The distribution of the first digit
Consider the powers of 2 (1, 2, 4, 8, 16, 32, 64, ...), or more specifically, the first digit of these powers. Can we expect all digits (1-9) to appear more or less with the same frequency (11.1%)?
It doesn't happen. From the first 1,000 powers, 30% start with the digit 1 (this is easily verifiable, for example with a simple Excel spreadsheet), 18% start with 2, 12% with 3, 10% with 4, 8% with 5, 7% with 6, 6% with 7, and 5% with the digits 8 and 9. Strange!
Another experiment: pick a newspaper and look at all numbers that appear on it. Record the first digit of every single number. Repeat the experience with stock prices, national statistical publications and company annual reports. A very similar pattern exists. A lot of numbers start with the digit 1. And the higher the digit, the lower the frequency.
Are these two experiments related? More on the topic here.
It doesn't happen. From the first 1,000 powers, 30% start with the digit 1 (this is easily verifiable, for example with a simple Excel spreadsheet), 18% start with 2, 12% with 3, 10% with 4, 8% with 5, 7% with 6, 6% with 7, and 5% with the digits 8 and 9. Strange!
Another experiment: pick a newspaper and look at all numbers that appear on it. Record the first digit of every single number. Repeat the experience with stock prices, national statistical publications and company annual reports. A very similar pattern exists. A lot of numbers start with the digit 1. And the higher the digit, the lower the frequency.
Are these two experiments related? More on the topic here.
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