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st: adding means to histograms (2)


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: adding means to histograms (2)
Date   Tue, 24 May 2005 21:45:46 +0100

I didn't add a comment that I had in mind on the use of 
a upward-pointing triangle, motivated
by the idea of a fulcrum about which a
beam supporting a histogram would balance. 

Many introductory texts and courses 
stress the mean as a balance point (centre
of gravity) for a distribution. Those 
with some physics background will recall
that there is a very good reason for calling the
mean a moment measure. 

Others may be reminded of the principle of a 
	see-saw 
	teeter totter
	bascule 
	Wippe 
or whatever you call it in your language. 
I am indebted to Vince Wiggins for the 
transatlantic translation (see-saw = teeter
totter) and also for implementing arrows. 

In the statistical literature, the main idea 
was discussed by 

Doane, D.P. and Tracy, R.L. 2000. 
Using beam and fulcrum displays to explore 
data. The American Statistician 54: 289--90. 

An earlier reference is 

Helsel, D.R. and Hirsch, R.M. 1992. 
Statistical methods in water resources. 
Amsterdam: Elsevier. p.5 

The whole of that textbook (which has 
much worthwhile material on graphics) is 
available free as a series of .pdf documents from 
http://water.usgs.gov/pubs/twri/twri4a3/html/pdf_new.html

A more versatile -beamplot- program will be released via SSC 
next month. For the help file, I would be grateful for 
any further literature references to the use of means as 
fulcrums (fulcra?) in descriptive or exploratory data graphics.
(Mentions of the mean as a theoretical balance point I 
trust to be too frequent to be worth citation.) 

Nick 
n.j.cox@durham.ac.uk 

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