RD Sharma Solutions for Class 8 Chapter 24 Data Handling - II ... - Free Printable

Problem Description:

The task is to draw a histogram for the given frequency distribution data. The data provided includes class intervals and their corresponding frequencies. A histogram is a graphical representation of data using bars, where the class intervals are represented on the x-axis and the frequencies are represented on the y-axis.

Given Data for Problem 2:

#### Class Intervals and Frequencies:
| Class Interval | Frequency |
|----------------|-----------|
| 10 – 15 | 30 |
| 15 – 20 | 98 |
| 20 – 25 | 80 |
| 25 – 30 | 58 |
| 30 – 35 | 29 |
| 35 – 40 | 50 |

Solution:

#### Step 1: Understand the Data
- Class Intervals: These are the ranges of values (e.g., 10–15, 15–20, etc.).
- Frequencies: These represent how many observations fall within each class interval.
- The task is to represent this data graphically using a histogram.

#### Step 2: Set Up the Axes
- X-axis (Horizontal Axis): This will represent the class intervals.
- Y-axis (Vertical Axis): This will represent the frequencies.
- Choose a suitable scale for both axes:
- For the X-axis, since the class intervals are continuous and evenly spaced, we can mark the midpoints of each interval (e.g., 12.5 for 10–15, 17.5 for 15–20, etc.).
- For the Y-axis, the scale should accommodate the maximum frequency (98 in this case). We can choose a scale where each unit represents a certain number of students (e.g., 1 unit = 10 students).

#### Step 3: Draw the Histogram
- Each class interval will be represented as a rectangle.
- The width of each rectangle corresponds to the width of the class interval.
- The height of each rectangle corresponds to the frequency of that class interval.

#### Step 4: Construct the Histogram
1. Mark the Class Intervals on the X-axis:
- Start from 10 and end at 40, with each class interval clearly marked.
- Use the midpoints of the intervals for labeling if needed (e.g., 12.5, 17.5, etc.).

2. Mark the Frequencies on the Y-axis:
- The Y-axis should start from 0 and go up to at least 100 (since the maximum frequency is 98).
- Choose a scale where each unit represents 10 students.

3. Draw the Rectangles:
- For each class interval, draw a rectangle with:
- Base: The width of the class interval.
- Height: The frequency of that class interval.

#### Step 5: Finalize the Histogram
- Ensure all rectangles are adjacent to each other (no gaps between them, as this is a continuous data set).
- Label the axes appropriately:
- X-axis: "Class Interval"
- Y-axis: "Frequency"

#### Example of the Histogram:
Here is a textual description of how the histogram would look:

- Class Interval 10–15: Rectangle with base from 10 to 15 and height 30.
- Class Interval 15–20: Rectangle with base from 15 to 20 and height 98.
- Class Interval 20–25: Rectangle with base from 20 to 25 and height 80.
- Class Interval 25–30: Rectangle with base from 25 to 30 and height 58.
- Class Interval 30–35: Rectangle with base from 30 to 35 and height 29.
- Class Interval 35–40: Rectangle with base from 35 to 40 and height 50.

Final Answer:

The histogram is constructed by following the steps above. Here is a boxed final answer summarizing the process:

\[
\boxed{\text{Histogram constructed with class intervals on the x-axis and frequencies on the y-axis.}}
\]

For a visual representation, you would need to plot the data using graph paper or a digital tool, ensuring that the rectangles are drawn according to the specified dimensions.