## Probability and Distributions

This chapter considers the distribution of sample means and how this distribution is related to the distribution of individual values. The mean and variance to a considerable extent characterize a distribution, although it is clearly possible to construct situations where two distributions have the same mean and variance but are entirely different in other respects. There is one particular form of population distribution that is completely defined by the mean and variance so that the probability of a single observation being in any particular range of values depends only on the mean and standard deviation of the distribution. There are two common statistical measures of position, the mean and the median. Of these the mean is defined to be the average of the values of the distribution and is the most commonly used measure because of its simplicity and other theoretical advantages. The normal distribution is important because a remarkably large number of observed variables are approximately normally distributed.