Please bear with me while I give some background.

I was reading in a textbook how IQ scores follow a normal distribution (bell shaped curve). This was predicted before IQ tests were commonly given. This curve was created using the millions of IQ tests that have been given and it is almost perfectly a bell shaped curve.

Does this help or harm the cause of IQ tests? Could perhaps this be based upon how the test was written and not intelligence factors?

I'd say the bell curve is appropriate, with the IQ of 100 being at the zenith of the bell. Fewer are more intelligent and fewer are less intelligent than those right on average. It was a good safe prediction, and I'm not surprised that it held true.

No. Bell Curve is mathematics of natures way with variables that are 'non-discrete - height for example' and measurable. That is no divide-by-zero or otherwise infinite data points

Does not work for discrete sets: coin flip=binary, and on to 3-way, 4-way, etc.

Actually, the bell curve is an amazing approximation to the binary distribution. If you flip a coin a bunch of times, it reduces to the normal (bell) curve. It will always be discrete, but for a larger numebr fo flips it is basically a continuous curve. Our measurement of IQ, beased on a test with finite questions, is a discrete varibale (IQ = 100, or 99, not 99.7964475). But the bell curve still works, and it works very very very well.

Yeah, take that, hamme! Go Nate! (hiding behind the smart guy)

Statistics 001....

The normal distribution is one which appears in a variety of statistical applications. One reason for this is the central limit theorem. This theorem tells us that sums of random variables are approximately normally distributed if the number of observations is large. For example, if we toss a coin, the total number of heads approaches normality if we toss the coin a lot of times. Even when a distribution may not be exactly normal, it may still be convenient to assume that a normal distribution is a good approximation. In this case, many statistical procedures, such as the t-test can still be used.

The normal distribution has two parameters, the mean mu and the standard deviation sigma. Once the parameters are known, the distribution is completely specified. It can be shown, although we will not do so (yet) that a good guess or estimate for mu is the mean of the observed values. An estimate for sigma is the standard deviation. Although the standard deviation is a positive number, the mean can assume any value. The distribution is symmetrical with mean, mode, and median all equal at mu. It is interesting to note that the exact specification of the figure shown here was taken from the German 10 DM banknote. The mean equals three, and the standard deviation equals one in this example. On the back of the banknote is a portrait of Gauss.

Some events are rather rare , they don't happen that often. For instance, car accidents are the exception rather than the rule. Still, over a period of time, we can say something about the nature of rare events. An example is the improvement of traffic safety, where the government wants to know wether seat belts reduce the number of death in car accidents. Here, the poisson distribution can be a usefull tool to answer question about benefits of seat belt use. Other phenomena that often follow a poisson distribution are death of infants, the number of misprints in a book, the number of customers arriving, and the number of activations of a geiger counter. The poisson distribution was derived by the french mathematician Poisson in 1837, and the first application was the describtion of the number of death by horse kicking in the prussian army (Bortkiewicz, 1898).

In statistics the so-called binomial distribution describes the possible number of times that a particular event will occur in a sequence of observations. The event is coded binary, it may or may not occur. The binomial distribution is used when a researcher is interested in the occurrence of an event, not in its magnitude. For instance, in a clinical trial, a patient may survive or die. The researcher studies the number of survivors, and not how long the patient survives after treatment. Another example is whether a person is ambitious or not. Here, the binomial distribution describes the number of ambitious persons, and not how ambitious they are. The binomial distribution is specified by the number of observations, n, and the probability of occurence, which is denoted by p.

A classic example that is used often to illustrate concepts of probability theory, is the tossing of a coin. If a coin is tossed 4 times, then we may obtain 0, 1, 2, 3, or 4 heads. We may also obtain 4, 3, 2, 1, or 0 tails, but these outcomes are equivalent to 0, 1, 2, 3, or 4 heads. The likelihood of obtaining 0, 1, 2, 3, or 4 heads is, respectively, 1/16, 4/16, 6/16, 4/16, and 1/16. In the figure on this page the distribution is shown with p = 1/2 Thus, in the example discussed here, one is likely to obtain 2 heads in 4 tosses, since this outcome has the highest probability. Other situations in which binomial distributions arise are quality control, public opinion surveys, medical research, and insurance problems.

The central limit theorem is one of the most remarkable results of the theory of probability. In its simplest form, the theorem states that the sum of a large number of independent observations from the same distribution has, under certain general conditions, an approximate normal distribution. Moreover, the approximation steadily improves as the number of observations increases. The theorem is considered the heart of probability theory, although a better name would be normal convergence theorem.

For example, suppose an ordinary coin is tossed 100 times and the number of heads is counted. This is equivalent to scoring 1 for a head and 0 for a tail and computing the total score. Thus, the total number of heads is the sum of 100 independent, identically distributed random variables. By the central limit theorem, the distribution of the total number of heads will be, to a very high degree of approximation, normal. This illustrated graphically by repeating this experiment many times. The results of this experiment are displayed in a diagram. The percentage computed over the number of experiments is arranged along the vertical axis, and the total score or the number of heads is arranged along the horizontal axis. After a large number of repetitions a curve appears that looks like the normal curve.

It has been empirically observed that various natural phenomena, such as the heights of individuals, follow approximately a normal distribution. A suggested explanation is that these phenomena are sums of a large number of independent random effects and hence are approximately normally distributed by the central limit theorem.

My memory is going, but Damn, the internet is full of 'stuff'....
:p

I agree that if the variable is truly random the probabilities or distribution will be flat. Yet, I haven't seen anything that is truly random. There are things that are theoretically random, but I haven't observed true randomness ever, that would require everything about the experiment to be absolutely perfect and it never is.

Therefore there is no random only chaos, which has a predictable envelope or maybe even a gaussian distribution...