Mean, median, and mode

[Josiah Carlson]

mfuhr at fuhr.org (Michael Fuhr) wrote:
> 
> Josiah Carlson <jcarlson at uci.edu> writes:
> 
> 
> > "Robert Brewer" <fumanchu at amor.org> wrote:
> > > 
> > > Josiah Carlson wrote:
> > > > 
> > > > median = lambda x: x.sort() or x[len(x)//2]
> > > 
> > > That...is a really sneaky use of null return values. I like. :)
> >
> > Thank you, I'm just using a paradigm (exploiting lambdas) that I picked
> > up while going through various functional programming modules.
> 
> print median([1, 2, 3, 4, 5, 6])
> 4
> 
> Shouldn't the median be 3.5?

The wikipedia entry (as mentioned by Peter Hanson in another post) is
incomplete. There are 3 valid medians for even-lengthed sequences:
    sorted(seq)[len(seq)//2]
    sorted(seq)[len(seq)//2-1]
    sum(sorted(seq)[len(seq)//2-1:len(seq)//2+2])/2.0

All are correct, what is /desired/ is generally application specific. If
you want the statistical median, 3.5 is the answer.  If you want a
computer science median (for quicksort, etc.), 3 or 4 is sufficient.  I
chose the shortest implementation (using the author's style, without
sorted, because I forgot about the new builtin), which gives the greater
(or equal) of the two possible computer science median values.


 - Josiah