Original report at SourceForge, opened Tue Jan 4 04:52:13 2011

If the boxplot is called with a small number of discrete, not unique values it shows a different median value than the median command. I consider this a bug.

How to reproduce:

example data

d = array([ 13., 9., 16., 8., 7., 14., 15., 5., 10., 16., 8., 15., 14., 19., 10., 10.], dtype=float32)
q1, med, q3 = mlab.prctile(d,[25,50,75]) # axes.py line 5005 axes.py (0.99.3 Rev 8345)
med_default = median(d) # for comparison
print((med,med_default)) # med = 13.0 med_default = 11.5

In the example I took the line in axes.py where the median value is computed and compare to a median directly computed. In my opinion the boxplot should use the median function to determine the median such that the same value is reported. I think the reason is in the different handling of equal values of prctile and median.

Anyway: Here is how to fix it:
Replace line 5005 with:
q1, q3 = mlab.prctile(d,[25,75])
And add a new line directly after it (new 5006):
med = np.median(d)

SourceForge Comments

On Thu Jan 13 04:42:32 2011, jmdb wrote:

And to add another point: matlab reports 8.5 for q1.

On Thu Jan 13 04:37:33 2011, jmdb wrote:

In addition: if one also computes:
from scipy import stats
stats.scoreatpercentile(d,25)

results in 8.75 while q1 from the example (which should be the same) is 9.0

I think either the mlab.prctle function should be fixed or be replaced by the function from the stats package.

On Tue Jan 4 05:03:55 2011, jmdb wrote:

Seems like this is also discussed here: http://permalink.gmane.org/gmane.comp.python.matplotlib.general/25835

I can add that the median function agrees with f.ex. matlab while the prctile function gives different results.