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To solve the problem displayed in the image, we need to calculate the standard deviation based on the provided frequency distribution. 

### Step-by-Step Solution:

#### 1. **Understand the Data:**
   - The table presents classes and their corresponding frequencies.

#### 2. **Calculate the Midpoint (x) of Each Class:**
   - For each class interval, the midpoint \( x \) is calculated as:
   \[
   x = \frac{\text{Lower Class Limit} + \text{Upper Class Limit}}{2}
   \]

#### 3. **Multiply the Midpoint by the Frequency (f):**
   - For each class, multiply the midpoint \( x \) by the corresponding frequency \( f \).

#### 4. **Calculate the Mean ( \( \bar{x} \) ):**
   - The mean \( \bar{x} \) can be calculated using:
   \[
   \bar{x} = \frac{\sum{f \times x}}{\sum{f}}
   \]

#### 5. **Calculate the Variance:**
   - Use the formula for the variance \( \sigma^2 \):
   \[
   \sigma^2 = \frac{\sum f(x - \bar{x})^2}{\sum f}
   \]

#### 6. **Calculate the Standard Deviation:**
   - The standard deviation \( \sigma \) is the square root of the variance:
   \[
   \sigma = \sqrt{\sigma^2}
   \]

### Summary:
   - The correct method for grouped frequency data is typically done using the **Grouped Frequency Distribution** method with midpoints.

### Final Step:
   - Select the answer corresponding to the method for calculating the standard deviation using grouped data and midpoints.

Would you like to proceed with the exact calculations for each step, or do you need further explanations on any of the steps?

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### Additional Questions to Explore:
1. How is the midpoint of a class interval calculated?
2. What is the significance of the mean in a frequency distribution?
3. Can you describe the difference between variance and standard deviation?
4. What does a higher standard deviation indicate about the data set?
5. How would you apply this method to a different frequency distribution?

### Tip:
When working with grouped data, always make sure to compute midpoints correctly, as this forms the foundation for calculating the mean and standard deviation.

Learn how to calculate the standard deviation from a grouped frequency distribution using midpoints. This problem covers key statistical concepts, including mean calculation, variance, and standard deviation formula application. Suitable for undergraduate level studies.

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