**) Select the correct graph depicting the correct ogive**

To select the correct graph depicting the correct ogive, we need to understand what an ogive is. 

### What is an Ogive?
An **ogive** is a graph that represents the cumulative frequency or cumulative relative frequency of data. It is a type of line graph that shows how many data points fall below or within a particular range. The key points of an ogive include:
- The x-axis represents the upper class boundaries (or midpoints).
- The y-axis represents the cumulative frequency.
- The graph is usually a rising curve that moves upwards from left to right.

### Steps to Select the Correct Ogive:
1. **Cumulative Frequency Calculation:**
   - Calculate the cumulative frequency for each age group:
     - 0-12 years: 6
     - 13-17 years: \(6 + 5 = 11\)
     - 18-24 years: \(11 + 10 = 21\)
     - 25-30 years: \(21 + 3 = 24\)
   - The final cumulative frequency should be equal to the total number of data points, which is 24.

2. **Analyze the Graphs:**
   - **Graph A:** If this graph shows a smooth upward trend starting from 0 and going up to the total cumulative frequency (24), it could be an ogive.
   - **Graph B:** This graph might show a bell-shaped curve, which is more indicative of a normal distribution, not an ogive.
   - **Graph C:** This graph shows a bar distribution, which is not an ogive.

### Correct Graph Selection:
Given the characteristics of an ogive, **Graph A** is the correct graph. It typically starts at the lowest cumulative frequency (0 or near the minimum value of the first class) and increases, ending at the total cumulative frequency (24 in this case).

**Answer:** The correct graph depicting the ogive is **Graph A**.

Would you like to delve into any of the concepts further, or have additional questions?

Here are 5 related questions to consider:
1. How would you create an ogive using different class intervals?
2. What are the differences between an ogive and a histogram?
3. How can an ogive be used to find the median or quartiles?
4. What are the steps to plot an ogive manually?
5. How does the shape of an ogive change with different data distributions?

**Tip:** When working with cumulative frequency distributions, ensure each class's cumulative frequency builds correctly on the previous ones to create an accurate ogive.

Learn how to select the correct ogive graph by understanding cumulative frequency and graph interpretation. This problem involves analyzing different graphs to identify the correct representation of cumulative data points. Suitable for Grades 9-12.

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