Most people assume that in a large set of data, the first digits of the numbers will be un...

Most people assume that in a large set of data, the first digits of the numbers will be uniformly distributed—that is. each digit 1 to 9 appears as the first digit in about 1/9 of the numbers. However, in the 1930s, Dr. Frank Benford, a physicist with General Electric, discovered (by looking at the wear pattern on a table of logarithms) that the proportion of number? having the digit d the first digit is given by the function f(d) =  This function is now referred to as Benford’s Law, and is used by income tax agencies and insurance companies as away to detect fraud.

a. Test Benford’s Law by writing down the first digit of each address on a randomly selected page of your local telephone directory. Find the total number of addresses beginning with each digit.

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b. Convert each value into a percentage of addresses beginning with that digit.

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c. A percentage form of Benford’s Law is ; this function gives the percentage of a set of data that has each number d (1 through 9) as the first digit. Complete the table to show both the actual percentage of addresses beginning with each digit and the percentage predicted by the function P(d).

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DIGIT d	ACTUAL PERCENTAGE OF ADDRESSES HAVING d AS THEIR FIRST DIGIT	PREDICTED PERCENTAGE P OF ADDRESSES HAVING d AS THEIR FIRST DIGIT
1
2
3
4
5
6
7
8
9

d. Was Benford’s Law a good predictor of the actual percentages?