distribution symmetry. If they are approximately equal, the data set is
roughly symmetric; otherwise, we are able to see the degree and direction
of skewness (Figure 2.11).- The line segments projecting out from the box extend in both directions
to theadjacent values. The adjacent values are the points that are 1.5
times the length of the box beyond either quartile. All other data points
outside this range are represented individually by little circles; these are
considered to be outliers or extreme observations that are not typical of
the rest of the data.
Of course, it is possible to combine a one-way scatter plot and a box plot so
as to convey an even greater amount of information (Figure 2.12). There are
other ways of constructing box plots; for example, one may make it vertically
or divide it into di¤erent levels of outliers.
2.3 SPECIAL CASE OF BINARY DATA
Observations or measurements may be made on di¤erent scales. If each ele-
ment of a data set may lie at only a few isolated points, we have adiscretedata
set. A special case of discrete data are binary data, where each outcome has
only two possible values; examples are gender and an indication of whether a
treatment is a success or a failure. If each element of this set may theoretically
lie anywhere on a numerical scale, we have acontinuousdata set; examples are
blood pressure and cholesterol level. Chapter 1 deals with the summarization
and description of discrete data, especially binary data; the primary statistic
was proportion. In this chapter the emphasis so far has been on continuous
measurements, where, for example, we learn to form sample mean and use it as
Figure 2.11 Typical box plot.Figure 2.12 Crude death rates for the United States, 1988: a combination of one-way
scatter and box plots.
SPECIAL CASE OF BINARY DATA 81