My understanding is that for an even number of values there is no universally accepted correct value for the median. The average of the two middle values (your defn (the same as that from stats/base/univariate)) is oftn used though.
Sent from my Windows® phone. -----Original Message----- From: Devon McCormick <[email protected]> Sent: Saturday, 17 October 2009 07:23 To: J-programming forum <[email protected]> Subject: [Jprogramming] "median" considered inaccurate? Members of the forum - while looking up some statistical definitions, I came across this example http://www2.le.ac.uk/offices/ssds/sd/ld/resources/numeracy/variability in which the calculation of the median disagrees with the result of the one listed as "m0=: median=: <....@-:@# { /:~" in "MathStats" on the J wiki. I was actually looking at the definition of quartiles when I noticed this. For the series #scrs=. 43 48 50 50 52 53 56 58 59 60 62 65 66 68 70 71 74 76 78 80 20 m0=: <....@-:@# { /:~ m0 scrs 62 median scrs NB. my own definition 61 median -:@(+/)@((<. , >.)@midpt { /:~) midpt -:@<:@# Also, this site's answers disagree with Excel and with my own quartile function, applied to "scrs" above, but I think the site is correct: NB. Quartiles 1-3 according to Excel: 52.75 61 70.25 NB. According to http://www2.le.ac.uk/offices/ssds/sd/ld/resources/numeracy/variability: 52.5 61 70.5 0 1 2 quartile&><scrs 52 60 70 NB. My "quartile" disagrees with my "median": the middle quartile should be the same as the median. quartile 4 : 'x{4 ntilebps y' ntilebps 4 : 0 NB.* ntilebps: return breakpoint values of x-tiles of y; e.g. 4 ntilebps y NB. -> quartiles; 0-based so "1st" quartile is 0{4 ntilebps y. quant=. x y=. /:~y wh=. 0 1#:(i.quant)*quant%~#y NB. Where partition points are exactly 'n f'=. |:wh NB. whole and fractional part of partitions 1|.+/"1 ((1-f),.f)*(n+/_1 0){y NB. "1|." moves top quantile to end. ) Anyone care to weigh in on this? Regards, Devon -- Devon McCormick, CFA ^me^ at acm. org is my preferred e-mail ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
