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I suspect Tim would have recommended computing the standard
deviation of this data set, in order to see how closely these
observed differences from the mean values match the expected
standard deviation. One does not "expect" all values in a
sample data set from a large population to match the mean
values, but one does expect that the mean of the deviations
is predictable. If it is, then you can make a case that your
data set is a good representation of a hypothetical sample.
If not, then the data set may be skewed, or your expected
sample may be incorrect (i.e. Tim's theory of distribution
may be incorrect).http://en.wikipedia.org/wiki/Standard_deviation
I just posted a table in the files section file that compares expected
and actual counts of boxcars by railroad in the NMRA Charles
collection. The file name is _Compare box car counts US RRs - Charles
The first two columns in the table list, in descending order, the
number of box cars owned on 12-31-1950 by 71 US railroads. These
numbers are from _The Handbook of American Railroads_.
There are 194 photos of boxcars in the Charles collection. Most of
them were taken in 1946 and 1947 in the greater Harrisburg PA area on
the PRR. The most common photo location is the PRR eastbound receiving
yard in Harrisburg. The third column in the table lists the expected
boxcar counts by railroad for a total of 194 boxcars, based on the
second column. The fourth column lists the actual number of boxcar
photos in the Charles collection.
Given the small size of the sample, I think that these numbers support
Tim Gilbert's hypothesis that the number of boxcars owned by railroad
can be used to predict the expected number of boxcars observed. Other
list members are welcome to draw their own conclusions about this data.