Re: st: Average of Sample vesus Sub-Samples

[Jeph Herrin <junk@spandrel.net>]

The original question was not whether these two
numbers could differ, but whether the average of the
larger group could be greater than the mean of the
two sub averages. In your case they differ, but the
average of the larger group is smaller.

I think you have to have negative numbers to reverse
the inequality.

cheers,
Jeph


Tim Scharks wrote:
> but what about
>
> A = 1, 1, 1
> B = 3
> m(A) = 1
> m(B) = 3
> (m(A)+m(B))/2=2
> mean (A+B) =1.5
>
> uh oh...
>
> The problem is not negative numbers--it is your failure to weight the
> subsample means according to their relative size:
>
> (m(A)*3+m(B)*1)/4 =1.5
> m(A+B) = 1.5
>
>
> On Fri, Mar 19, 2010 at 6:49 AM, Jeph Herrin <junk@spandrel.net> wrote:
> > Yes, if they are negative.
> >
> >
> >  A = -1,-1,-1
> >  B = -3
> > then
> >  mean(A) = -1
> >  mean(B) = -3
> >  (mean(A)+mean(B))/2 = -2
> >  mean(A+B)= -6/4 = -1.5
> >
> > -1.5 > -2
> >
> > So the average of all 4 numbers is larger than
> > the average of the means of the two subsamples.
> >
> >
> > hth,
> > Jeph
> >
> >
> >
> >
> >
> > Erasmo Giambona wrote:
> > > Dear Statalisters,
> > >
> > > Is it possible that the arithmetic average of a sample is larger than
> > > the averages of two sub-samples containing overall all the
> > > observations of the full samples?
> > >
> > > Any thoughts would be appreciated,
> > >
> > > Erasmo
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