Sunday, March 30, 2014

The Three Strange Statistics

Here are three statistics that will make you scratch your head.
  • Of all people that ever lived, 6.7% are still alive today.
  • Whenever you give a deck of cards a proper shuffle, it is safe to say that the order that comes out has never been dealt before in all of human history.
  • Statistically, people who get injured will more often be living in an odd-numbered house than an even-numbered house.
Explanations after the jump!

Of all people that ever lived, 6.7% are still alive today.

The Population Reference Bureau did a thorough guesstimate of how many people (homo sapiens, to be exact) have ever been born. At the time of writing this would be 107.8 billion. Between now and 52,000 years ago the world population has increased tremendously; most notably in the last century. It's currently counting 7.2 billion and the percentage is then easily determined. Graphs here.

Whenever you give a deck of cards a proper shuffle, it is safe to say that the order that comes out has never been dealt before in all of human history.

Let's pick random cards from a deck of 52 and put them on the table. The first card you pick can be any one within the deck, so that's 52 possibilities. The second card can be any card except for the one you already picked, that's 51 possibilities. Then there are 50 possibilities left for the third card, and so on.

Ultimately all 52 cards are on the table, in some random order. There's a a lot of unique arrangements that can be made from 52 cards. How much is a lot? You can calculate by multiplying the number of possibilities for each card. 52 × 51 × 50 × … × 3 × 2 × 1. An easier way to write this is “52!”. You will need a big calculator for this one, as there are 80658175170943878571660636856403766975289505440883277824000000000000 possible unique arrangements.

That's an incomprehensible amount. If every person that ever lived would have been shuffling cards for the last two millennia (which is longer than playing cards exist), churning out a new order every second, you would still come up short a factor of 10 quadrillion quadrillion quadrillion arrangements. With such a massive difference, it is extremely unlikely¹ that a certain order repeats. For all practical purposes, we can say this will not happen. A more comprehensive explanation here.

¹ If each of the 400 billion stars in our galaxy had a trillion planets, each with a trillion people living on them who had each been shuffling a trillion decks of cards 500 times a second since The Big Bang (13.8 billion years ago)... then you finally breached that big number above. And thus be guaranteed that a repeat has occurred.

Statistically, people who get injured will more often be living in an odd-numbered house than an even-numbered house.

This one has particular phrasing. It is not really the same as saying “people who live in odd-numbered houses are more likely to get injured”, is it?

I admit this statistic is a bit misleading. The actual point is that people are more likely to live in odd-numbered houses, period. And this has nothing to do with preference. There are just, on average, about 0.2% more odd than even-numbered houses.

So why is this so? Because there are actually (slightly) more odd-numbered than even-numbered houses in the world. In general, streets with an odd number of houses will have one more odd house number than even; streets with an even number of houses will have an equal number of both odd and even house numbers. Or simply put: There is a (very) small bias towards you living in an odd-numbered house, because most streets starts with house number 1, which is an odd number. Of course there are exceptions, but on average this seems to hold true. A video here.

To be sure: there is not actually a casual link between house numbers and injuries. But in a large group of people, it is easy to make this claim for any characteristic!

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