Once categories have been established, there are a
number of standard methods for presenting and sum-
marizing data.
Ways of Presenting Data
A frequency distribution is a table or visual chart that
shows the frequency (number) of individuals in each
possible category considered. For example, of the 100
army inductees tested above, suppose 20 have blood
type A, 27 blood type B, 16 blood type AB, and 37
blood type O. This information can be summarized in
a table.
This frequency distribution can also be presented
visually. A pie chart (also called a pie graph) is a circle
divided into sections, one for each category, and each
with area in proportion to the frequency of that cate-
gory. A bar chart is a graph with vertical bars repre-
senting the frequency of occurrence for each category.
If the data are categorical, then the bars are drawn
spaced apart to emphasize the separate nature of the
descriptive categories. If the data presented are numeri-
cal, the bars are drawn without spaces to indicate that
the data come from a range of numerical values, and
also to indicate how the data were grouped. In this
case, the bar chart is called a histogram.
A frequency polygon is similar to a histogram
except that a broken line is drawn to connect the mid-
point of each class considered at the height of the verti-
cal bar for that class. As a matter of convention, the
line is drawn touching the horizontal axis at both sides
of the distribution.
A time-series graph depicts the nature of a mea-
surement taken over a period of time. The values of
stocks, for example, are often depicted via time-line
graphs. Such a diagram does not represent a frequency
distribution, however.
Tables of whole-number values are sometimes sum-
marized via stem-and-leaf plots. Each number is
divided into two parts: the units digit (the “leaf”) and
the set of digits to its left (the “stem”). In one column
all the stems are listed, and the corresponding leaves
are arranged in a second column to the right.
Ways of Summarizing Data
There are three general features statisticians observe to
summarize numerical data.
1. The General Shape of a Histogram: The following
table shows some common frequency distribution
shapes. Distributions rarely conform to exact
shapes, but statisticians still find it useful to describe
the general nature of the distribution.
statistics: descriptive 479
Representing data
Plotting data