The word statistics has its origin in the numerical study of states and their populations. How big is the population? How many are there to pay the taxes or join the army? As a consequence of this original usage we use the term


to represent all the possible observations that might have been made. For the case of a state where we do, say, a one in ten sample as part of a full census, the sample comes from the finite population, which is the population of the state. If we take a sample of 50 items manufactured on a machine as part of a quality inspection, the sample is envisaged as coming from the theoretically infinite population of items that could have been produced on that machine. The bigger the sample taken the more likely it is to reflect the statistical characteristics of the population. We now need to define more formally the population and these statistical characteristics. That is the purpose of this chapter.