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# Re: st: Average of Sample vesus Sub-Samples

 From Tim Scharks To statalist@hsphsun2.harvard.edu Subject Re: st: Average of Sample vesus Sub-Samples Date Fri, 19 Mar 2010 08:24:12 -0700

```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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```