• agamemnonymous@sh.itjust.works
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      11 months ago

      An actual measured data point, as opposed to a randomly generated number. Also this principle applies specifically to the first digit. Overall the title is a complete mess.

      Basically, when you gather a bunch of data points about real world quantitative phenomena (e.g. town population, lake surface area, etc), you find this distribution curve of leading digits where 1 is something like 30% most frequent, gradually decreasing down to 9 being least frequent.

      This is called Benford’s Law, it’s basically an emergent property about how orders of magnitude work. It’s useful because you can use it to detect fake data, since if your data faker doesn’t know about it they’ll generate fake data that looks random but doesn’t follow this distribution.

  • themoonisacheese@sh.itjust.works
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    11 months ago

    This is used to catch tax fraud. People who forge reciepts tend to use random numbers, so they stand out as outliers, and they get caught that way.

  • Akasazh@feddit.nl
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    11 months ago

    Title needs some work. I would suggest:

    TIL about Benfords law: In many real life data-sets the leading number is ‘1’ 30% of the time.

    Also you could’ve included the wiki link in the post, so people could read up on what you just wrote:

    https://en.wikipedia.org/wiki/Benford's_law

  • JCSpark
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    11 months ago

    This is a bit weird. I was just listening to Infinity 2 today (great book. Totally recommend), and there’s a section where the characters use Benford’s Law to prove reality. I then had to look it up myself.

    Just a super weird coincidence…unless Lemmy is listening to me…

    • bane_killgrind@lemmy.ml
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      11 months ago

      https://en.m.wikipedia.org/wiki/Benford's_law

      Look at the logarithmic scale. This law has to do with number sets in the wild, so apparently the scaling is flat over the set of data they examined. If you look at the distribution of the number sets over the logarithmic scale, they are evenly distributed. If you looked at the same numbers on a linear scale, they would become more and more sparse as they grow in size.

      • Pogbom@lemmy.world
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        11 months ago

        Cool! Now imagine I’ve got severe brain damage… can you explain that again?

        • ShakeThatYam@lemmy.world
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          11 months ago

          In real life distributions you are always going to have situations where you fill up the bigger digits last, so it becomes less likely they show up. The best example of this is the population of cities. For cities between 100k and 999k you’ll have a larger number of cities with 100k-300k because cities of those sizes are smaller and more common.

          • lunarul@lemmy.world
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            11 months ago

            Benford’s law is about the leading digit, so it doesn’t matter if the numbers are rounded or not.

        • bane_killgrind@lemmy.ml
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          11 months ago

          No problem!

          So if you have a small amount of something, you’ll have maybe 2, maybe 3, or 4, or 5, or 6, 7, 8, 9, 10, 11, 12, 13, 14 or so. If you have a medium amount of something, the numbers might be 20, or 30 ish, or 40 ish, 50s, 60s, 70s, 80s, 90s, 100ish, 110ish, 120 or so, around 130. Larger amounts of stuff end up being 200ish, 300, 400, 500, 600, 700, 800, 900, 1000ish, around 1100, 1200 something, 1300

          All the numbers I’ve mentioned are about evenly spaced on this logarithmic scale. You can see that a bunch of them start with 1 just because of how big we think they are! It turns out there is a math reason for this, instead of just being about the weird way humans think.

    • lunarul@lemmy.world
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      11 months ago

      The distribution shown in this post is for base 10, but Benford’s Law includes distributions for other bases too. The wiki article linked in another comment goes into detail on that too.

    • davidgro@lemmy.world
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      11 months ago

      The percentages change. At the lower end, in binary every number that isn’t 0 itself starts with a 1.

      This fact is actually used to save one bit in the format that computers usually use to store floating point (fractional instead of integer) numbers.

  • J12@lemmy.world
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    11 months ago

    So if I rolled a 10 sided dice 1000 times 30% of those rolls would be a 1?

        • ssboomman@lemm.ee
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          11 months ago

          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.

          • J12@lemmy.world
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            11 months ago

            Thanks, that makes sense. I must be missing a link or article on my client otherwise I would’ve read it lol

            • idiomaddict@feddit.de
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              11 months ago

              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.

              • halvo317@sh.itjust.works
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                11 months ago

                The “1” of the “1000” is the real life number. He didn’t pick “785” or “462”.

    • GenderNeutralBro@lemmy.sdf.org
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      11 months ago

      It works on things that operate on a logarithmic scale. 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.

    • ooli@lemmy.worldOP
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      11 months ago

      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.