--- <dasimov@earthlink.net> wrote:
Jim writes:
<<
But: For very small samples, the median doesn't generally convey much information. For a large sample, however, this "bar-graph" median can be unduly influenced by outlying data -- much as an average can.
Really? It seems to me that the bar-graph median is very close to the "true" median. In one case, your probability measure on R is a combination of point-masses; in the other case, it's a combination of uniform distributions on disjoint intervals. But it's only near the median that it makes any difference which you're using.
I agree that if Jim's idea is translated into the corresponding thing for a continuous probability density, it's exactly thr usual median of a continuous distribution.
I don't think it's the same for a discrete distribution. (There's a big difference between a discrete distribution and one that's a combination of uniform continuous distributions on intervals.)
For example, given just one datum for each n, 1 <= n <= 100, one gets
the bar-graph median at x = 50.5.
But now say you just replace the single datum of 100 by a datum of 1000. The vertical line bisecting the area under the bar graph is at x = 999.9505 .
--Dan
No, the vertical bisector remains the same. You have just moved a little bit of the area to the right of the bisector further to the right. Gene __________________________________ Yahoo! Mail - PC Magazine Editors' Choice 2005 http://mail.yahoo.com