If I understand median, the convential median index is median_index=: (<.~.@,>.)@(0.5 * # - 1:)
This gives you indices into the sorted list. This is also apparently an arbitrary convention. Based on the current description at http://en.wikipedia.org/wiki/Quantile the general approach apparently looks like this: quantile_indices=: >.@((%~ }.@i.)@[ * #@]) - 1: 2 quantile_indices i.100 49 3 quantile_indices i.100 33 66 4 quantile_indices i.100 24 49 74 -- Raul On Tue, Jan 10, 2012 at 1:16 PM, Roger Hui <[email protected]> wrote: > Yes, but if you are writing a verb to compute the median, what are the > results of: > median 1 2 3 4 5 6 7 8 9 10 > median 1 2 3 4 5 6 7 8 9 10 11 > > > > On Tue, Jan 10, 2012 at 9:57 AM, Brian Schott <[email protected]>wrote: > >> >> >> Think of the median as its position in the ordered list, not as the number >> in that position. Then to compute the quartiles, only use the values in >> positions above and below the position of the median. So for example if >> there are three numbers that all equal the median, only the middle one has >> the median's position. >> >> --- >> (B=) >> >> On Jan 10, 2012, at 11:58 AM, Roger Hui <[email protected]> wrote: >> >> > Thanks to you and all other respondents for their helpful replies. >> > >> > Do Moore & McCabe offer any guidance on how to compute the medians? >> > Wikipedia says "there is no universal agreement on choosing the quartile >> > values". As well, in computing the IQR I have seen methods that make >> sense >> > to me but are quite tricky depending on whether #x is odd or even. >> > >> > e.g Suppose x is 1 2 3 4 5, 6 7 8 9 10. The descriptions I have seen say >> > that the median is 5.5. When you then compute the median of the lower >> half >> > (q1), you exclude the 5.5, and report that q1 is 3, and likewise q3 is 8. >> > In contrast, if y is 1 2 3 4 5, 6, 7 8 9 10 11, the median is 6, but when >> > you compute q1 you *include* the 6 with the lower half, and report that >> q1 >> > is 3.5, likewise you include 6 with the upper half so that q3 is 8.5. >> > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
