Q. 4	Describe method for Cumulative Frequency Polygon or Ogive by giving examples.		

### Cumulative Frequency Polygon (Ogive) – Method and Examples

A **Cumulative Frequency Polygon**, also known as an **Ogive**, is a graphical representation of the cumulative frequency distribution of a dataset. It is useful for understanding the number of observations below a particular value in a dataset. Here's how to construct an ogive:

### Method to Construct an Ogive

1. **Prepare a Frequency Distribution Table**:
   - Organize the data into a frequency distribution table. The table should include class intervals, frequency (number of observations in each interval), and cumulative frequency (sum of frequencies up to the current interval).

2. **Calculate Cumulative Frequencies**:
   - Start from the first class interval and add up the frequencies progressively to obtain cumulative frequencies. The cumulative frequency of the last class interval should equal the total number of observations.

3. **Plot Points**:
   - On a graph, plot points using:
     - **X-axis**: The upper class boundary (or mid-point) of each class interval.
     - **Y-axis**: The corresponding cumulative frequency.
   - Each point on the graph represents the cumulative frequency corresponding to the upper boundary of a class interval.

4. **Draw the Ogive**:
   - Connect the plotted points using straight lines to form the ogive. This line graph will typically start at the lower boundary of the first class interval with a cumulative frequency of zero.

5. **Interpret the Ogive**:
   - The ogive allows you to estimate median, quartiles, and percentiles. For example, drawing a horizontal line from the cumulative frequency axis to the ogive and dropping a vertical line down to the X-axis gives the value of the corresponding percentile.

### Example

Consider the following dataset of marks scored by students in a test:

| Class Interval | Frequency |
|----------------|-----------|
| 0 - 10         | 5         |
| 10 - 20        | 8         |
| 20 - 30        | 12        |
| 30 - 40        | 20        |
| 40 - 50        | 10        |

**Step 1: Create a Frequency Distribution Table with Cumulative Frequencies**

| Class Interval | Frequency | Cumulative Frequency |
|----------------|-----------|----------------------|
| 0 - 10         | 5         | 5                    |
| 10 - 20        | 8         | 13                   |
| 20 - 30        | 12        | 25                   |
| 30 - 40        | 20        | 45                   |
| 40 - 50        | 10        | 55                   |

**Step 2: Plot the Points**

- For the interval 0-10, plot at (10, 5)
- For the interval 10-20, plot at (20, 13)
- For the interval 20-30, plot at (30, 25)
- For the interval 30-40, plot at (40, 45)
- For the interval 40-50, plot at (50, 55)

**Step 3: Draw the Ogive**

- Connect these points with straight lines to form the ogive.

**Step 4: Interpretation**

- You can estimate values such as the median by finding the cumulative frequency that corresponds to half of the total (27.5 in this case), and then identifying the corresponding value on the X-axis.

### Conclusion
The cumulative frequency polygon (ogive) is a powerful tool for visualizing and analyzing cumulative data. It is particularly helpful for determining median, quartiles, and percentiles.

---

Would you like more details on any part of the process? Here are some related questions:

1. How do you find the median using an ogive?
2. Can you explain the difference between less than and more than ogives?
3. How can an ogive be used to estimate quartiles?
4. What are some practical applications of an ogive in real-world data analysis?
5. How does an ogive differ from a histogram?

**Tip:** When plotting an ogive, ensure that the cumulative frequency always starts at zero at the lower boundary of the first class interval.

Learn how to construct a cumulative frequency polygon (ogive) with examples. Understand the method involving frequency distribution tables, cumulative frequencies, plotting points, and drawing the ogive. Suitable for high school students studying statistics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation