EXAMPLE 4.30 The Mean of First digits That Follow Benford's Law
CASE 4.1 Here is the distribution of the first digit for data that follow Benford's law. We use the letter for this random variable to distinguish it from the one that we studied in Example 4.29. The distribution of is
| 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 |
The mean of is
The mean reflects the greater probability of smaller first digits under Benford's law than when first digits 1 to 9 are equally likely.