FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 4.11OGIVE
Ogive of cumulative frequency polygon: If the cumulative frequencies are plotted against the class-
boundaries and successive points are joined by straight lines, we get what is known as Ogive (or cumulative
frequency polygon). There are two types of Ogive.
(a) Less than type – Cumulative Frequency from below are plotted against the upper class-boundaries.
(b) Greater than type – Cumulative frequencies from above are plotted corresponding lower
boundaries.
The former is known as less than type, because the ordinate of any point on the curve (obtained) indicates
the frequency of all values less than or equal to the corresponding value of the variable reprpresented by
the abscissa of the point.
Similarly, the latter one is known as the greater than type.
Frequency Distribution of marks obtained by 170 students.
Cumulative Frequency
Class-intervals Class Frequency from below from above
(less than (greater than
30.5, 40.5 etc 20.5, 30.5 etc)
21-30 20.5-30.5 15 15 170
31-40 30.5-40.5 25 40 155
41-50 40.5-50.5 40 80 130
51-60 50.5-60.5 60 140 90
61-70 60.5-70.5 20 160 30
71-80 70.5-80.5 10 170 10
Total 170 – –
Note. From the above figure, it is noted that the ogives cut at a point whose ordinate is 85, i.e. half the
total frequency corresponding and the abscissa is 51.33 which is the median of the above frequency
distribution (see the sum on median in the chapter of Average). Even if one ogive is drawn, the median