From: Dan Duchardt
To: Teacher2Teacher Public Discussion
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 analysis. 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 ratio. 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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