Frequency
Distribution Graphs (Visualizations)
for Category Variables

 Bar Graphs
 A Bar Graph is used to portray the (grouped) frequency
distribution of a variable at the Nominal level of
measurement. Such variables are called Category
Variables in ViSta. It consists of vertical bars drawn
above categories such that
 The height of the bar corresponds to the frequency
 The bars are separated by empty space since the
nominal level of measurement has separate, discrete
categories.
Example: Consider the information given in
the following table about the percent of those in the
age group 2534 who have completed various amounts of
education (from Moore and McCabe, p. 186):
These percentages can be represented by the following
bar graph:
This bar graph shows us right away that the educational
level of most of those in the 2534 age group is the
completion of highschool.
 Stacked (Segmented) Bar Graphs
 While a bar graph represents the frequencies of categories
of one variable, a stacked (segmented) bar graph represents
the frequencies of combinations of categories of two variables.
In a stacked (or segmented) bar graph:
 The horizontal axis still represents one variable,
with each bar representing one of the catgories of
the variable.
 Each bar is segmented according to the categories
of the second variable. Alternatively, each bar can
be seen as being made up of smaller bars stacked on
top of each other.
Example: Consider the entire set of data about
educational level given by Moore and McCabe:
Here is the stacked bar graph:
 Mosaic Plots
 A mosaic plot presents the same information as is presented
by a stacked bargraph: The frequencies of combinations
of categories of two variables. Furthermore, it represents
the information in a similar, but slightly different fashion:
 A mosaic plot consists of rectangles laid out in
a mosaic. The rectangles are like the subbars in
a stacked bargraph.
 In a mosaic plot, each column of rectangles represents
a category of the variable on the horizontal axis.
 In a stacked bargraph, each bar represents the
overall frequency of a category of the variable plotted
on the horizontal axis. In a mosaic, the several column
of tiles are all the same height, representing 100%.
 Whereas a stacked bargraph's subbars representing
the joint frequency of a category of each of the two
variables, in a mosaic plot each rectangle represents
the joint probability of a category of each of the
two variables.
Here is the mosaic plot for the data shown above:
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