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by synnik 5469 days ago
Why is this not common sense?

For the numbers 1-19, more than half of them start with 1. For the numbers 1-199, more than half of them start with one.

Change the examples to 1-299, 1-399, etc, and you'll get percentages of all digits matching Benford's law.
3 comments
jcarreiro 5469 days ago
Benford's Law predicts the first digit will be 1 about 30% of the time, not 50% of the time.

Your method also seems to depend heavily on the choice of starting and ending points. If I chose 1-99, then only 1/10th of the numbers in the interval will start with 1. So why choose 199 and not 99?

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synnik 5468 days ago
It is not "my method". Just an explanation of why the law seems intuitive to me. I expected everyone to extrapolate out from my examples for other ending points, and which point, yes, the % for the digit of "1" would drop, and approach that 30% rate.

I just selected end points to illustrate the concept. I think this place is getting a little too literal. :)

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brown9-2 5469 days ago
I am not a mathematician but the "law" seems to be an inherent property to any number system based on exponential increases, i.e. the hundreds digit, tens digit etc (is there any other kind of number system?)

I think it seems "counter-intuitive" to some because they are not used to thinking of numbers and counting as being related to exponents and bases.

This may seem more intuitive to those of us that work with computers all day since we are intimately familiar with how to count in a handful of different bases (base-2, base-10, base-16 etc).

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jcarreiro 5469 days ago
I am curious as to why you think that Benford's Law in intuitive. I certainly would not have expected it. Could you explain your thinking in more detail?
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brown9-2 5469 days ago
I wouldn't say intuitive as much as "not totally surprising". I meant "more intuitive" in relation to those who think it is non-intuitive.
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sheffield 5469 days ago
For the numbers 0-100, only 10 start with 1, exactly as many those start with 2, or 3, etc.
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st0p 5469 days ago
No, 11 numbers start with 1 in that range.
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albedoa 5469 days ago
No, 12 numbers begin with 1 in the range [0,100] if that's indeed what the OP meant:

1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 100

I think he most likely meant to exclude 1 and 100, but I don't know.

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st0p 5469 days ago
Kudos for spotting, that. I feel stupid now.
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