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The problem in the image asks to determine the mode (modus) of the data from the frequency distribution table. Here's how we can solve it step by step:

### Step 1: Identify the class with the highest frequency
The mode is found in the class with the highest frequency. From the frequency table:

- Class 50–52: \( f = 5 \)
- Class 53–55: \( f = 10 \)
- Class 56–58: \( f = 14 \)
- Class 59–61: \( f = 26 \) ← **Highest frequency**
- Class 62–64: \( f = 8 \)

Thus, the modal class is 59–61.

### Step 2: Use the formula for the mode
The formula for calculating the mode for grouped data is:
\[
\text{Mode} (Mo) = L + \left(\frac{f_1 - f_0}{2f_1 - f_0 - f_2}\right) \times h
\]
Where:
- \( L \) is the lower boundary of the modal class.
- \( f_1 \) is the frequency of the modal class.
- \( f_0 \) is the frequency of the class before the modal class.
- \( f_2 \) is the frequency of the class after the modal class.
- \( h \) is the class width.

From the table:
- \( L = 59 \) (lower boundary of the modal class)
- \( f_1 = 26 \) (frequency of the modal class)
- \( f_0 = 14 \) (frequency of the class before the modal class)
- \( f_2 = 8 \) (frequency of the class after the modal class)
- \( h = 3 \) (class width, since each class is of length 3: 50–52, 53–55, etc.)

### Step 3: Plug in the values
\[
Mo = 59 + \left(\frac{26 - 14}{2(26) - 14 - 8}\right) \times 3
\]
Simplifying the equation:
\[
Mo = 59 + \left(\frac{12}{52 - 22}\right) \times 3
\]
\[
Mo = 59 + \left(\frac{12}{30}\right) \times 3
\]
\[
Mo = 59 + (0.4 \times 3)
\]
\[
Mo = 59 + 1.2
\]
\[
Mo = 60.2
\]

### Conclusion:
The mode of the data is approximately **60.2**.

Would you like any further details or have any questions?

Here are 5 related questions to deepen your understanding:
1. What is the difference between the mode, mean, and median?
2. How do you calculate the median in grouped data?
3. Why is the mode a good measure for categorical data?
4. How would the mode change if the highest frequency class changed?
5. What are other statistical measures that can be derived from a frequency distribution?

**Tip:** The mode is the value that appears most frequently in a dataset, making it useful in cases where the most common observation is of interest.

Determine the mode (modus) from the frequency distribution table given in the image.

Learn how to find the mode (modus) of a dataset using a frequency distribution table. This example walks through each step, using the formula to calculate the mode for grouped data. Suitable for students in Grades 10-12.

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