Because a list of raw data may be difficult to interpret, sociologists
prefer to represent their data in an organized way. Two of the most
common ways are frequency distributions and graphs.
Frequency Distributions
Suppose that you had a set of 20 scores from a 100-point sociology
exam. You might arrange them in a frequency distribution, listing the
frequency of each score or group of scores in a set of scores. Using
the set of scores in Table B.1, you would set up a column including the
highest and lowest scores, as well as the possible scores in between. In
this case, the highest score is 94 and the lowest is 80. You would then
count the frequency of each score and list it in a separate column. The
total of the frequencies in the distribution is symbolized by the letter N.
The frequency distribution might show a pattern in the set of scores
that is not apparent when simply examining the individual scores. In this
example (presented in Table B.1), the exam scores do not bunch up
toward the lower, middle, or upper portions of the distribution. In
some cases, typically when the difference between the highest score
and the lowest score is greater than 15, you might prefer to use a
grouped frequency distribution. The scores are grouped into intervals,
and the frequency of scores in each interval is listed in a separate
column. The intervals can be of any size, but, for ease of construction,
a grouped frequency distribution should end up with no more than
about 10 groups. A grouped frequency distribution provides less
precise information than does an ungrouped one, because the
individual scores are lost. However, the benefit of a grouped frequency
distribution is that one can understand any trends in the data at a quick
glance.
Learning Check #1: Suppose we ask 23 students how many music
CDs they own. Present the following data in a frequency
distribution: 43, 15, 52, 24, 84, 36, 75, 70, 98, 44, 56, 60, 48, 41,
38, 7, 62, 49, 32, 71, 25, 46, 58.
Click here for Answer.
Graphs
If a picture is worth a thousand words, then a graph is worth several paragraphs
in a research report. Because it provides a pictorial representation of the
distribution of scores, a graph can be an even more effective representation
of research data than a frequency distribution. Among the most common kinds
of graphs are pie graphs, frequency histograms, frequency polygons, and line
graphs.
Pie Graph
A simple, but visually effective, way of representing data is the pie graph.
It represents data as percentages of a pie-shaped graph. The total of the slices
of the pie must add up to 100 percent.
Learning Check #2: Suppose in a class of 150 students there are 13 First-year
students, 68 Sophomores, 50 Juniors, and 19 Seniors. Construct a pie chart to
illustrate this data.
Click here for Answer.
Frequency Polygon
A frequency polygon serves the same purpose as a frequency histogram. As shown
in Figure B.2, the frequency polygon is drawn by connecting the points, representing
frequencies, located above the scores. Note that the polygon is completed by
extending it to the abscissa one score below the lowest score and one score
above the highest score in the distribution.
An advantage of the frequency polygon over the frequency histogram is that
it permits the plotting of more than one distribution on the same set of axes.
Plotting more than one frequency histogram on a set of axes would create a confusing
graph. If more than one frequency polygon is plotted on a set of axes, they
should be distinguished from one another. This can be done by drawing a different
kind of line for each polygon (perhaps a solid line for one and a broken line
for the other), drawing the lines in different colors (perhaps red for one polygon
and blue for the other), or representing the points above the scores with geometric
shapes (perhaps a circle for one polygon and a triangle for the other).
There are a few shapes that a frequency polygon can take that are particularly
interesting to sociologists and other social researchers. A graph in which scores
bunch up toward either end of the abscissa (as shown in Figure B.3) is said
to be skewed. The skewness of a graph is in the direction of its "tail." If
the scores bunch up toward the high end, the graph has a negative skew. If the
scores bunch up toward the low end, the graph has a positive skew. A distribution
is said to be normal (or bell-shaped) if the scores bunch up in the middle and
then taper off fairly equally on each side. Finally, a distribution is called
a rectangular distribution if the scores are fairly evenly distributed throughout
the graph.
Learning Check #3: Remember the 23 students who reported the number of music
CDs that they own? Present the following data in a frequency polygon: 43, 15,
52, 24, 84, 36, 75, 70, 98, 44, 56, 60, 48, 41, 38, 7, 62, 49, 32, 71, 25, 46,
58.
Learning Check #4: What shape is the distribution graphed in?
Learning Check #5? What would have made the distribution take on a positive
skew? A negative skew? A rectangular shape?
Click here for Answer.
Line Graph
Whereas pie graphs, frequency histograms, and frequency polygons are useful
for plotting frequency data, a line graph is useful for plotting data generated
by experimental social research. It uses lines to represent the relationship
between independent variables and dependent variables. If you skim through your
introductory sociology textbook, you will see several examples of line graphs.
The graph shown in Figure B.4 represents the data from an investigation of the
relationship between exercise and weight loss. Note in this figure that one
line represents a group of people who agree to exercise regularly and the other
line represents a group of people who do not engage in exercise. In all other
ways these two groups are equal. They are weighed one week after agreeing to
participate in the study and again two weeks after agreeing to participate.
Note that this graph allows the reader to note quickly the benefits of exercise
on weight loss.
