An Ogive is a graph that shows the cumulative frequency distribution of a continuous or discrete variable. It is a graph of the cumulative frequency distribution, and it is a smooth curve that represents the cumulative frequencies of the data set.

To understand Ogive, let’s take an example of a class of students who have taken a test and the marks obtained by each student are as follows:

Marks: 20, 25, 30, 35, 40, 45, 50, 55

Frequency: 2, 3, 4, 5, 6, 7, 8, 9

To find the cumulative frequency of each student, we need to add the frequency of the current class to the frequency of the previous class. The cumulative frequency of each class can be represented in the following table:

Marks: 20, 25, 30, 35, 40, 45, 50, 55

Frequency: 2, 3, 4, 5, 6, 7, 8, 9

Cumulative Frequency: 2, 5, 9, 14, 20, 27, 35, 44

The above table shows the cumulative frequency distribution of the marks obtained by the students. We can plot the cumulative frequency distribution on a graph, which is called an Ogive.

The Ogive is a graphical representation of the cumulative frequency distribution. It is a smooth curve that represents the cumulative frequencies of the data set. It is also known as a cumulative frequency curve or a cumulative frequency graph.

To construct an Ogive, we need to follow the below steps:

Draw the horizontal axis, which represents the variable (in this case, marks).

Draw the vertical axis, which represents the cumulative frequency.

Mark the points on the horizontal axis (marks) corresponding to the lower limits of each class (in this case, 20, 25, 30, 35, 40, 45, 50, 55).

Mark the points on the vertical axis (cumulative frequency) corresponding to the cumulative frequency of each class (in this case, 2, 5, 9, 14, 20, 27, 35, 44).

Join the points with a smooth curve.

The resulting graph is the Ogive.

Now, let’s take another example of a class of students who have taken a test and the marks obtained by each student are as follows:

Marks: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60

Frequency: 5, 10, 15, 20, 25, 30

To find the cumulative frequency of each class, we need to add the frequency of the current class to the frequency of the previous class. The cumulative frequency of each class can be represented in the following table:

Marks: 0-10, 10-20, 20-30, 30-40, 40-50, 50-60

Frequency: 5, 10, 15, 20, 25, 30

Cumulative Frequency: 5, 15, 30, 50, 75, 105

To construct an Ogive, we need to follow the same steps as mentioned above.

The Ogive is a useful tool for understanding the distribution of a variable. It helps us to understand the patterns in the data and to make predictions about the future. It is also useful for comparing the distribution of a variable across different groups or at different points in time.

In conclusion, an Ogive is a graph that represents the cumulative frequency distribution of a continuous or discrete variable. It is a smooth curve that represents the cumulative frequencies of the data set.