full2.gif (11401 bytes)
Cumulative Percent Polygon
(A worked Problem:  Procedure explained in more detail in Chapter 3)

Using the following frequency distribution of 100 IQ scores create a Cumulative Percent Polygon:

Real Lim

App Lim

 Freq

Mid Pt

Rel F

Cum F

C R F

Cum %


129.5-134.5
124.5-129.5
119.5-124.5
114.5-119.5
109.5-114.5
104.5-109.5
99.5-104.5
94.5-99.5
89.5-94.5
84.5-89.5
79.5-84.5
74.5-79.5
69.5-74.5


130-134
125-129
120-124
115-119
110-114
105-109
100-104
95-99
90-94
85-89
80-84
75-79
70-74


5
5
5
10
10
15
15
10
10
5
5
5
0


132
127
122
117
112
107
102
97
92
87
82
77
72


.05
.05
.05
.10
.10
.15
.15
.10
.10
.05
.05
.05
0


100
95
90
85
75
65
50
35
25
15
10
5
0


1.00
.95
.90
.85
.75
.65
.50
.35
.25
.15
.10
.05
0


100
95
90
85
75
65
50
35
25
15
10
5
0

I. To create a frequency polygon we use only the cumulative percent and the upper real limit

II. We also need to create one extra interval at the bottom with cumulative percent = 0.

III.  Label the axes

    A.  Label the X axis

        a.  It is best to label the X axis with the real limits, beginning with the upper real limit
                of the extra interval, because the points will be plotted at the upper real limits.

        b.  Remember also to provide a label that tells the units (in this case it is IQ).

    B. Label the Y axis

        a.  Always begin at 0 and label up to 100 percent.

        b.  Remember to also put the label "Cumulative Percent" next to the numeric labels.
cp1.gif (8225 bytes)

IV.  The next graph shows the plotting of the first two points.

    A.  The first point goes at 74.5, the upper real limit of the extra interval, where the X value = 0.

    B.  The second point goes at 79.5 where the cumulative percent (X) = 5.
cp2.gif (8271 bytes)
V.  The next graph shows all the cumulative percent points from the frequency distribution.
cp3.gif (8438 bytes)
VI.  To complete the cumulative percent polygon you connect the points with straight lines.
cp4.gif (10037 bytes)
Hint:  The Cumulative Percent Polygon starts at C% = 0 and climbs to C% = 100.

Hint:  Remember that to plot a Cumulative Percent Polygon you must first
            generate an extra class interval at the bottom. 

Hint:  Remember that all the points must be plotted at the upper real limit.

Hint:  Remember to connect the points with straight lines.

Hint:  You do not bring the graph down to the X axis after the last class interval.

Hint:  Remember that without the proper labels the entire graph is wrong.

Copyright © 2004 by Mark W. Vernoy