Statistical Inference: A Short Course

3.1 The Search for Summary Characteristics

Up to this point in our data analysis, we have been working with the entire set of observations, either in tabular form (e.g., an absolute frequency distribution) or in graphical form (e.g., an absolute frequency function or an absolute frequency histogram). Is there a more efficient way of squeezing information out of a set of quantitative data? As one might have anticipated, the answer is yes. Instead of working with the entire mass of data in the form of a table or graph, let us determine concise summary characteristics of our variable X, which are indicative of the properties of the data set itself.

If we are working with a population of X values, then these descriptive measures will be termed “parameters.” Hence a parameter is any descriptive measure of a population. But if we are dealing with a sample of X values drawn from the X population, then these descriptive measures will be called “statistics.” Thus a statistic is any descriptive measure of a sample. (You now know what this book is ultimately all about —you are going to study descriptive measures of samples.) As we shall see later on, statistics are used to measure or estimate (unknown) parameters. For any population, parameters are constants. However, the value of a statistic is variable; its value depends upon the particular sample chosen, that is, it is sample sensitive. (This is why sampling error is an important factor in estimating a parameter.)

This said, what are some ...