# Variables and Descriptive Statistics

In this chapter you’ll learn about a branch of statistics called descriptive statistics. In descriptive statistics we use various mathematical tools to summarize the values of a data set. Our goal is to take data that may contain thousands of observations and reduce it to a few calculated values. For example, we might calculate the average salaries of employees at several companies in order to get a general impression about which companies pay the most, or we might calculate the range of salaries at those companies to convey the same idea.

Note that we should be very careful in drawing any general conclusions or making any predictions on the basis of our descriptive statistics. Those tasks belong to a different branch of statistics called inferential statistics, a topic we’ll discuss in later chapters. The goal of descriptive statistics is to describe the contents of a specifi c data set, and we don’t have the tools yet to evaluate any conclusions that might arise from examining those statistics.

When descriptive statistics involve only a single variable, as they will in this chapter, we are employing a branch of statistics called univariate statistics. Now we’ve used the term variable several times in this book. What is a variable? A variable is a single characteristic of any object or event. In the last chapter, you looked at data sets that contained several variables describing graduation rates of the Big Ten universities. Each column in that worksheet contained information on one characteristic, such as the university’s name or total enrollment, and thus was a single variable.

Variables can be classifi ed as quantitative and qualitative. Quantitative variables involve values that come in meaningful (not arbitrary) numbers. Examples of quantitative variables include age, weight, and annual income—anything that can be measured in terms of a number. The number itself can be either discrete or continuous. Discrete variables are quantitative variables that assume values from a defi ned list of numbers.

The numbers on a die come in discrete values (1, 2, 3, 4, 5, or 6). The number of children in a household is discrete, consisting of positive integers and zero. 130 Fundamentals of Statistics Continuous variables, on the other hand, have values from a wide range of possible values. An individual’s weight could be 185, 185.5, or 185.5627 pounds.

To be sure, there is some blurring in the distinction between discrete and continuous variables. Is salary a discrete variable or a continuous variable? From one point of view, it’s discrete: The values are limited to dollars and cents, and there is a practical upper limit to how high a specifi c salary could go. However, it’s more natural to think of salary as continuous.