Data Handling and Presentation — Class 6 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 6 Mathematics chapter "Data Handling and Presentation" — 8 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 6 Mathematics chapter "Data Handling and Presentation" — 8 important questions with detailed answers for C…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
NCERT Solutions for Class 6 Mathematics — Data Handling and Presentation. Step-by-step answers to all 8 textbook questions from this chapter, written for CBSE board preparation and free to use.
Data Handling and Presentation — All 8 Questions Solved
Q1. What is the difference between a pictograph and a bar graph?
Step 1: Define a pictograph
A pictograph uses small pictures or symbols to represent data
Each symbol represents a certain number of items
Example: One smiley face = 5 students
Step 2: Define a bar graph
A bar graph uses rectangular bars of different heights to represent data
The height or length of each bar shows the quantity
Step 3: List key differences
Pictograph: uses symbols/pictures, simple for young children to understand
Bar graph: uses bars, more precise for comparing quantities, easier to read exact values
Both show data in an easy-to-understand visual format
Answer: A pictograph uses pictures or symbols to represent data (each symbol = fixed amount). A bar graph uses rectangular bars of varying heights. Bar graphs are more precise; pictographs are simpler to understand.
Q2. If a pictograph shows 4 hearts where each heart = 10 students, how many students does it represent?
Step 1: Identify the given information
Number of hearts shown = 4
Value of each heart = 10 students
Step 2: Calculate total students
Total students = Number of hearts × Value per heart
Total students = 4 × 10
Total students = 40
Answer: 4 hearts represent 40 students
Q3. Draw a tally mark table for the following data: 3 apples, 5 bananas, 4 oranges, 2 grapes. Use tally marks.
Step 1: Create a table with three columns: Item, Tally Marks, Count
Step 2: Represent data using tally marks
Tally marks are drawn as | | | | | (five marks, with the fifth crossing through)
For 1-4 items: use individual marks
For 5+ items: use the crossed group
Step 3: Show tally marks for each fruit
Apples (3): | | |
Bananas (5): | | | | | (shown as a group of 5)
Oranges (4): | | | |
Grapes (2): | |
Step 4: Write the complete table
Item | Tally Marks | Count
Apples | | | | | 3
Bananas | | | | | | 5
Oranges | | | | | 4
Grapes | | | 2
Answer: Table above shows tally marks. Tally marks provide a quick way to count and record data.
Q4. What information can you get from a bar graph? Name three things.
A bar graph displays data visually and allows us to extract multiple types of information.
Step 1: First piece of information
You can find the exact value or frequency of each category by reading the height of the bar
Example: The bar for Monday shows 20 visitors
Step 2: Second piece of information
You can compare quantities between different categories
Example: Which day had more visitors? Compare bar heights.
Step 3: Third piece of information
You can identify the maximum and minimum values
Example: Which category has the highest bar (maximum)? Which has the lowest (minimum)?
Step 4: Additional information you can get
You can calculate totals, find trends, and spot patterns
Answer: From a bar graph, you can: (1) read exact values for each category, (2) compare quantities between categories, and (3) identify maximum and minimum values
Q5. A class collected data on favorite colors: 8 students like red, 6 like blue, 5 like green, and 7 like yellow. What is the total number of students surveyed?
Step 1: List the data
Red: 8 students
Blue: 6 students
Green: 5 students
Yellow: 7 students
Step 2: Add all the frequencies
Total = 8 + 6 + 5 + 7
Total = 14 + 5 + 7
Total = 19 + 7
Total = 26
Answer: 26 students were surveyed
Q6. In a bar graph, what does the x-axis usually represent, and what does the y-axis represent?
Step 1: Identify the x-axis
The x-axis is the horizontal line at the bottom of the graph
The x-axis typically shows categories or different groups being compared
Example: Days of the week, types of fruits, names of students
Step 2: Identify the y-axis
The y-axis is the vertical line on the left side of the graph
The y-axis typically shows the scale or quantity being measured
Example: Number of students, number of items sold, temperature
Step 3: How they work together
Each bar has a category on the x-axis and a height based on the y-axis scale
Step 4: Example
In a graph showing fruit sales:
X-axis: Apple, Banana, Orange (categories)
Y-axis: 0, 10, 20, 30, 40 (number of fruits sold)
Answer: The x-axis shows categories or types (horizontal). The y-axis shows quantity or scale (vertical).
Q7. Make a simple frequency table for the following scores: 5, 8, 5, 9, 8, 5, 7, 9, 8, 5
A frequency table shows how many times each value appears in the data.
Step 1: List all unique scores
Scores: 5, 7, 8, 9
Step 2: Count how many times each score appears
Score 5: appears 4 times (5, 5, 5, 5)
Score 7: appears 1 time (7)
Score 8: appears 3 times (8, 8, 8)
Score 9: appears 2 times (9, 9)
Step 3: Create the frequency table
Score | Frequency
5 | 4
7 | 1
8 | 3
9 | 2
Step 4: Verify the total
Total frequency = 4 + 1 + 3 + 2 = 10
This matches the total number of scores given ✓
Answer: Frequency table shown above
Q8. Why is presenting data in a graph better than showing raw numbers? Give two reasons.
Step 1: First reason - Easy comparison
With a graph, you can visually compare values at a glance
Example: In a bar graph, you can immediately see which bar is tallest (highest value)
Comparing raw numbers requires reading and calculating
Step 2: Second reason - Pattern recognition
Graphs help us spot trends and patterns quickly
Example: In a line graph, you can see if sales are increasing or decreasing
With raw numbers, you would need to study each number carefully
Step 3: Additional advantages
Graphs are more interesting and engaging
Graphs make data easier to remember
Graphs can tell a story effectively
Answer: (1) Graphs allow quick visual comparison of values (you can see differences at a glance). (2) Graphs help identify patterns and trends easily (you can spot increases, decreases, or relationships quickly). Graphs are also more interesting and memorable than lists of numbers.
Data Handling and Presentation — Practice MCQs with Answers
Attempt these 20 multiple-choice questions after working through the solutions above. Each carries the correct option and the reasoning behind it, so a wrong answer tells you which idea to revisit.
MCQ 1. What do we call a collection of facts, such as numbers, words, measurements, observations, or even just descriptions of things?
- A. Information
- B. Data
- C. Report
- D. Graph
Answer: B. Data — Data is the raw material, a collection of facts and figures, from which information can be derived after processing.
MCQ 2. Which of the following correctly represents the number 12 using tally marks?
- A. |||| |||| ||
- B. |||| |||| |||
- C. |||| |||| | | |
- D. |||| |||| ||| |
Answer: A. |||| |||| || — In tally marks, every fifth mark is drawn diagonally across the previous four to form a block of five, making counting easier. So, 12 is represented as two blocks of five and two single marks.
MCQ 3. A pictograph shows the number of cars sold in a week. If each symbol '🚗' represents 5 cars, and on Monday, there are 3 '🚗' symbols, how many cars were sold on Monday?
- A. 3 cars
- B. 5 cars
- C. 15 cars
- D. 8 cars
Answer: C. 15 cars — Since each car symbol (🚗) represents 5 cars, 3 such symbols represent 3 multiplied by 5, which equals 15 cars.
MCQ 4. In a pictograph, if one umbrella symbol (☂️) represents 10 umbrellas, what is this representation called?
- A. Key
- B. Bar
- C. Axis
- D. Title
Answer: A. Key — The 'key' or 'scale' in a pictograph tells us what each symbol represents in terms of numerical value.
MCQ 5. A bar graph shows the number of students who like different fruits. If the bars for Apple, Banana, Orange, and Mango are 10 units, 15 units, 8 units, and 12 units high respectively, which fruit is liked by the maximum number of students?
- A. Apple
- B. Banana
- C. Orange
- D. Mango
Answer: B. Banana — The height of the bar represents the number of students. The bar for Banana is 15 units high, which is the tallest, indicating it is liked by the maximum number of students.
MCQ 6. Reena collected data about the favorite colors of her 30 classmates by asking each of them directly. What type of data did Reena collect, and what is the data in its original form called?
- A. Processed data, Organized data
- B. Raw data, Unorganized data
- C. Primary data, Raw data
- D. Secondary data, Grouped data
Answer: C. Primary data, Raw data — When data is collected directly from the source, it is called primary data. Before it is organized or processed, it is in its original, unarranged form, known as raw data.
MCQ 7. The marks obtained by 5 students in a Math test are 25, 30, 28, 35, and 22 out of 50. What is the total score of these 5 students?
- A. 130
- B. 140
- C. 150
- D. 120
Answer: B. 140 — To find the total score, we add all the individual scores: 25 + 30 + 28 + 35 + 22 = 140.
MCQ 8. What do we call the data that has been arranged in a systematic way, for example, in a table?
- A. Random data
- B. Raw data
- C. Organized data
- D. Unprocessed data
Answer: C. Organized data — When data is arranged in a systematic manner, such as in a table or a list, it becomes organized data, which is easier to understand and interpret.
MCQ 9. A bar graph shows the number of trees planted in two different parks. Park A has a bar height of 40 units, and Park B has a bar height of 25 units. If each unit represents 10 trees, how many more trees were planted in Park A than in Park B?
- A. 15 trees
- B. 150 trees
- C. 250 trees
- D. 400 trees
Answer: B. 150 trees — Trees in Park A = 40 units × 10 trees/unit = 400 trees. Trees in Park B = 25 units × 10 trees/unit = 250 trees. The difference is 400 - 250 = 150 trees.
MCQ 10. What is the main purpose of making a frequency distribution table from raw data?
- A. To make the data colorful
- B. To collect more data
- C. To organize data and easily see how often each value occurs
- D. To delete unnecessary data
Answer: C. To organize data and easily see how often each value occurs — A frequency distribution table helps to arrange raw data systematically by listing each item and the number of times it appears (its frequency), making it easier to analyze.
MCQ 11. In a bar graph, what does the 'scale' on the vertical axis help us understand?
- A. The width of the bars
- B. The title of the graph
- C. The quantity that each unit length on the axis represents
- D. The colors of the bars
Answer: C. The quantity that each unit length on the axis represents — The scale on the axis defines the value represented by each unit length, which is crucial for accurately interpreting the magnitudes shown by the bars.
MCQ 12. A pictograph shows the number of students who own pets. If one dog symbol (🐕) represents 4 students, and there are 3 full dog symbols and half a dog symbol (half of 🐕) for students owning dogs, how many students own dogs?
- A. 12 students
- B. 14 students
- C. 10 students
- D. 16 students
Answer: B. 14 students — 3 full dog symbols represent 3 × 4 = 12 students. Half a dog symbol represents half of 4, which is 2 students. So, the total number of students owning dogs is 12 + 2 = 14.
MCQ 13. You want to make a bar graph showing the number of books read by students in a month. The numbers are 5, 10, 15, 20, 25. Which of the following would be the most appropriate scale for the vertical axis?
- A. 1 unit = 1 book
- B. 1 unit = 2 books
- C. 1 unit = 5 books
- D. 1 unit = 10 books
Answer: C. 1 unit = 5 books — Choosing a scale where 1 unit represents 5 books allows all the given data points (multiples of 5) to be represented accurately and clearly on the graph without making it too long or too condensed.
MCQ 14. In a class, students were asked about their favorite sport. The tally marks collected were: Cricket: |||| |||| Hockey: |||| || Football: |||| ||| Basketball: ||||. How many students chose Football as their favorite sport?
- A. 7
- B. 5
- C. 6
- D. 4
Answer: A. 7 — The tally marks for Football are |||| |||. This represents one group of five marks and two individual marks, totaling 5 + 2 = 7 students.
MCQ 15. A bar graph shows the favorite colors of 40 students. If the bar for 'Blue' is twice as tall as the bar for 'Green', and 5 students like 'Green', how many students like 'Blue'?
- A. 5 students
- B. 10 students
- C. 15 students
- D. 20 students
Answer: B. 10 students — If 5 students like 'Green' and the bar for 'Blue' is twice as tall, it means twice the number of students like 'Blue'. So, 2 × 5 = 10 students like 'Blue'.
MCQ 16. What is a collection of numbers gathered to give some information called?
- A. Graph
- B. Data
- C. Tally
- D. Pictograph
Answer: B. Data — Data is a collection of information, often in the form of numbers, gathered to provide insights.
MCQ 17. How is the number 7 represented using tally marks?
- A. |||||
- B. |||| ||
- C. |||| |
- D. |||| |||
Answer: B. |||| || — For every group of five, four vertical lines are crossed by a fifth diagonal line. So, 7 is represented as one group of five and two additional lines.
MCQ 18. In a survey, 15 students chose mango, 10 chose apple, and 8 chose banana. What would be the frequency for 'mango' in a frequency distribution table?
- A. 10
- B. 8
- C. 15
- D. 33
Answer: C. 15 — The frequency of an observation is the number of times it occurs. Here, 15 students chose mango, so its frequency is 15.
MCQ 19. A pictograph shows fruits where each apple symbol represents 5 apples. If there are 3 apple symbols, how many actual apples are there?
- A. 3
- B. 5
- C. 15
- D. 8
Answer: C. 15 — Since each symbol represents 5 apples, 3 symbols represent 3 multiplied by 5, which equals 15 apples.
MCQ 20. A bar graph shows the number of books read by students in a week. If the bar for 'Monday' reaches '20' on the y-axis, how many books were read on Monday?
- A. 1
- B. 20
- C. 10
- D. 5
Answer: B. 20 — In a bar graph, the height of the bar directly represents the quantity it stands for. So, a bar reaching 20 means 20 books were read.
How to Use These Solutions
Attempt each question yourself first and only then compare with the worked answer. Marks in the CBSE board exam are awarded for the METHOD as much as the final result, so reproduce the steps rather than memorising the last line. Where a solution states a law, a formula or a definition, learn that wording — examiners look for it.
Related practice for this chapter: chapter MCQs, previous-year questions, revision notes and sample papers.