Choice of plot or statistic for data with wide range

Question

I have some simple datasets that consist of a discrete integer-valued variable together with frequency counts. The frequencies vary a lot as does the value of the variable. For example one set has values from 1 to a little less than 15000 with frequencies from 1 to half a million. The small values have the many occurrences, e.g. no value higher than 10 occurs more than 50000 times whereas the values 1 through 10 together appear around 1.5 million times.

I am looking for a good kind of plot (preferably) or statistic to use for presenting and overviewing this data. What is a good choice? At the moment I am plotting a line segment from (n,0) to (n, freq) for the data point (n, freq) but due to the distribution this is not very informative.

Answer 1

The first thing that comes to mind is taking the log of both variables and plotting those values against each other. That would deal fairly well with the range issue. Log10 of .5 million (your largest value) is only 5.69.

Then there's the problem of the density of points. One solution that I presented at a recent SAS conference is to use parallel box plots with a density plot beneath the x axis. I have code for this in SAS if you are using that; it could also be done in `R' pretty easily.