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To calculate the mode of the given frequency distribution using the grouping method, I'll guide you through the process step by step. Here's the frequency distribution provided:

| Class Interval | Frequency (f) |
|----------------|---------------|
| 0 - 5          | 1             |
| 5 - 10         | 2             |
| 10 - 15        | 10            |
| 15 - 20        | 6             |
| 20 - 25        | 9             |
| 25 - 30        | 2             |

### Steps to Calculate the Mode Using the Grouping Method:

1. **Identify the Modal Class**: The modal class is the class interval with the highest frequency. Here, the class interval with the highest frequency is 10-15, with a frequency of 10.

2. **Create a Grouping Table**:
   - We create a table to analyze the frequency distribution further, breaking it into different columns to help with mode calculation.

| Column 1 | Column 2 (1st Differences) | Column 3 (2nd Differences) |
|----------|----------------------------|----------------------------|
| 1        |                            |                            |
| 2        | 1                          |                            |
| 10       | 8                          | 7                          |
| 6        | -4                         | -12                        |
| 9        | 3                          | 7                          |
| 2        | -7                         |                            |

   - **Column 1** contains the frequencies.
   - **Column 2** represents the first differences of the frequencies.
   - **Column 3** represents the second differences.

3. **Determine the Mode**:
   - The mode is located within the modal class. To calculate it precisely, we use the formula:
   
   \[
   \text{Mode} = L + \left(\frac{f_1 - f_0}{2f_1 - f_0 - f_2}\right) \times h
   \]

   Where:
   - \( L \) = lower boundary of the modal class = 10 (since the modal class is 10-15)
   - \( f_1 \) = frequency of the modal class = 10
   - \( f_0 \) = frequency of the class preceding the modal class = 2 (class 5-10)
   - \( f_2 \) = frequency of the class succeeding the modal class = 6 (class 15-20)
   - \( h \) = class width = 5

   Plugging in the values:

   \[
   \text{Mode} = 10 + \left(\frac{10 - 2}{2(10) - 2 - 6}\right) \times 5
   \]
   \[
   \text{Mode} = 10 + \left(\frac{8}{20 - 8}\right) \times 5
   \]
   \[
   \text{Mode} = 10 + \left(\frac{8}{12}\right) \times 5
   \]
   \[
   \text{Mode} = 10 + \left(\frac{2}{3}\right) \times 5
   \]
   \[
   \text{Mode} = 10 + 3.33 \approx 13.33
   \]

Thus, the mode of the distribution is approximately **13.33**.

Would you like further details on any of the steps, or do you have any questions?

Here are some related questions to explore further:
1. How is the class interval determined in a frequency distribution?
2. What are the different methods to calculate the mode?
3. Why is the mode important in statistics, and in what scenarios is it most useful?
4. Can a dataset have more than one mode, and how is it calculated in such cases?
5. How does the grouping method differ from other methods for finding the mode?

**Tip:** When calculating the mode, it's crucial to accurately identify the modal class, as it directly influences the result.

Learn how to calculate the mode from a frequency distribution using the grouping method with a step-by-step guide. This problem covers statistical concepts such as frequency distribution, modal class identification, and mode calculation formula. Suitable for advanced high school students and those interested in statistics.

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