PostHeaderIcon Numbers

Here’s another quiz:

Consider a list of naturally occurring numbers. And by naturally occurring is meant numbers like for example stock prices, number of inhabitants of cities, your electricity bills of the past few years, prices on your Saturday grocery receipt, lengths of rivers, number of books in the bookcases of all your friends, you name it.

The question then is about how often a particular digit appears as the first digit of the numbers in such a list.

Let’s take for example the digit ‘1’. The question then becomes: how often (in %) will ‘1’ be the first digit of these numbers in a given list? Or to put the same question differently: How many numbers in that list (in % of the total number of numbers) start with a ‘1’?

Hint: keep in mind the first category this post is published in!

6 Responses to “Numbers”

  • Injun says:

    the “intuitive” answer would be one-out-of-nine (numbers don’t typically start with zero), or about 11,11% of the time. Now, if I find some time between work-and-riding-my-new-bike, I’ll try to think why this is not the correct answer.

  • Paul says:

    @Injun, since I don’t expect anyone else to comment on this post, I will go ahead and

    1. give the answer
    2. give a hint as to where to look for an explanation

    So, the counter-intuitive answer is indeed NOT "about 11%", but "about 30%".

    As for a hint: "Benford’s law".

    While I do understand the "logarithmic" argument given, I still have a hard time understanding why the example lists follow that rule.
    What makes these lists of seemingly random numbers actually non random? To be sure, if you create a list of random numbers and you DON’T get that 11% distribution, then something’s REALLY wrong with your randomizing algorithm!
    So what makes a list of stock prices logarithmic in nature? Or death rates? Or even more perplexing: a list of unrelated physical or mathematical constants?

    ANYWAY, I think Injun should have some Internet presence himself, if ONLY to show off pictures of his new bike!

  • Dawnell says:

    I think you should be tasked to write a manual for software. I am gonna call your boss.

  • Paul says:

    @Dawnell: you’re going to call my boss? Hmm.. let me give you his number… let’s see… here… oh wait, no, that’s YOUR boss’s numnber! Hmm.. Maybe I should call THAT number…
    I mean, I need to talk to him anyway .. about those Chilis’ gift cards!

  • Dawnell says:

    I STILL laugh about those Chili’s gift cards…! HAHAHAHAA

  • Paul says:

    @Dawnell, well.. you’d better NEVER tell him, and be REAL nice to the man!

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