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.