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Histograms, Frequency Polygons, and Ogives
Histogram: A graph that displays data by using
contiguous vertical bars.
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
Plot the Mid Points
9.5 19.5 29.5 39.5 49.5 59.5 69.5 79.5
Frequency Polygon: A graph that displays the data by using lines that connect points plotted for the frequencies at the midpoints
of the classes.
Plot the Mid Points
9.5 19.5 29.5 39.5 49.5 59.5 69.5 79.5
Connect the dots, bring down to the x axis
Ogive: A graph that displays the cumulative frequencies for the classes
in a frequency distribution.
Frequency
0
10
20
30
40
50
60
99.5 -104.5
104.5 -109.5
109.5 -114.5
114.5 -119.5
119.5 -124.5
124.5 -129.5
129.5 -134.5
Frequency
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
Plot the upper boundary points
9.5 19.5 29.5 39.5 49.5 59.5 69.5 79.5
Connect the dots, start at zero
9.5 19.5 29.5 39.5 49.5 59.5 69.5 79.5
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.
Note that percentages are used.
0%
10%
20%
30%
40%
50%
0 to10
11 to17
19 to23
24 to45
46 to64
65+
New York
Elysburg
Ages
Distribution Shapes
Uniform Shape
0
12
34
5
1 2 3 4 5 6 7 8 9
Bell Shaped
0
2
4
6
8
1 2 3 4 5 6 7 8 9
J shaped
0
2
4
6
1 2 3 4 5 6 7 8 9
Reverse J shaped
0
2
4
6
1 2 3 4 5 6 7 8 9
More Distribution Shapes
Right Skewed
0
12
34
5
1 2 3 4 5 6 7 8 9
Left Skewed
0
12
34
5
1 2 3 4 5 6 7 8 9
Bimodal
0
12
34
5
1 2 3 4 5 6 7 8 9
U shaped
0
2
4
6
1 2 3 4 5 6 7 8 9
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