Essential Statistics

39 / 762

Chapter 1: Introduction and Graphical Displays 39
Section Review
Next, we will discuss frequency and relative frequency polygons.
1- 6 Frequency and Relative Frequency Polygons
A frequency or relative frequency polygon may be obtained from the
histogram of a data set. It is obtained by joining, with straight line segments,
the ordered pairs of (class midpoint, frequency) or (class midpoint, relative
frequency). The frequency or relative frequency for the ordered pairs is for
the respective classes in the histogram. The polygon is “tied down” at both
ends where the frequency or relative frequency is zero. The class where the
polygon is tied down to the left is at the midpoint in the class with zero
frequency or relative frequency just before the first class in the histogram.
The class where the polygon is tied down to the right is at the midpoint in
the class with zero frequency or relative frequency just after the last class in
the histogram.
Definition: Frequency and Relative Frequency Polygon
A frequency or a relative frequency polygon is a graph that displays the data
using straight line segments to connect points plotted for the frequencies or
relative frequencies and the midpoints of the classes. The polygon is tied
down at the midpoint of the class preceding the first class and at the
midpoint of the class just after the last class.
Note: A frequency polygon provides an estimate of the shape of the
distribution of the population.
Example 1-8: Display a frequency and relative frequency polygon for the
data in Example 1-3.