Histograms, Frequency Polygons, and Ogives

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Histograms, Frequency Polygons, and Ogives
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Histogram A graph that displays data by using
contiguous vertical bars.
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Organize Data, Prepare Table
Limit Boundary Number
10 19 9.5 19.5 6
20 29 19.5 29.5 8
30 39 29.5 39.5 15
40 49 39.5 49.5 11
50 59 49.5 59.5 7
60 69 59.5 69.5 3
70 79 69.5 79.5 1
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Plot the Mid Points
9.5
19.5
29.5
39.5
49.5
59.5
69.5
79.5
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Frequency Polygon A graph that displays the data
by using lines that connect points plotted for
the frequencies at the midpoints of the classes.
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Plot the Mid Points
9.5
19.5
29.5
39.5
49.5
59.5
69.5
79.5
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Connect the dots, bring down to the x axis
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Ogive A graph that displays the cumulative
frequencies for the classes in a frequency
distribution.
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Organize Data, Prepare Table
Limit Boundary Number Cumulative
10 19 9.5 19.5 6 6
20 29 19.5 29.5 8 14
30 39 29.5 39.5 15 29
40 49 39.5 49.5 11 40
50 59 49.5 59.5 7 47
60 69 59.5 69.5 3 50
70 79 69.5 79.5 1 51
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Plot the upper boundary points
9.5 19.5 29.5 39.5
49.5 59.5 69.5 79.5
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Connect the dots, start at zero
9.5 19.5 29.5 39.5 49.5
59.5 69.5 79.5
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Relative Frequency Graphs

• Use relative frequencies when the proportion of
  data values that fall into a given class is more
  important than the actual number of data values
  that fall into the class.
• Example Compare age distributions in New York
  City and Elysburg.

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Note that percentages are used.
Ages
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Distribution Shapes
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More Distribution Shapes