Economics · Ch 4 — Presentation of Data

Ogive

4.5.2.4

Ogive

An ogive, also called the cumulative frequency curve, plots cumulative frequencies (instead of simple frequencies) along the y-axis against the class limits. Because cumulative frequency can be counted two ways, there are two ogives for any grouped distribution:

The 'less than' ogive plots each cumulative frequency against the upper limit of its class. It is never decreasing (it rises or stays level).
The 'more than' ogive plots each cumulative frequency against the lower limit of its class. It is never increasing (it falls or stays level). …

Figure 4.8a'Less than' and 'More than' ogive for data given in Table 4.10

Fig. 4.8a — 'Less than' and 'More than' ogive for data given in Table 4.10

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your textbook's own diagram.

Two cumulative-frequency curves (ogives) drawn separately. The 'less than' ogive plots cumulative frequency against the upper class limit — points (20,6),(40,11),(60,44),(80,58),(100,64) — giving a rising, never-decreasing curve. The 'more than' ogive plots cumulative frequency against the lower class limit — (0,64),(20,58),(40,53),(60,20),(80,6) — giving a falling curve. Reading eit …

Figure 4.8b'Less than' and 'More than' ogive for data given in Table 4.10

Fig. 4.8b — 'Less than' and 'More than' ogive for data given in Table 4.10

Drawn by us to help you understand the concept clearly, and verified to make sure it's accurate. For exams, practice from your textbook's own diagram.

Both ogives drawn on one set of axes: the rising 'less than' curve and the falling 'more than' curve for the same marks data. Where the two curves cross, an equal number of students lie below and above that value, so a dotted line dropped from the intersection to the x-axis reads off the Median ( $\approx 55$ marks). Plotting both together …

Table 4.10Frequency distribution of marks obtained in mathematics (parts a/b/c)

Table 4.10(a) — frequency distribution

Marks	Number of students
0–20	6
20–40	5
40–60	33
60–80	14
80–100	6
Total	64

Table 4.10(b) — 'Less than' cumulative frequency distribution

Marks	'Less than' cumulative frequency
Less than 20	6
Less than 40	11
Less than 60	44
Less than 80	58
Less than 100	64

Table 4.10(c) — 'More than' cumulative frequency distribution

| Marks | 'More than' cumulative frequency |

|---|---| …

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