Figure 3. Ogive from Table 2
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A frequency polygon that uses cumulative frequencies, is called an ogive (oh-jive).
| Ogive “The graphs of cumulative frequencies” (Kenney, 1939). |
The points are now the upper boundaries of each bin, and the cumulative frequency is used. We first need to determine the cumulative frequency as shown in Table 2.
| Age | Frequency | Cumulative Frequency | upper bound |
|---|---|---|---|
| 0 < 10 | 5 | 5 | 10 |
| 10 < 20 | 7 | 12 | 20 |
| 20 < 30 | 10 | 22 | 30 |
| 30 < 40 | 8 | 30 | 40 |
| 40 < 50 | 4 | 44 | 50 |
The upper bounds now determine the position on the horizontal axis, and the cumulative frequency the position vertically. The ogive of Table 2 is shown in Figure 3.
Figure 3. Ogive from Table 2
Note that because the Ogive uses cumulative frequencies, the graph will almost always show an increase. If the slope is less steep than the previous segment it indicates that the frequency for that bin was less than the previous one.
From the ogive you can obtain the cumulative frequencies, to convert these back to absolute frequencies simply subtract the cumulative frequency of the previous bin, as was also discussed here.
An early reference to an ogive had the description: "When the objects are marshalled in the order of their magnitude along a level base at equal distances apart, a line drawn freely through the tops of the ordinates..will form a curve of double curvature... Such a curve is called, in the phraseology of architects, an ‘ogive’." (Galton, 1875, p. 35).