The methods for displaying and analyzing data depend upon the type of data being used.

**TYPES OF DATA**

The methods for displaying and analyzing data
depend upon the type of data being used. In this section, we will define and
provide examples of the two major types of data: qualitative and quantitative.
Quantitative data can be continuous or discrete. Chapter 11 will give more
information about the related topic of measurement systems. We collect data to
characterize populations and to estimate parameters, which are numerical or
categorical characteristics of a population probability distribution.

In order to describe types of
data, we need to be familiar with the concept of variables. The term “variable”
is used to describe a quantity that can vary (i.e., take on various values),
such as age, height, weight, or sex. Variables can be characteris-tics of a
population, such as the age of a randomly selected individual in the U.S. population.
They can also be estimates (statistics) of population parameters such as the
mean age of a random sample of 100 individuals in the U.S. population. These
variables will have probability distributions associated with them and these
distrib-utions will be discussed in Chapter 5.

Variables that can be identified for individuals
according to a quality are called qualitative variables. These variables place
individuals into categories that do not have numerical values. When the
observations are not ordered, they form a nominal scale. (A dichotomous
scale—true/false, male/female, yes/no, dead/alive—also is a nominal scale.)
Many qualitative variables cannot be ordered (as in going from worst to best).
Occupation, marital status, and sex are examples of qualitative data that have
no natural ordering. The term nominal refers to qualitative data that do not have
a natural ordering.

Some qualitative data can be ordered in the manner
of a preference scale (e.g., strongly agree, agree, disagree, strongly
disagree). Levels of educational attainment can be ordered from low to moderate
to high: less than a high school education might be categorized as low;
education beyond high school but without a four year bachelor’s degree could be
considered moderate; a four year bachelor’s degree might be considered high;
and a degree at the masters, Ph.D., or M.D. level consid-ered very high.
Although still considered qualitative, categorical data that can be or-dered
are called ordinal.

Qualitative data can be summarized and displayed in
pie charts and bar graphs, which describe the frequency of occurrence in the
sample or the population of par-ticular values of the characteristics. These
graphical representations will be de-scribed in Section 3.3. For ordinal data
with the categories ordered from lowest to highest, bar graphs might be more
appropriate than pie charts. Because a pie chart is circular, it is more
appropriate for nominal data.

Quantitative data are numerical data that have a
natural order and can be continuous or discrete. Continuous data can take on
any real value in an interval or over the whole real number line. Continuous
data can be classified as interval. Continuous data also can be summarized with
box-and-whisker plots, histograms, frequency polygons, and stem-and-leaf
displays. Examples of continuous data include vari-ables such as age, height,
weight, heart rate, blood pressure, and cholesterol level.

Discrete data take on only a finite or countable
(equivalent to the set of integers) number of values. Examples of discrete data
are the number of children in a house-hold, the number of visits to a doctor in
a year, or the number of successful ablation treatments in a clinical trial.
Often, discrete data are integers or fractions. Discrete data can be described
and displayed in histograms, frequency polygons, stem-and-leaf displays, and
box-and-whisker plots (see Section 3.3).

If the data can be ordered, and we can identify
ratios with them, we call the data ratio data. For example, integers form a
quantitative discrete set of numbers that are ratio data; we can quantify 2 as
being two times 1, 4 as two times 2, and 6 as three times 2. The ability to
create ratios distinguishes quantitative data from qualitative data.
Qualitative ordinal data can be ordered but cannot be used to produce ratios.
We cannot say, for example, that a college education is worth twice as much as
a high school education.

Continuous interval data can be
used to produce ratios but not all ratio data are continuous. For example, the
integers form a discrete set that can produce ratios, but such data are not
interval data because of the gaps between consecutive inte-gers.

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