Listed Here Are 4 Http: Ways Everybody Believes In. Which One Do You Favor

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In the year 1881, American astronomer and physicist Simon Newcomb was seated at his desk where he was performing a set of calculations using a book of logarithms. As he worked he noticed that the pages that were the closest to the front of the book were more well-used and dirty than those nearer the end of the book. He was puzzled by this and, over the next several days, manually counted the value of the first digit in each entry. Newcomb, expecting the digits 1 - 9 to be both randomly distributed and to occur with a frequency of just over 11%, was more than surprised with his results.

But first, let's take a quick look back at Statistics 101. The previously mentioned "11%"is the probability (p)that the first number (we'll use "1" in this example) will have a particular value. This gives us P = 1/9 = ~ 11% What he had discovered was that, in any set of data, the number "1" will appear as the first digit will be the number "1" approximately 30 % of the time. The number "2" will be the first number in ~17 % and so on until the number "9," which appears as the first digit in only 4.6 % of the data.

Newcomb published his finding in 1881. It was ignored by the professional community and soon forgotten. In 1938 Frank Bedford "rediscovered" the numerical curiosity Newcomb had discovered almost 60 years earlier and, after further examination, derived an equation that would give the occurrence percentage of n numbers 1 - 9: Log10 ((n + 1) / n) Where n = 1, 2, 3...9. The actual distribution under Benford's Law is: 1 30.1% 2 17.6% 3 12.5% 4 9.7% 5 7.9% 6 6.7% 7 5.8% 8 5.1% 9 4.6% Here's another example of having a bit of fun with statistics.

Dr. Theodore P. Hill, of the Georgia Institute of Technology, has a task that he gives each student in his mathematics class. On the first day of class they are instructed to go home and either flip a coin 200 times and record the results, or merely pretend to flip a coin and fake 200 results. The following day he runs his eye over the homework data, and to the students' amazement, he easily identifies nearly all those who faked their tosses. He does this by looking for the presence of 5 consecutive heads or tails, explaining that over a range of 200 consecutive tosses that, according to probability law, at least one "string" of 5 heads or 5 tails is expected to occur.

Should a student's homework not show 5 consecutive, identical tosses, the results presented are presumed to be faked as described above. There are many applications based on Benford's law currently in use. While those that are dedicated to the detection of financial fraud and cases of income tax evasion have been in use for many years, newer programs are under development that will aid in the detection of spurious data sets in both the social and applied sciences.