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Re: st: Average of Sample vesus Sub-Samples


From   Jeph Herrin <junk@spandrel.net>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Average of Sample vesus Sub-Samples
Date   Fri, 19 Mar 2010 11:59:05 -0400

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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