# [tor-dev] tor's definition of 'median'

Virgil Griffith i at virgil.gr
Tue Aug 11 13:44:48 UTC 2015

I mean the median.

>From Wikipedia...

For example, if *a* < *b* < *c*, then the median of the list {*a*, *b*, *c*}
is *b*, and, if *a* < *b* < *c* < *d*, then the median of the list {*a*, *b*
, *c*, *d*} is the mean of *b* and *c*; i.e., it is (*b* + *c*) / 2.

-V

On Tue, Aug 11, 2015 at 9:29 PM John <oneofthem at riseup.net> wrote:

> I think you are confusing the median with the mean:
>
> https://en.wikipedia.org/wiki/Median
> https://en.wikipedia.org/wiki/Mean
>
> Taking the median instead of the mean can be beneficial in situations
> where you have larger outliers in your data, which typically affect the
> mean very much.
>
> -j
>
> Virgil Griffith:
> > Is there some implementation-specific reason not to use the standard
> > mathematical definition of "median"?  If not, I propose changing the
> > implementation to become it.
> >
> > -V
> >
> > On Tue, Aug 11, 2015 at 2:44 AM Nick Mathewson <nickm at alum.mit.edu>
> wrote:
> >
> >> On Mon, Aug 10, 2015 at 1:11 PM, nusenu <nusenu at openmailbox.org> wrote:
> >>> -----BEGIN PGP SIGNED MESSAGE-----
> >>> Hash: SHA512
> >>>
> >>> Hi,
> >>>
> >>> https://gitweb.torproject.org/torspec.git/tree/dir-spec.txt#n2028
> >>>
> >>>> If 3 or more authorities provide a Measured= keyword for a router,
> >>>> the authorities produce a consensus containing a "w" Bandwidth=
> >>>> keyword equal to the median of the Measured= votes.
> >>>
> >>> a random sample from recent votes:
> >>>
> >>> grep 37.59.38.117 -A 3 *|grep Measured
> >>> w Bandwidth=6869 Measured=7570
> >>> w Bandwidth=6869 Measured=15500
> >>> w Bandwidth=6869 Measured=18100
> >>> w Bandwidth=6869 Measured=30500
> >>>
> >>> Tor says the median value is
> >>> 15500
> >>>
> >>> 2015-08-10-16-00-00-consensus:
> >>> w Bandwidth=15500
> >>>
> >>> but the median of these 4 values is actually:
> >>> (18100+15500)/2 = 16800
> >>> no?
> >>>
> >>> Has tor a different definition of 'median' and simply takes always the
> >>> second ordered measurement vote out of 4 votes or is there a bug in
> >>> the spec or implementation?
> >>
> >> There's one misplaced throwaway sentence in dir-spec.txt:
> >>
> >> "  All ties in computing medians are broken in favor of the smaller or
> >>    earlier item.
> >> "
> >>
> >> We should bring this, and probably other things, into a "definitions"
> >> section earlier in dir-spec.txt.  Patches welcome. ;)
> >>
> >> --
> >> Nick
> >> _______________________________________________
> >> tor-dev mailing list
> >> tor-dev at lists.torproject.org
> >> https://lists.torproject.org/cgi-bin/mailman/listinfo/tor-dev
> >>
> >
> >
> >
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> >
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