As mentioned, for relative-frequency polygons, we label the horizontal axis with class marks in limit grouping and class midpoints in cutpoint grouping. How do you think the horizontal axis is labeled in single-value grouping?

Ogives. Cumulative information can be portrayed using a graph called an ogive (o¯

j¯ıv). To construct an ogive, we first make a table that displays cumulative frequencies and cumulative relative frequencies.

A cumulative frequency is obtained by summing the frequencies of all classes representing values less than a specified lower class limit

(or cutpoint). A cumulative relative frequency is found by dividing the corresponding cumulative frequency by the total number of observations.

For instance, consider the grouped days-to-maturity data given in Table 2.10

(b) on page 79. From that table, we see that the cumulative frequency of investments with a maturity period of less than 50 days is 4 (3 + 1) and, therefore, the cumulative relative frequency is 0.1 (4/40). Table 2.14 shows all cumulative information for the days-to-maturity data.

TABLE 2.14 Cumulative information for days-to-maturity data Cumulative Cumulative Less than frequency relative frequency 30 0 0.000 40 3 0.075 50 4 0.100 60 12 0.300 70 22 0.550 80 29 0.725 90 36 0.900 100 40 1.000 Using Table 2.14, we can now construct an ogive for the days-tomaturity data. In an ogive, a point is plotted above each lower class limit (or cutpoint) at a height equal to the cumulative relative frequency. Then the points are connected with lines. An ogive for the days-to-maturity data is as follows.
Days to maturity Short-Term Investments Cumulative relative frequency 0.0 10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 0 20 30 40 50 60 70 80 90 100