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Introduction: Benford's First Digit Law and Tax Day

•  Introduction  •  Introduction (cont.)   
•  Benford's Law and the IRS  •  The Math  •  The Answers

Did you know that the IRS can start to identify cheating by simply looking at the first digits of the figures on a tax return? That is, by looking at how often the numbers start with 1, or 2, or 3, and so on, they can get an idea of whether or not someone might be cheating. The vast majority of Americans are honest and wouldn t even think about cheating on their tax returns, but there are a small percentage of taxpayers who try to cheat the government. No fair! says the common taxpayer, and he s right. Not to worry, though: The IRS pursues and prosecutes cheats, and they can use mathematics to catch them!

The following is a table of real data. The numbers are a list of half-lives for 64 radionuclides. The individual elements have not been named here, since our focus is on the numbers themselves. When looking for first-digit data, ignore any leading zeros. For instance, the first number in our table is 0.006 and has first-digit 6, since 6 is the left-most, non-zero number. Your task is to count up the first digits and enter your findings here to create a bar graph. To start you in the right direction, the first three digits have been done for you. There are 19 first digit 1s, so in the dialogue box under the graph you will enter 19,1. When all the data has been collected, you should enter your findings in the dialog box in the form that you see to the right of the table. The first three first digits have been done for you.

19, 1
12, 2
11, 3
#, 4
#, 5
#, 6
#, 7
#, 8
#, 9

 

0.0063.0432.5119.8950.9
0.073.2636.34121.11007
0.253.7139.31137.71739
0.555.2444.51186.11925
0.626.6446.61239.43145
0.718.0259.49244.13854
1.1111.9364.85249.93935
1.6712.4669.78272.14500
1.9212.7570.77284.54947
2.161473.831211018
2.6914.2683.83463.211523
2.7427.7106.6698.622154
2.8032.01115.1753.8 

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