Example 23

EXAMPLE 23 Standard Deviation of the Probability Model for benford’s Law

If the first digits in a set of records obey Benford’s law, the discrete probability model is as follows:

First digit	1	2	3	4	5	6	7	8	9
Probability	0.301	0.176	0.125	0.097	0.079	0.067	0.058	0.051	0.046

We saw in Example 21 that the mean is . To find the standard deviation,

You can follow the same pattern to find the standard deviation of the equally likely model and show that the Benford’s law model, by virtue of clustering near the left side, has less variability than the equally likely model.