When dealing with a large volume of data and wanting to fit this data to five different bins (the number of bins is fixed), how might one find a good fit for the different bins relative to the data?
For instance, the data that I am currently using are classes with discrete frequencies. Like so:
class1: 10 class2: 382
In an example of the data I'm using there are 489 classes, an absolute sum of over 100,000 for the frequencies. A reasonable approach would be to delineate the bins for the histograms by the total frequencies/5 (which is 20,800 here). In an ideal world this might have 20 classes in the first bin, maybe sixty in the next, a hundred in the next and so on. However, because the data is exponential (a standard deviation of over 17,000), not even the first class would adequately fit into the bin (it has a frequency of 34,000).
What options do I have in order to create a decent fit for the different histogram bins?