Ogive in Statistics:

Ogive may be expressed using a single line. It is a cumulative line graph . The relative slopes from point to point will indicate greater or lesser increases.

For example At a time we are interested in knowing how many workers of a factory earn less than Rs. 400 per month or how many workers earn more than Rs. 2,000 per month, percentage of students who have failed in board exam, cricket score between two teams at a particular score with particular time interval  etc. To answer these questions it is necessary to add the frequencies. When frequencies are added they are called cumulative frequencies. Then a table of cumulative frequencies is drawn, which when plotted on a graph paper is called the cumulative frequency curve or more popularly known as 'Ogive'.

The cumulative frequency, also known as an Ogive, is another way to analyze the frequency distribution table. Unlike a frequency distribution which tells you how many data points are with in each class, a cumulative frequency tells you how many are less than or within each of the class limits.

There are two methods of constructing ogives:

Less than Method: In the less than method we start with upper limits of class and go on adding the frequencies. When these frequencies are plotted we get a rising curve.

More than Method : Here, we start with lower limit and go on subtracting the frequencies of each class. When these frequencies are plotted we get a decreasing curve

For example the following table show the marks obtained by the students in mathemtics test.
Nos A B C D E F G H
  Class Interval Mid-point Frequency f/n % Cum Fre Cum %
1 10 to 20 15 5 0.16 16% 0 0%
2 20 to 30 25 10 0.33 33% 5 16%
3 30 to 40 35 11 0.36 36% 15 33%
4 40 to 50 45 4 0.13 13% 26 36%
        total = 30     30 13%

An ogive, however, is not the ideal graphic for showing comparisons between categories because it simply combines the values in

 each category and thus indicates an accumulation, a growing or lessening total.If you  want to keep track of a total and your individual values are periodically combined,  it is the apt method to displace.It is useful for analyses that require quick results about the proportion of data that lies below a certain level.