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Subject: Age distributions, distance and shape
Date: Wed, 4 Nov 2009 10:31:02 +0000 (UTC)
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Dear all,
i have age distributions by district of the entire population and of a sample.
I want to compare the age distribution of the population with the sample one.

I can't do it by graphical representation because I have 110 districts and my data covers 5 periods which would require plotting more than 500 distribution comparisons.

I should be able to calculate somehow a measure of distance between the two distributions and rank each district from most-to-least different.
If you have any advice on how to calculate this measure of distance, any scientific reference on the matter (ages distributions, distributions comparisons etc...) plz post it.

The simplest way would be an area difference between the population distributions but here comes a problem, plz look at picture in the link (On the "x-axis" is the age and on the "y-axis" is the number of people):
http://i36.tinypic.com/2a9r22q.png
In the case "A" I would obtain an area difference, significantly different from 0. The same would be for the case "B". 
Suppose that case A and case B would yieald the same difference, the thing that makes the two examples totally different are the shapes! 

So, how can i calculate the difference between the age distribution of the population against that of the sample "weighting" the result for the shape of the distributions (with similar shapes reducing the final distance making the case A of the picture "acceptable")

Any comment would be greatly appeciated!