CBSE Class 8 Mathematics Data Handling Assignment Set 10

Question. The following data represent the production of Hundai - Santros Vehicles in Delhi in various months. Represents this data in the form of pictograph.

Answer:
To represent the data in the form of a pictograph, let one vehicle symbol 🚗 represent \( 50 \) vehicles.
The number of symbols required for each month is calculated below:

• Jan: \( \frac{300}{50} = 6 \) symbols (🚗 🚗 🚗 🚗 🚗 🚗)
• Feb: \( \frac{250}{50} = 5 \) symbols (🚗 🚗 🚗 🚗 🚗)
• March: \( \frac{400}{50} = 8 \) symbols (🚗 🚗 🚗 🚗 🚗 🚗 🚗 🚗)
• April: \( \frac{300}{50} = 6 \) symbols (🚗 🚗 🚗 🚗 🚗 🚗)
• May: \( \frac{150}{50} = 3 \) symbols (🚗 🚗 🚗)
• June: \( \frac{350}{50} = 7 \) symbols (🚗 🚗 🚗 🚗 🚗 🚗 🚗)

The resulting pictograph is shown below:

Question. Total no. of Students of a school in various years are given below.

Represent the above data by a pictograph.
Answer:
To represent the given student population data, let one full symbol 👤 represent \( 50 \) students and a half symbol 👤_half represent \( 25 \) students.
The number of symbols required for each year is calculated as follows:

• 2010: \( \frac{700}{50} = 14 \) symbols
• 2009: \( \frac{650}{50} = 13 \) symbols
• 2008: \( \frac{600}{50} = 12 \) symbols
• 2007: \( \frac{575}{50} = 11.5 \) symbols (11 full symbols and 1 half symbol)
• 2006: \( \frac{625}{50} = 12.5 \) symbols (12 full symbols and 1 half symbol)

The resulting pictograph is shown below:

Question. Represent the following data in the form of pictograph.

Answer:
To represent the data using a pictograph, let one full bulb symbol 💡 represent \( 2 \) bulbs, and a half bulb symbol 💡_half represent \( 1 \) bulb.
The calculations for the symbols required for each month are:

• September: \( \frac{10}{2} = 5 \) symbols (💡 💡 💡 💡 💡)
• October: \( \frac{8}{2} = 4 \) symbols (💡 💡 💡 💡)
• Nov.: \( \frac{12}{2} = 6 \) symbols (💡 💡 💡 💡 💡 💡)
• Dec.: \( \frac{15}{2} = 7.5 \) symbols (7 full symbols and 1 half symbol)

The pictograph is shown below:

Question. Construct a histogram for the following data

Answer:
To construct a histogram for the given frequency distribution, follow these steps:
1. Define the Axes: Draw two perpendicular lines on graph paper. Label the horizontal axis (X-axis) as "Marks obtained" and the vertical axis (Y-axis) as "No. of Students".
2. Determine Scales:
- Along X-axis: Set \( 1\text{ cm} = 10\text{ marks} \). Since the intervals begin at \( 0 \), start the plotting directly from the origin.
- Along Y-axis: Set \( 1\text{ cm} = 1\text{ student} \) (or \( 1\text{ cm} = 2\text{ students} \) based on your graph grid size).
3. Plot the Rectangles: Construct adjacent bars of the following heights:
- For class interval \( 0 - 10 \), draw a bar of height \( 4\text{ units} \).
- For class interval \( 10 - 20 \), draw a bar of height \( 6\text{ units} \).
- For class interval \( 20 - 30 \), draw a bar of height \( 7\text{ units} \).
- For class interval \( 30 - 40 \), draw a bar of height \( 10\text{ units} \).
- For class interval \( 40 - 50 \), draw a bar of height \( 8\text{ units} \).
- For class interval \( 50 - 60 \), draw a bar of height \( 6\text{ units} \).
- For class interval \( 60 - 70 \), draw a bar of height \( 4\text{ units} \).
Ensure there are no gaps between the rectangular bars, as the data represents continuous classes.

Question. Draw a histogram to represent the following data.

Answer:
To draw a histogram for the given frequency distribution, follow these steps:
1. Define the Axes: Draw two perpendicular axes on a graph. Label the horizontal axis (X-axis) as "Height (in cm)" and the vertical axis (Y-axis) as "No. of Students".
2. Draw a Kink (or Broken Line): Since the height values begin at \( 140 \) instead of \( 0 \), draw a kink or zigzag mark along the X-axis between the origin \( 0 \) and the first interval starting point \( 140 \) to indicate a scale break.
3. Determine Scales:
- Along X-axis: Set \( 1\text{ cm} = 5\text{ cm} \) of height.
- Along Y-axis: Set \( 1\text{ cm} = 2\text{ students} \) (or \( 1\text{ cm} = 1\text{ student} \)).
4. Plot the Rectangles: Construct adjacent bars of the following heights:
- For class interval \( 140 - 145 \), draw a bar of height \( 5\text{ units} \).
- For class interval \( 145 - 150 \), draw a bar of height \( 9\text{ units} \).
- For class interval \( 150 - 155 \), draw a bar of height \( 15\text{ units} \).
- For class interval \( 155 - 160 \), draw a bar of height \( 10\text{ units} \).
- For class interval \( 160 - 165 \), draw a bar of height \( 8\text{ units} \).
- For class interval \( 165 - 170 \), draw a bar of height \( 7\text{ units} \).