Consider the following statements :
The appropriate number of classes while constructing a frequency distribution should be chosen such that
1. the class-frequency that increases to a peak and then declines.
2. the class-frequency should cluster around the class mid point.
Which of the statements given is/are correct?

Options

A. 1 only
B. 2 only
C. Both 1 and 2
D. Neither 1 nor 2

Explanation

To solve the question, we need to analyze the two statements regarding the construction of a frequency distribution and determine their correctness.

### Step-by-Step Solution:

1. **Understanding the First Statement**:
- The first statement claims that "the class frequency that increases to a peak and then declines" is appropriate when constructing a frequency distribution.
- In a well-constructed frequency distribution, we typically expect the frequencies to show a certain pattern, but they do not necessarily need to form a peak and then decline. Frequencies can vary based on the data set, and a peak followed by a decline is not a requirement for a good frequency distribution.

**Conclusion**: The first statement is **false**.

**Hint**: Consider how frequency distributions can vary based on the nature of the data. Not all distributions will have a peak.

2. **Understanding the Second Statement**:
- The second statement asserts that "the class frequency should cluster around the class midpoint."
- This is a valid point. When constructing a frequency distribution, it is desirable for the frequencies to cluster around the midpoints of the classes. This helps in accurately representing the data and understanding its distribution.

**Conclusion**: The second statement is **true**.

**Hint**: Think about how midpoints are calculated and their significance in representing the data accurately.

3. **Final Conclusion**:
- Based on the analysis, we find that only the second statement is correct while the first statement is incorrect. Therefore, the correct answer is that **only the second statement is correct**.

### Final Answer:
Only the second statement is correct.