Pretty much the title.
I understand this is a law but can there be a reason why this happens?
For background: for almost all real life data like population, GDP and other real word stats, probability of it having 1 is like almost 30% which keeps decreasing with 9 to be least probable.
But why this happens, is this just a fascinating pattern in randomness?
In: 130
Imagine a statistic that grows by 10% every year. Let’s say the statistic starts at 100,000 in the first year.
In the second year, it will be 110,000.
Third year, it will be 121,000. Fourth year; 133,100. Fifth year; 146,410. Sixth year; 161,051. Seventh year; 177,156. Eighth year; 194,872.
Finally, having spent 8 years in the “starts with 1” category, it will graduate to the “starts with 2” category in the 9th year, hitting 214,359, and it will stay in the “starts with 2” category for just three more years, until the 13th year, when it hits 313,843.
The “starts with 3 category” lasts for three total years.
Then the categories for 4, 5, and 6 last for two years each.
Some years later, the statistic in year 24 sits at 895,430, and will grow to 984,973 in year 25, which is the only year that the statistic spends in the “starts with 9” category, until it grows into the millions the following year.
Once it is in the millions, it will again start with 1 from year 26 (at 1,083,471) to year 32 (at 1,919,434).
So for statistics that grow at a natural rate, they tend to spend more time in the “starts with 1” category, because that’s where they grow the slowest. Once they reach the other “starts with *x*” categories, they grow faster and faster, thus spending less time in those categories.
Latest Answers