I wanted to put up a brain teaser yesterday, but the little one got his first cold. Baby coughs are sad.
Anyway, one of the more famous statistical brain teasers is the birthday problem. There are a few variations, but essentially the question goes something like this:
You're at a party with 23 guests, including you. What are the chances that two people there have the same birthday?
The trick of course is that no one has to have a specific birth date, so the answer is not 23/366, but instead around 50% (interestingly, if the party were 50 people, it goes up to 97%). For a further explanation, see here.
What's interesting about this problem is that you have to assume every birth date is equally likely...which of course isn't true. I've written before about uneven distribution of birthdays in the US, due in part to scheduled c-sections or induced labor. Anyway, I saw an interesting heat map today of birthday distributions from the Daily Viz, which is what got me thinking about the brain teaser.
I was a little struck by this, because I was thinking about how terrible I am at estimating things like this on my own. The most common birthday in my circle of friends/family is Halloween. The first week in April has the birth dates of my mother, sister and husband. Neither of those time frames are overly popular within the general population, although I'd guess the difference between "most popular" and "least popular" are relatively small. It was a good reminder that those I spend the most time with are not terribly representative of the population in general, on average.