Chapter 4 Describing Your Data 129C
hapter 4 introduces the different tools that statisticians use to
describe and summarize the values in a data set. You’ll work with
frequency tables in order to see the range of values in your data.
You’ll use graphical tools like histograms, stem and leaf plots, and
boxplots to get a visual picture of how the data values are distributed.
You’ll learn about descriptive statistics that reduce the contents of your
data to a few values, such as the mean and standard deviation. Applying
these tools is the fi rst step in the process of evaluating and interpreting
the contents of your data set.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 con-
tain 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) num-
bers. 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 quantita-
tive variables that assume values from a defi ned list of numbers. The num-
bers 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.