Looked up the definition of "median" and it appears that there are several
definitions of "median". And, according to
http://en.wikipedia.org/wiki/Median median and quartiles can be messy with
badly skewed data. Best I can tell this is a measurement that should be used
with care.
I wrote a quick verb which gives the same answers as the site you referenced
and it does strange things, depending on the data. If the count of the set
is odd, which group should have the extra number? What if the data is really
skewed?
qr=.([:([:(+/%#)]{~[:(<:,:])[:>.0.25 0.5 0.75"_*#)]/:]) NB. Needs
cleaning up.
qr scrs
52.5 61 70.5
qr i.4
0.5 1.5 2.5
qr i.5
1.5 2.5 3.5
qr i.12
2.5 5.5 8.5
qr i.11
2.5 5.5 8.5
qr i.13
3.5 6.5 9.5
-~/0 2{qr scrs
18
qr 1 1 1 1 1 2 3 4
1 1 2.5
On Fri, Oct 16, 2009 at 1:21 PM, Devon McCormick <[email protected]> wrote:
> 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
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