How to find the ranges in Equal frequency/depth binning?
As far as I can see the choice of the bin size /frequency is arbitrary in those examples. Frequency binning is simple choosing you bin boundaries in a way that the bin content size is the same. For the frequency approach it looks like the order the elements by size and calculate the bin edges in the middle between the highest element of bin A and the lowest of bin B.

If you want to be really fancy you can use methods like bayesian blocks that actually choose bin size dynamically with respect of information content.