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# Re: st: Quintiles

 From Maarten Buis To statalist@hsphsun2.harvard.edu Subject Re: st: Quintiles Date Wed, 8 Aug 2012 18:40:49 +0200

```--- Leonardo Jaime Gonzalez Allende asked:
>>> I'm trying to divide a sample of households (expanded)
>>> into quintiles using the xtile command. I want to create
>>> 5 groups with the exactly same quantity of population,
>>> but using the xtitle command, the quantity of households
>>> in each quintil is very slightly different to 20% when the
>>> number of observations isn't exactly dividable by 5.
>>> Do you know any command to divide the population
>>> (sample expanded) into 5 groups of exactly same weight?

>> That is logically impossible.

-- Leonardo Jaime Gonzalez Allende wrote me privately:
> sorry for write you directly, but I like to know, why is
> logically impossible separate the population (by
> incomes) in 5 groups of the same weith?

Don't sent such follow-up questions privately. If you find my answer
puzzling, than chances are that someone else who is following this
discussion finds that too. This is explained in the Statalist FAQ.

Think of it this way: How can you divide 6 persons in 5 equally sized
groups? You could assign one person to each group, and than you are
left with one person. If you could split the remaining 1 person up
into 5 1/5th persons, than we could create 5 equally sized groups.
However, that is impossible (or rather bloody, if we take that too
literally). So given the inherently discrete nature of the number of
observations you cannot divide your data up into 5 groups of exactly
the same size if the number of observations in not dividable by 5.

-- Maarten

---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

http://www.maartenbuis.nl
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