Benford's Law states that the probability of a number starting with digit d in a large set of numbers with distribution over several orders of magnitude equals log 10 (1 + 1 / d ). I wanted to put this law to the test on several datasets, and see how different data plots onto a graph together with a plot of the actual Benford's Law set.
In the graphs below, the green lines represent the ideal Benford's Law occurrences. This is a plot of the formula described above. The other line is a plot of the data that has been analysed by taking the first digit of each number in a set and calculating its occurrence in the set it came from. If a line is more red, it means the average difference between the ideal graph and the analysis result is quite large. If a line is more blue, it means that the average difference was rather small.