Cumulative Frequency Curve: Graph & Examples

Table of Content

1. Cumulative Frequency Curve 
2. Cumulative Frequency Distribution
3. Statistics and data
4. Things to Remember
5. Sample Questions

Example of Less than Ogive

• When we represent this in graphs, we would take the upper limit in the x-axis and the cumulative frequency in the y-axis.

Example of More than Ogive

Note that if you make a more than ogive from this, the lower limit of the classes has to be taken in the x-axis and the cumulative frequencies are taken in the y-axis.

Note that you can make ogive from table 2 also (frequency table). There you would have to take the CGPA value in the x-axis and the frequency (number of students) in the y-axis.

Example of Cumulative Frequency Distribution 

Example: We have discussed above what a frequency table is, through an example. We saw how data was shortened for representation, by counting the number of times CGPA is repeated (frequency) in the first table.

• Now imagine that your school management has decided to give medals to the students who have made achievements.
• According to your school’s parameter, students who got a CGPA between 9- 10 would be given a gold medal.
• Those who got a CGPA between 9-7(Less than 9 but above or equal to 7) would be given a silver medal.
• Those who got a CGPA below 7 would be given a bronze medal.

Now you are sure that this will again shorten the list into three rows: gold medal winners, silver medal winners, and bronze medal winners. From table 2, we can create that table as below:

Table 3:

The table you see above is called the frequency distribution table. Here we have a range of CGPA rather than the number. How did we make this range? When we want to know the number of students who fall between the range 10-8, we added the number of students who got CGPA 10, 9.8, and 9.0 (24+50+12+2) and we got it as 76.

• Similarly, you can find the frequency of other classes of the range. (Note that the range of a frequency table is called class). 
• From table 3, we can easily make a cumulative frequency table.
• In a cumulative frequency table, we have the frequencies (in table 3, number of students) to be added up.
• Since words have limitations to explain statistics, we can continue this example in the next part and see how a table showing less than cumulative frequency and a more than frequency table are shown.

Example of Statistics and Data

Example: Let us go through an example to understand this. Imagine your CBSE board exam results were declared yesterday. You know very well that the final results are declared as CGPA, which can range from 1-10.

• Think that there are 100 students in your class.
• Every teacher would have a curiosity to know the CGPA that everyone had scored.
• For, this, your class teacher asked everyone to Whatsapp her CGPA they scored.
• From the messages you send, if your class teacher made a list, it would be something like this:

Table 1:

This list would be lengthy and would have a hundred names and their respective CGPA. This is ungrouped data of ‘CGPA scored by the students of your class.

• From the list, the principal of your school wants to know how many students have scored 10 as CGPA.
• The principal doesn't know any of the students personally, and for him, the name of the students is something irrelevant.
• So from the above list, your class teacher will start to count how many students have scored each CGPA.
• Think that only the students we see in the list have scored 10 as CGPA (i.e. Arun das and Ajay Varma).
• Then, your class teacher reports to the principle that ‘the number of students in my class who scored 10 as CGPA is 2.’
• In other words, the frequency of students who have scored 10 as CGPA is 2.
• Like this, if your class teacher makes a table showing a number of students who scored different CGPA it would be something like this:

Table 2:

(Note: the frequencies marked here are imaginary, except the first one. But you can count it easily if you are provided with a complete list).

This is a frequency table. So through this example, statistics have proved to summarise data in a useful manner, making it easier to make an analysis. Now, let us move on to the higher level of statistics, with this same example.