Statistics | Lecture -4 | Class 10 | Math Term -1 | CBSE NCERT | Free Education

Statistics | Lecture -4 | Class 10 | Math Term -1 | CBSE NCERT | Free Education

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Statistics : CBSE Class 10 Math. Let's watch this amazing topic - Triangles for your effective Board Exam - Math Preparation with proper explanation by your favorite teacher. In this session, you will find Tips, Tricks, and Strategies in detail to score full marks in class 10 maths. So, Don't Miss It!!

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*Summary of Cumulative Frequency Polygon (Ogive)*

*Introduction*
In this section, we will explore the concept of the Cumulative Frequency Polygon, also known as Ogive. This is a graphical representation of cumulative frequency data derived from a continuous frequency distribution table.

*What is a Cumulative Frequency Polygon?*
A Cumulative Frequency Polygon is simply a graph that represents cumulative frequency data. It is created by plotting cumulative frequencies against the upper class limits of the data.

*Methods to Plot Cumulative Frequency*
There are two methods to plot the cumulative frequency data:
1. *Less Than Method*
2. *More Than Method*

*Less Than Method*
- In this method, the upper class limits are used as the x-coordinates, and the cumulative frequencies are used as the y-coordinates.
- The cumulative frequency is calculated by adding the frequencies of all classes up to the current class.

*Example of Less Than Method*
1. Create a table with columns for Class, Frequency, and Cumulative Frequency.
2. Calculate the cumulative frequency for each class.
3. Plot the points on a graph using the upper class limits for the x-axis and cumulative frequencies for the y-axis.
4. Connect the points to form the cumulative frequency polygon.

*More Than Method*
- In this method, the lower class limits are used as the x-coordinates, and the cumulative frequencies are calculated in reverse order.
- The cumulative frequency is calculated by subtracting the frequencies from the total frequency.

*Example of More Than Method*
1. Create a table similar to the Less Than Method but calculate cumulative frequencies from the bottom up.
2. Use the lower class limits for the x-coordinates and the cumulative frequencies for the y-coordinates.
3. Plot the points and connect them to form the cumulative frequency polygon.

*Finding the Median Using Ogive*
The median can be easily found using the Ogive:
1. Calculate \( \frac{\Sigma f}{2} \) (where \( \Sigma f \) is the total frequency).
2. Draw a perpendicular line from this point on the Ogive to the x-axis.
3. The point where this line intersects the x-axis gives the median value.
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