Talk:Normal distribution
Should "Bell curve" be capitalized? I think not, because it is not the curve of Graham Bell, but it is a curve that looks like a bell. --AxelBoldt
You're right! --LMS
I don't like the examples at all. If a species shows sexual dimorphism, the size of specimens won't be a gaussian, just like the text points out about human blood pressure. Also, test scores are basically an example of the Gaussian limit of Binomials, and GPAs certainly do not follow a gaussian distribution because of grade inflation and limited range of grade points.
To me, these examples smack of the fallacy that "everything is gaussian". See Zipfs law
My rewrite of this page is still under way, in any case. -- Miguel
You could add those counter examples to the list of variables that don't follow the Normal distribution.
I don't understand the point about IQ scores and binomials, though. Which binomials are you thinking of? AxelBoldt
It's a bit more complicated than I made it sound, but the point is that the test score is basically a count of the number of correct answers, and therefore is a discrete variable like a Binomial and not a continuous variable like a Normal, so there is a Binomial-to-Normal limit involved. Here's the actual argument, written out:
Take a test that is composed of N True/False questions. Characterize a test-taker by their probability p of getting a right answer. Then their score will be a binomial B(N,p).
Now, consider a population of test takers. There will be a function F(p) on [0,1] which is the probability density that a randomly selected test-taker will have probability p of getting the right answer. Then, when you administer the test to a sample of test-takers, the probability distribution of the number of correct answers will be the convolution of B(N,p) and F(p), or
P(n) = int_[0,1] P(B(N,p)=n) F(p) dp
-- Miguel
If N is big enough, then the distribution of n/N should be pretty much the same as the distribution of p though (is that right?). So the truly interesting question is then: Why is p approximately normally distributed (or is it?). I would claim that it is, because of the central limit theorem (p pretty much describes the "intelligence" of a person, which is the result of many small mostly indepedent additive effects). AxelBoldt