Frequency Polygons2.22001/07/182002/11/07 00:00:00.002 US/CentralDavidLanelane@rice.eduAdanGalvanjago@rice.edufrequency polygonsstatisticsIntroduction to frequency polygons.
Frequency polygons are a graphical device for understanding the
shapes of distributions. They serve the same purpose as
histograms, but are especially helpful in comparing sets of
data. Frequency polygons are also a good choice for
displaying cumulative frequency distributions.
To create a frequency polygon, start just as for histograms, by
choosing a class interval. Then draw an X-axis representing the
values of the scores in your data. Mark the middle of each class
interval with a tick mark, and label it with the middle value
represented by the class. Draw the Y-axis to indicate the
frequency of each class. Place a point in the middle of each
class interval at the height corresponding to its frequency.
Finally, connect the points. You should include one class
interval below the lowest value in your data and one above the
highest value. The graph will then touch the X-axis on both
sides.
A frequency polygon for 642 psychology test scores is shown in
. The first label on the X-axis is
35. This represents an interval extending from 29.5 to
39.5. Since the lowest test score is 46, this interval has a
frequency of 0. The point labeled 45 represents the interval
from 39.5 to 49.5. There are three scores in this
interval. There are 150 scores in the interval that surrounds
85.
You can easily discern the shape of the distribution from . Most of the scores are between 65 and
115. It is clear that the distribution is not symmetric inasmuch
as good scores (to the right) trail off more gradually than poor
scores (to the left). In the terminology of Chapter 3 (where we
will study shapes of distributions more systematically), the
distribution is skewed.
Frequency polygon for the psychology test scores.
A cumulative frequency polygon for the same test scores is shown
in . The graph is the same as before
except that the Y value for each
point is the number of students in the corresponding class
interval plus all numbers in lower intervals. For example, there
are no scores in the interval labeled "35," three in the
interval "45,"and 10 in the interval "55."Therefore the
Y value corresponding to "55" is
13. Since 642 students took the test, the cumulative frequency
for the last interval is 642.
Cumulative frequency polygon for the psychology test scores.
Frequency polygons are useful for comparing distributions. This
is achieved by overlaying the frequency polygons drawn for
different data sets. provides an
example. The data come from a task in which the goal is to move
a computer mouse to a target on the screen as fast as
possible. On 20 of the trials, the target was a small rectangle;
on the other 20, the target was a large rectangle. Time to reach
the target was recorded on each trial. The two distributions
(one for each target) are plotted together in . The figure shows that although there is some
overlap in times, it generally took longer to move the mouse to
the small target than to the large one.
Overlaid frequency polygons.
It is also possible to plot two cumulative frequency
distributions in the same graph. This is illustrated in using the same data from the mouse task. The
difference in distributions for the two targets is again
evident.