Boxplot (seemingly) does not show outlier

Posted by Tom Werner on Apr 05, 2007; 3:37pm
URL: http://spssx-discussion.165.s1.nabble.com/Boxplot-seemingly-does-not-show-outlier-tp1074926.html

In SPSS (12.0 for Windows, Student version) when I attempt to produce a
boxplot of four data points (62, 61, 59, and 33), SPSS generates the boxplot...

...but does NOT show 33 as an outlier (even though 33 would seem to be an
outlier relative to 62, 61, and 59 to the casual observer).

(I'm analyzing the scores of sets of four judges and would like to use SPSS
to produce boxplots to indicate 'outlier' judge scores.)

Even if I change the value of 33 to 13, it still does not show in a boxplot
as an outlier.

If I add a fifth data point (with a value as low as 50), 33 shows in a
boxplot as an outlier.

Can anyone explain this?

1.  Is it because of the even number of data points (four), thus requiring
that the median be a calculated value?

2.  Are five data points that much more powerful than four data points at
producing a tighter intraquartile range (i.e., a tighter box in the
boxplot), and thus generating an outlier?

3.  Is this perhaps a quirk of SPSS?

Much thanks for any help!