Benford's law

English Etymology Named after physicist Frank Benford, who stated it in 1938. Proper noun en Q817168 A law concerning the frequency distribution of digits in much real-world data, where the number 1 occurs as the leading digit about 30% of the time, and the expected distribution for digits beyond the first approaches a uniform distribution. en 2010 Grimvall Göran Chapter 1: Numbers Quantify! A Crash Course in Smart Thinking Johns Hopkins University Press 9780801899676 The following argument can give an intuitive feeling for Benford's law.¹¹ Consider a set of numbers x, which are randomly chosen in the interval between 1 and 10. All x between 1 and 1.999 have 1 as the first digit, all x between 2 and 2.999 have 2 as the first digit, and so on. The ratio of the largest and the smallest x is (almost) 2 in the first interval. In the next interval it is 3/2, followed by 4/3, and so on, up to 10/9. The widths of the intervals decrease as in a logarithmic scale. There is more “room” for a number between 1 and 2 than there is between 8 and 9. In other words, the numbers between 1 and 2 are more dissimilar to one another, quantitatively (regarding how big a factor it takes to get from one to another), than the numbers between other consecutive-integer pairs. en eponyms