Normal Distribution

Up to this point we have been concerned with how scores are distributed and how best to describe the distribution. We have discussed several different measures, but the mean will be the measure that we use to describe the centre of the distribution and the standard deviation will be the measure we use to describe the spread of the distribution. Knowing these two facts gives us ample information to make statements about the probability of observing a certain value within that distribution. If I know, for example, that the average I.Q. score is 100 with a standard deviation of 20, then I know that someone with an I.Q. of 140 is very smart. I know this because 140 deviates from the mean by twice the average amount as the rest of the scores in the distribution. Thus, it is unlikely to see a score as extreme as 140 because most the I.Q. scores are clustered around 100 and on average only deviate 20 points from the mean.