Consider the following statements in respect of a histogram:
1. The total area of the rectangles in a histogram is equal to the total area bounded by the corresponding frequnecy polygon and the x-axis.
2. When class intervals are unequal in a frequency distribution, the area of the rectangle is proportional to the frequency.
Which of the above statements 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 regarding the statements about histograms, we will analyze each statement one by one.

### Step 1: Analyze Statement 1
**Statement 1:** The total area of the rectangles in a histogram is equal to the total area bounded by the corresponding frequency polygon and the x-axis.

**Explanation:**
- A histogram is a graphical representation of the frequency distribution of continuous data. Each rectangle in a histogram represents the frequency of data within a certain interval (class).
- The area of each rectangle is proportional to the frequency of the corresponding class interval.
- When we connect the midpoints of the tops of these rectangles, we form a frequency polygon. The area under this frequency polygon represents the total frequency.
- Therefore, the total area of the rectangles in a histogram indeed equals the total area bounded by the frequency polygon and the x-axis.

**Conclusion for Statement 1:** This statement is **correct**.

### Step 2: Analyze Statement 2
**Statement 2:** When class intervals are unequal in a frequency distribution, the area of the rectangle is proportional to the frequency.

**Explanation:**
- In a histogram with unequal class intervals, the width of each rectangle varies.
- The area of each rectangle is calculated as the product of the frequency and the width of the class interval.
- Thus, while the area of each rectangle is proportional to the frequency, it is also influenced by the width of the class interval.
- Therefore, if the class intervals are unequal, the area of the rectangle is not solely proportional to the frequency; it is proportional to both the frequency and the width of the class interval.

**Conclusion for Statement 2:** This statement is **incorrect**.

### Final Conclusion:
- Statement 1 is correct.
- Statement 2 is incorrect.

Thus, the answer to the question is that only **Statement 1** is correct.

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