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Let's break down the problem and find the class boundaries, midpoint, and width for the given class interval:

### Given:
Class interval: \( 8.24 - 12.36 \)

#### 1. **Class Boundaries**:
Class boundaries are the lower and upper limits of the class, adjusted to ensure that there are no gaps between successive classes.

- The **lower boundary** is found by subtracting 0.5 units from the lower limit of the class.
- The **upper boundary** is found by adding 0.5 units to the upper limit of the class.

For the class \( 8.24 - 12.36 \):
- Lower boundary = \( 8.24 - 0.5 = 7.74 \)
- Upper boundary = \( 12.36 + 0.5 = 12.86 \)

So, the class boundaries are **7.74** and **12.86**.

#### 2. **Midpoint**:
The midpoint is the average of the upper and lower limits of the class.

\[
\text{Midpoint} = \frac{8.24 + 12.36}{2} = \frac{20.6}{2} = 10.3
\]

So, the midpoint is **10.3**.

#### 3. **Class Width**:
The class width is the difference between the upper and lower limits of the class.

\[
\text{Class Width} = 12.36 - 8.24 = 4.12
\]

So, the class width is **4.12**.

### Final Answer:
- **Class Boundaries**: 7.74 and 12.86
- **Midpoint**: 10.3
- **Class Width**: 4.12

Would you like any further details or clarifications on these concepts?

Here are some related questions you might consider:
1. How would you calculate class boundaries if the class interval were a whole number?
2. What is the significance of class boundaries in a frequency distribution?
3. How would overlapping class intervals affect the calculation of class boundaries?
4. Can class width vary within a data set, and how would that impact the analysis?
5. What is the relationship between the midpoint and the median in a grouped frequency distribution?

**Tip**: Always check for any gaps or overlaps between class intervals, especially when preparing a frequency distribution table. This ensures accurate representation of the data.

Find class boundaries, midpoint, and width for the class 8.24 - 12.36.

Learn how to calculate class boundaries, midpoint, and class width for the interval 8.24-12.36. This statistical concept is crucial for constructing frequency distributions and summarizing data effectively. Suitable for students in Grades 8-10.

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