Q&A #6249

Teachers' Lounge Discussion: Statistics coursework

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From: Dan Duchardt

To: Teacher2Teacher Public Discussion
Date: 2005033115:21:32
Subject: Re: Re: Re: I ned help with statistics coursework

The question posed has no obvious connection to statistics, perhaps
because it is taken out of context.  A statistics problem about weight
vs height might have something to do with correlation, or regression

 From basic principles of scaling, taller people should generally weigh
more than shorter people because people are all made of the same
stuff, and as we have often heard, most of that stuff is water which
has the same density regardless of whose body it is in.  Bone is bone,
and has nearly the same density in everyone.  No matter how much you
break it down, people all have about the same weight density (weight
per unit volume), so their weight is the product of that common weight
density and their volume.

Volume varies a great deal from one person to another.  Roughly
speaking, the size of a body can be characterized by the height of the
body and the girth of body parts (waist, chest, hips, arms, legs). 
Two people have similar shapes if the corresponding height and girth
measurements are proportional.  Volume is a 3-dimensional quantity; it
always involves the product of 3 linear measurements.  Two people with
similar shapes that differ in height will have a volume ratio that is
the cube of their height ratio, and since weight is proportional to
volume, their weight ratio would also be the cube of their height

Think about a child who is 3 feet tall and an adult who is 6 feet
tall.  The child would weigh somewhere in the vecinity of 20 to 30
pounds, while the adult would generally weigh somewhere in the range
of 160 to 240 pounds.  If the shapes were exactly similar, and the
densities exactly the same, the adult would weigh 8 times as much as
the child.

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