Question

6. Creating a bar graph and Benford's Law Aa Aa Here's an interesting exercise: Write down all the numbers you see on the front page of your college newspaper (excluding the page number). Calculate the proportion of numbers beginning with 1 and the proportion of numbers beginning with 4. Which proportion is greater? Your intuition may suggest that you are equally likely to find both kinds of numbers, so the proportions should be roughly the same. However, more often than not, the proportion of numbers beginning with 1 is about three times that of numbers beginning with 4 This is a consequence of a phenomenon known as Benford's Law, which was observed independently by mathematician Simon Newcomb in 1881 and General Electric physicist Frank Benford in 1938. A set of numbers obeying Benford's Law would have the relative frequency distribution shown in Table 1. In addition, a bar graph of the distribution is shown to the right of Table 1 Table 1 0.301 0.176 0.125 0.097 0.079 0.067 0.058 0.051 0.046 Tota 1.000 RELATIVE FREQUENCY 0.40 0.35 0.30 0.25 0.20 0.15 4 7 0.05 0.00 FIRST DIGIT

Answer 1

Bar graph:

For the preceding data the first digit with the highest frequency is 6.

Its relative frequency is 29/136 = 0.2132.

If the distribution follows Benford's Law, the relative frequency expected for this particular first digit is 0.067, and the expected frequency is about 136*0.067 = 9.112 = 9 occurrences.