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


Note about Relative Frequency Polygons:  Relative Frequency Polygons are used
        for comparing 2 frequency distributions that have different numbers of
        scores (n's).  You would never plot only one Relative Frequency Polygon.  You
        would always have 2 lines on the graph.   This page will show you how to plot one
        of the lines and then will demonstrate the comparison with the other frequency
        distribution.

Use the following frequency distribution of 100 IQ scores create a Relative Frequency Polygon:

Real Lim

App Lim

 Freq

Mid Pt

Rel F

Cum F

C R F

Cum %


134.5-139.5
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


135-139
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


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


137
132
127
122
117
112
107
102
97
92
87
82
77
72


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


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


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


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

Use the following frequency distribution of 250 IQ scores create a Relative Frequency Polygon:

App Lim

 Freq

Mid Pt

Rel F


135-139
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


0
15
30
35
40
50
65
55
45
40
45
50
30
0


137
132
127
122
117
112
107
102
97
92
87
82
77
72


0
.03
.06
.07
.08
.10
.13
.11
.09
.08
.09
.10
.06
0


I. To create a relative frequency polygon we use only the relative Frequency and the midpoint

II. We also need to create two extra intervals with zero relative frequency for each of the
        frequency distributions that we are going to graph.

    A.  An extra interval at the top with relative frequency = 0
           
This allows us to bring the graph back down to the X axis.

    B.  An extra interval at the bottom with relative frequency = 0
           
This allows us to start the graph at the X axis.

III.  Label the axes

    A.  Label the X axis

        a.  It is best to label the X axis with the midpoints beginning with the midpoint
             of that extra low interval that you created.  Remember to check that you have
             covered the midpoints of both frequency distributions.

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

    B. Label the Y axis

        a.  Begin at 0 and label up to the largest relative frequency in both of the distributions.
                (It is very rare for a relative frequency to be greater than .5.)

        b.  Remember to also put the label "Relative Frequency" next to the numeric labels.
rf1.gif (6938 bytes)

IV.  This next graph shows how to plot the first two points of the frequency distribution at the top
            of the page.

    A.  The first (extra interval) has a midpoint (X) = 72 and a relative frequency (Y) = 0.

    B.  The second point has a midpoint (X) = 77 and a relative frequency (Y) = .05.

rf2.gif (6980 bytes)

V.  Now we continue with the rest of the relative frequency distribution by plotting points for the
            rest of the class intervals.

rf3.gif (7141 bytes)

VI.  Once all the points are plotted we then connect them with straight lines.

rf4.gif (9333 bytes)

VII.  Finally we plot the relative frequency graph for the other frequency distribution with n = 250.

rf5.gif (9215 bytes)
Hint:  Remember that Relative Frequency Graphs always have two lines.

Hint:  Remember that to plot a Relative Frequency Polygon you must first generate the
            two extra class intervals. 

Hint:  Remember that all the points must be plotted at the midpoint

Hint:  Remember to connect the points with straight lines.

Hint:  Remember that without the proper labels the entire graph is wrong.
            This also means that you must somehow distinguish between the two different lines.
            Use different markers or different colors for the different lines.

  Copyright 2004 by Mark W. Vernoy