Statistics, love them or hate them

[SteveP]

a couple of statistics that have always been surprising.

A well shuffled deck of cards.
It is unlikely in history if a well shuffled deck has EVER been duplicated.
do the math, the odds against it are astronomical.
(google 52 factorial... you will see )

Many, many ( millions?) people do brackets for the NCAA bball tournament.
This year not a single bracket made it past the first round ( thanks Virginia ).
Most years something like 4 or 5 make it past round 1 and essentially zero make it further.

There are probably a bunch more like this.
anyone add any?

[monadnocky]

Not really stats, but basic math I guess.
How large a gathering of people does it take to have a 50-50 chance that two of them have the same birthday? Almost everyone answers "around 180" (i.e., roughly 365/2).
The answer is 23. And in a room of 75 people, there's a 99.99% chance that two will have the same birthday.

Oh and don't get me started on misperceptions of the normal curve and IQ
... no, I can assure you that your IQ is not 160.
(well, maybe yours is...)

[Saab2000]

My bracket is still unblemished. Warren Buffet is starting to get nervous.

[rwsaunders]

Not my quote...often attributed to Mark Twain who I believe attributed the quote to another. "There are three kinds of lies...lies, damned lies and statistics." I like this one too..."99% of all statistics tell only 49% of the story."

[Bob Ross]

I came across this tidbit in the book Darwin's Dangerous Idea by Daniel C. Dennett that I am currently re-reading for the 2nd or 3rd time:

If you held a coin-tossing tournament (set up as elimination-style, like NCAA brackets, but with ten rounds) you would only need 1,024 competitors before one of them would successfully throw ten consecutive heads.

[SteveP]

good one.

[monadnocky]

I came across this tidbit in the book Darwin's Dangerous Idea by Daniel C. Dennett that I am currently re-reading for the 2nd or 3rd time:

If you held a coin-tossing tournament (set up as elimination-style, like NCAA brackets, but with ten rounds) you would only need 1,024 competitors before one of them would successfully throw ten consecutive heads.

Read somewhere about a stats/prob professor who, on her first day of teaching the college-level course, would ask her students to write on the blackboard two conditions

1) Imagine a coin-flipping sequence of 100 flips. Write down this imaginary sequence (i.e., HHTHTTTHHTHTH and so on)
2) Actually flip a coin 100 times and write down the sequence.

The professor would not watch either of these. Upon re-entering the class, she would correctly pick the "real" sequence. She had done this, successfully, on the first day of class for many years. Never got it wrong. Had something to do with our aversion to writing down a string of more than five (or six?) "H" or "T" in a row, which I believe is likely in a string of 100 flips - anyone?
Our brains are really good at making connections (relatively speaking) and TERRIBLE with randomness.

[thollandpe]

If you held a coin-tossing tournament (set up as elimination-style, like NCAA brackets, but with ten rounds) you would only need 1,024 competitors before one of them would successfully throw ten consecutive heads.

If you bet that one of those 1024 people flips 10 heads in a row, and I bet against, I think I would quickly clean you out. Try having 2046 players.

[davids]

Not really stats, but basic math I guess.
How large a gathering of people does it take to have a 50-50 chance that two of them have the same birthday? Almost everyone answers "around 180" (i.e., roughly 365/2).
The answer is 23. And in a room of 75 people, there's a 99.99% chance that two will have the same birthday.

Right. This one makes sense once you understand numbers a little.

It's like the "miraculous" coincidence of meeting someone who knows a mutual friend/relative. I mean, I know a couple hundred people, who each know a couple hundred people, etc. Even 3 degrees of separation would offer a well over a million possible connections. So it shouldn't be surprising that two people, with a little conversation, can trace those.

On the other hand, the odds of any specific connection can be very, very low. The odds that those same two people are connected through one specific chain are very, very low - one in over a million, quite possibly.

It's our observer bias that makes those coincidences seem meaningful, rather than simply fun.