from Amazon
Tuesday, December 28, 2010
Mathematical sleight of hand
Steve Landsburg offers this very ambiguous question (and the answer is here). Phil Birnbaum explains the answer Steve is looking for by using baseball (always a winner with me).
If you don’t want to read all that, suppose you have this:
1 boy, 0 girls = 0% girls
1 boy, 1 girl = 50% girls
1 boy, 2 girls = 67% girls
The total is obviously 3 boys and 3 girls, meaning 50% of the kids are girls. But, if you take the simple average of 0%, 50% and 67%, you are obviously not going to get 50% girls as the average.
Landsburg however phrases his question that the obvious answer is no longer obvious, by asking this:
There’s a certain country where everybody wants to have a son. Therefore each couple keeps having children until they have a boy; then they stop. What fraction of the population is female?… But in expectation, what fraction of the population is female?
And then he adds:
In other words, if there were many such countries, what fraction would you expect to observe on average?
His “other words” in no way is “other words”. It basically adds a totally new question to the question he originally has. Furthermore, what he should have said is:
In other words, if there were many such countries, what fraction would you expect to observe on average from a random country?
Why for example is it presumed that you would poll each country equally? I don’t know about you, but when I sample results, I’m going to weight results in USA more than in Canada. If one country has 1 million boys and 1.5 million girls, and another country has one million boys and 0.5 million girls, why would I sample the two countries the same, see that one has 60% girls, the other has 33% girls and come away with an average of 47%?
By adding “from a random country”, he makes it clear that the sampling unit is countries, and not people.
Landsburg however defends himself presuming that his question was clear, honest and unambiguous. It could have been a fantastic question, properly worded. Instead, it’s a mathematical sleight of hand.
Recent comments
Older comments
Page 1 of 344 pages 1 2 3 > Last »Complete Archive – By Category
Complete Archive – By Date