Let’s say you have a series of numbers that represent real life data. In general the first number of all of these numbers will be a 1, 30% of the time.
It works on things that operate on a logarithmic scale and span many orders of magnitude. It’s odd how many real-world things fit that mold that don’t intuitively seem like they would.
Another factor promoting it in real-world data sets is that they often have restricted ranges that favor lower numbers. Days of the month, for example, only go from 1 to 31. There’s only one way for the leading digit to be 4, but there are eleven ways for the leading digit to be 1.
Another type of data includes values of varying ranges, which also favors lower leading numbers. Street numbers start at 1 and go up, ending at some point within a fairly large range in the real world. All of these ranges will have their fair share of leading 1s. They will NOT all have a fair share of leading 2s (what if it ended before 20?), and as you go up it gets progressively less likely. So if you took all street addresses, you’d expect to see more leading 1s than 9s.
Your theoretical dice roll is not such a case. You would expect a uniform distribution of leading numbers. This would hold true with a 99-sided die as well.
No it is a property of real life thing. It come from the fact that most thing in real world, dont go over 30 or 300 so often. Like number of houses in a street.
So if I rolled a 10 sided dice 1000 times 30% of those rolls would be a 1?
No
Thanks. Now I understand
From what I understand it works like this.
Let’s say you have a series of numbers that represent real life data. In general the first number of all of these numbers will be a 1, 30% of the time.
Thanks, that makes sense. I must be missing a link or article on my client otherwise I would’ve read it lol
Such as “1000 rolls”
It applies to situations with more than one order of magnitude being counted, such as d20 rolls, 55% of which will start with a 1.
The “1” of the “1000” is the real life number. He didn’t pick “785” or “462”.
I don’t know why you’re being downvoted.
It works on things that operate on a logarithmic scale and span many orders of magnitude. It’s odd how many real-world things fit that mold that don’t intuitively seem like they would.
Another factor promoting it in real-world data sets is that they often have restricted ranges that favor lower numbers. Days of the month, for example, only go from 1 to 31. There’s only one way for the leading digit to be 4, but there are eleven ways for the leading digit to be 1.
Another type of data includes values of varying ranges, which also favors lower leading numbers. Street numbers start at 1 and go up, ending at some point within a fairly large range in the real world. All of these ranges will have their fair share of leading 1s. They will NOT all have a fair share of leading 2s (what if it ended before 20?), and as you go up it gets progressively less likely. So if you took all street addresses, you’d expect to see more leading 1s than 9s.
Your theoretical dice roll is not such a case. You would expect a uniform distribution of leading numbers. This would hold true with a 99-sided die as well.
While that’s true with a 10-sided die 20% of your rolls will start with a one and all other digits only have a 10% chance.
Oh, yes. Thanks for the correction!
No it is a property of real life thing. It come from the fact that most thing in real world, dont go over 30 or 300 so often. Like number of houses in a street.