2.00???11.25???14.00???20.30???31.00???47.00
> 
> > IQR(x)
> [1] 19.75
> However, I test the same data set in SAS "proc univariate",
> and SAS shows
> that Q1=11, Q2=14 and Q3=31. I think most of us agree that
> Q1 is 11 not
> 11.25. 
> 
> Could someone please explain to me why R shows Q1=11.25 not
> 11?
> 
> Many Thanks
> Tu
> 
> 
> -- 
> View this message in context:
http://www.nabble.com/strange-results-in-summary-and-IQR-functions-tp25348079p25348079.html
> Sent from the R help mailing list archive at Nabble.com.
> 
> ______________________________________________
> R-help at r-project.org
> mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained,
> reproducible code.
> 

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