Question

Frequency Polygon. In Exercises 15 and 16, construct the frequency polygons.

Tornadoes Use the frequency distribution from Exercise 12 in Section 2-1 on page 49 to construct a frequency polygon. Does the graph suggest that the distribution is skewed? If so, how?

Short answer

The following frequency polygon is constructed:

There are low frequencies toward the right of the graph. This indicates that the graph has a tail toward the right.

Thus, the graph suggests that the distribution is skewed to the right.

Step-by-step solution

Given information

A frequency distribution is constructed showing the F-scale measurements of a set of tornadoes in the United States.

Refer to Exercise 12 for the frequency distribution of F-scale intensities:

F-scale intensity	Frequency
0	24
1	16
2	2
3	2
4	1

Define a frequency polygon

A frequency polygon is a graph that is constructed for frequency distribution using midpoints of classes and their frequencies.

The midpoints of the class intervals are plotted on the x-axis, and the y-axis shows the frequencies. Points are plotted and then joined using line segments to form a closed-shaped polygon.

Determine the midpoints for the polygon

The following frequency distribution is used to construct the frequency polygon:

F-scale intensity	Frequency
0	24
1	16
2	2
3	2
4	1

Since the classes are not bounded, the discrete values are plotted on the graph.

To form a polygon (a closed figure), the two ends of the line should touch the horizontal axis. Thus, two additional categories need to be added:

• Category (-0.5) needs to be added before category 0 with a frequency equal to 0 for each of them.
• Category (4.5) needs to be added after category 4, a class with a frequency equal to 0 for each of them.

Thus, the new frequency distribution including two additional categories is as follows:

F-scale intensity	Frequency
-0.5	0
0	24
1	16
2	2
3	2
4	1
4.5	0

Sketch the frequency polygon 

The given steps help to plot the frequency polygon:

• Plot the values -1, 0, 1, and so on up to 5 on the horizontal axis.
• Plot the frequencies on the vertical axis starting from 0, 5, 10, and so on up to 30.
• Mark the points on the graph for each F-scale value shown in the table above corresponding to the frequency.
• Join the points using a straight line.

The frequency polygon is plotted as shown below:

Examine the skewness

The tail of the distribution helps to examine the skewness and its type. A lengthier right tail indicates the right skewness of the data, while a long left tail is indicative of the left skewness.

As the right tail of the polygon appears elongated, the given distribution is skewed to the right.