# [rc5] Re: OS/2 ramdisk and spindown

James Mastros root at jennifer-unix.dyn.ml.org
Wed Oct 15 01:12:47 EDT 1997

```On Mon, 13 Oct 1997 wooledge at kellnet.com wrote:
> James Mastros wrote:
> > (I
> > think.  I can't describe the median of an infinite set, wheras I can
> > describe the mean).
>
> Hmm... I'm no mathematician, but perhaps this will work:
>
> The median of a set of real numbers S is the number m such that for any
> randomly chosen element n of set S, there is precisely a 0.5 chance that
> n < m.
>
> That's probably not rigorous enough for real math, because "randomly
> chosen" isn't something I'd care to define except in vague terms.  But
> I think it's pretty clear for messy engineers like me. :-)
Actualy, it's chance that I have a problem with here.  (That def. simply
says "average" to me.)  The primary difficulty I have isn't with defining
median of an infinite set, it's defining it without steping through the set.
(Infinity/2 = infinity, so you need to start at the ends and work in.  Wait.
No ends either.)

> > In any case, I'm fairly certian that as the sample size increases,
> > the mean and median tend to converge.  I could be completly wrong here.  In
> > fact, I wouldn't be at all surprised.
>
> In "real life", that may be accurate, but it's not hard to construct
> a counterexample.  Consider the sequence {1, 2, 6}.  The mean is 3,
> but the median is 2.  Now double the sample size by using the sequence
> {1, 1, 2, 2, 6, 6}.  The mean and median have not changed.  Extending
> this to an arbitrary 3n-member sequence yields no convergence no matter
> how large n is.
Even better -- J-{-7000, 2} (the integers except -7,000 and two).  Median =
0, Mean = 3,491.  (Compute both exactly as before.  Hint: you need only
consider [-7k,7k].)

> Maybe I'll stick to computers. :-/
Sigh...

> ------------                  Greg Wooledge                  -------------

-=- James Mastros
---
"I'm not saying you should flash your hooters... but it would help"
-=- Howard Stern

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