-Does- average always mean the same thing? I learned (correctly, I
Larry posted his comparison spreadsheet showing a straight line
fleet-percentage vs observed-percentage for each railroad. I then
said that one really needs to compute a standard deviation (using
multiple data sets as Larry added) to know how closely observations
match the Tim's theory of random distribution.
A simple way is to consider a sample of 50 box cars. For a railroad
that owns 2% of the U.S. fleet, the "average" number of its box cars
in the sample would be 1. But for a SINGLE sample, what's the chance
that NONE of its cars are present? Easy .98**50 ~= .36. That is, 36%
chance. For a railroad with 10% of the U.S. fleet, .90**50 ~= .005.
That is, there's only a 1 in 200 probability that NONE of those cars
are in the sample.
If you have a layout that has 100 box cars, you probably should own
300 to 400 box cars proportionately distributed among railroads except
for the home road, which should be over-represented. (You need so many
cars because this gives you a "precision" of 0.25% so you can have
examples from very small as well as large railroads.)
Then allow random assignments to take their course -- over time you'll
see different trains but the 'average' train (after hundreds of samples)
will match the national fleet percentages (after discounting for the
home road cars).
Of course, you can then add to this random mix, local facts that skew
the mix. Perhaps you have an auto parts or assembly plant. Or maybe a
grain elevator that receives only corn, or only wheat. Or it may be a
certain time of year -- e.g. grain rush. Etc etc. Then you can 'skew'
some car assignments to reflect those traffic patterns.