In a histogram when we join midpoints of the tops of the rectangles (bars) we get:

Options

A. Bar graph
B. line graph
C. frequency polygon
D. pie graph

Answer

To solve the question, we will analyze what happens when we join the midpoints of the tops of the rectangles (bars) in a histogram.

### Step-by-Step Solution:

1. **Understanding the Histogram**:
- A histogram is a graphical representation of the distribution of numerical data. It consists of bars where the height of each bar represents the frequency of data within a certain interval (class).

2. **Identifying the Midpoints**:
- Each bar in a histogram corresponds to a class interval. To find the midpoint of each class interval, we use the formula:
\[ \text{Midpoint} = \frac{\text{Lower Limit} + \text{Upper Limit}}{2} \]
- For example, if we have a class interval of 0-10, the midpoint would be:
\[ \text{Midpoint} = \frac{0 + 10}{2} = 5 \]

3. **Plotting the Midpoints**:
- Once we have the midpoints for each class interval, we can plot these midpoints on the x-axis against the corresponding frequencies on the y-axis.

4. **Joining the Midpoints**:
- After plotting the midpoints, we connect these points with straight lines. This creates a continuous line graph.

5. **Identifying the Resulting Graph**:
- The graph formed by joining the midpoints of the tops of the rectangles in a histogram is known as a **frequency polygon**. This is a line graph that represents the frequencies of the class intervals.

6. **Conclusion**:
- Therefore, when we join the midpoints of the tops of the rectangles in a histogram, we get a frequency polygon.

### Final Answer:
When we join the midpoints of the tops of the rectangles in a histogram, we get a **frequency polygon**.