Relative Cumulative
Frequency Graphs
AP Statistics
How to construct an ogive (relative
Cumulative Frequency Graph)
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Step 1: Decide on class intervals and make a frequency table just as in
making a histogram. Add three columns to your frequency table: relative
frequency, cumulative frequency, and relative cumulative
frequency
-To get the values in the relative frequency column, divide the count in
each class interval by the total number of the frequency. Multiply by
100 to convert to a percentage.
-To fill the cumulative frequency column, add the counts in the
frequency column that fall in or below the current class interval.For the
relative cumulative frequency column, divide the entries in the
cumulative frequency column by the total number of individuals.
Step 2: Label and scale your axes and title your graph. Label the horizontal
axis “Age at Inauguration” and the vertical axis according to your choice of
class intervals and the vertical axis from 0% to 100%
Step 3: Plot a point corresponding to the relative cumulative frequency in
each class interval at the left endpoint of the next class interval the last point
you plot should be at a height of 100%
Lets refer back to example 1.6
done yesterday in class.
• How can you do this
quickly? Make a
histogram on your
calculator. We will
use yesterday’s
histogram.
Construct your Table by ANALYZING your Histogram
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Class
40-44
45-49
50-54
55-59
60-64
65-69
Frequency
2
6
13
12
7
3
Relative Frequency
Cumulative Frequency
2/43= 0.047 or 4.7%
2
6/43= 0.140 or 14%
8
13/43= 0.302 or 30.2%
21
12/43 = 0.279 or 27.9%
33
7/43= 0.163 or 16.3%
40
3/43= 0.070 or 7%
43
Relative Cumulative Frequency
2/43= 0.047 or 4.7%
8/43= 0.186 or 18.6%
21/43= 0.488 or 48.8%
33/43= 0.767 or 76.7%
40/43= 0.930 or 93%
43/43= 1.000 or 100%
The following is a relative cumulative
frequency plot of the US presidents’ ages at
inauguration
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•
•
•
•
•
•
Class
40-44
45-49
50-54
55-59
60-64
65-69
Frequency
2
6
13
12
7
3
Relative Frequency
Cumulative Frequency
2/43= 0.047 or 4.7%
2
6/43= 0.140 or 14%
8
13/43= 0.302 or 30.2%
21
12/43 = 0.279 or 27.9%
33
7/43= 0.163 or 16.3%
40
3/43= 0.070 or 7%
43
Relative Cumulative Frequency
2/43= 0.047 or 4.7%
8/43= 0.186 or 18.6%
21/43= 0.488 or 48.8%
33/43= 0.767 or 76.7%
40/43= 0.930 or 93%
43/43= 1.000 or 100%
In the following (a) shows how we locate Bill Clinton’s age in the distribution
and (b) shows how to determine the 60th percentile and the center of the
distribution.
QUIZ REVIEW
• Know how to construct Bar Graphs, Dot
Plots, Stem Plots, Pie Charts, histograms
• Know how to read ogives (relative
cumulative frequency graphs).
• Know the difference between a categorical
variable and a quantitative variable
• Be able to describe a distribution
(remember this means to give the shape,
center AND spread)