Histograms, Frequency Polygons, and Ogives. Histogram: A graph that displays data by using...
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Transcript of Histograms, Frequency Polygons, and Ogives. Histogram: A graph that displays data by using...
![Page 1: Histograms, Frequency Polygons, and Ogives. Histogram: A graph that displays data by using contiguous vertical bars.](https://reader035.fdocuments.in/reader035/viewer/2022072005/56649cf35503460f949c10fb/html5/thumbnails/1.jpg)
Histograms, Frequency Polygons, and Ogives
![Page 2: Histograms, Frequency Polygons, and Ogives. Histogram: A graph that displays data by using contiguous vertical bars.](https://reader035.fdocuments.in/reader035/viewer/2022072005/56649cf35503460f949c10fb/html5/thumbnails/2.jpg)
Histogram: A graph that displays data by using
contiguous vertical bars.
![Page 3: Histograms, Frequency Polygons, and Ogives. Histogram: A graph that displays data by using contiguous vertical bars.](https://reader035.fdocuments.in/reader035/viewer/2022072005/56649cf35503460f949c10fb/html5/thumbnails/3.jpg)
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
![Page 4: Histograms, Frequency Polygons, and Ogives. Histogram: A graph that displays data by using contiguous vertical bars.](https://reader035.fdocuments.in/reader035/viewer/2022072005/56649cf35503460f949c10fb/html5/thumbnails/4.jpg)
Plot the Mid Points
9.5 19.5 29.5 39.5 49.5 59.5 69.5 79.5
![Page 5: Histograms, Frequency Polygons, and Ogives. Histogram: A graph that displays data by using contiguous vertical bars.](https://reader035.fdocuments.in/reader035/viewer/2022072005/56649cf35503460f949c10fb/html5/thumbnails/5.jpg)
Frequency Polygon: A graph that displays the data by using lines that connect points plotted for the frequencies at the midpoints
of the classes.
![Page 6: Histograms, Frequency Polygons, and Ogives. Histogram: A graph that displays data by using contiguous vertical bars.](https://reader035.fdocuments.in/reader035/viewer/2022072005/56649cf35503460f949c10fb/html5/thumbnails/6.jpg)
Plot the Mid Points
9.5 19.5 29.5 39.5 49.5 59.5 69.5 79.5
![Page 7: Histograms, Frequency Polygons, and Ogives. Histogram: A graph that displays data by using contiguous vertical bars.](https://reader035.fdocuments.in/reader035/viewer/2022072005/56649cf35503460f949c10fb/html5/thumbnails/7.jpg)
Connect the dots, bring down to the x axis
![Page 8: Histograms, Frequency Polygons, and Ogives. Histogram: A graph that displays data by using contiguous vertical bars.](https://reader035.fdocuments.in/reader035/viewer/2022072005/56649cf35503460f949c10fb/html5/thumbnails/8.jpg)
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
![Page 9: Histograms, Frequency Polygons, and Ogives. Histogram: A graph that displays data by using contiguous vertical bars.](https://reader035.fdocuments.in/reader035/viewer/2022072005/56649cf35503460f949c10fb/html5/thumbnails/9.jpg)
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
![Page 10: Histograms, Frequency Polygons, and Ogives. Histogram: A graph that displays data by using contiguous vertical bars.](https://reader035.fdocuments.in/reader035/viewer/2022072005/56649cf35503460f949c10fb/html5/thumbnails/10.jpg)
Plot the upper boundary points
9.5 19.5 29.5 39.5 49.5 59.5 69.5 79.5
![Page 11: Histograms, Frequency Polygons, and Ogives. Histogram: A graph that displays data by using contiguous vertical bars.](https://reader035.fdocuments.in/reader035/viewer/2022072005/56649cf35503460f949c10fb/html5/thumbnails/11.jpg)
Connect the dots, start at zero
9.5 19.5 29.5 39.5 49.5 59.5 69.5 79.5
![Page 12: Histograms, Frequency Polygons, and Ogives. Histogram: A graph that displays data by using contiguous vertical bars.](https://reader035.fdocuments.in/reader035/viewer/2022072005/56649cf35503460f949c10fb/html5/thumbnails/12.jpg)
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.
![Page 13: Histograms, Frequency Polygons, and Ogives. Histogram: A graph that displays data by using contiguous vertical bars.](https://reader035.fdocuments.in/reader035/viewer/2022072005/56649cf35503460f949c10fb/html5/thumbnails/13.jpg)
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
![Page 14: Histograms, Frequency Polygons, and Ogives. Histogram: A graph that displays data by using contiguous vertical bars.](https://reader035.fdocuments.in/reader035/viewer/2022072005/56649cf35503460f949c10fb/html5/thumbnails/14.jpg)
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
![Page 15: Histograms, Frequency Polygons, and Ogives. Histogram: A graph that displays data by using contiguous vertical bars.](https://reader035.fdocuments.in/reader035/viewer/2022072005/56649cf35503460f949c10fb/html5/thumbnails/15.jpg)
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