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CBSE Class 6 Mathematics Chapter 4 Data Handling and Presentation Worksheet with Answers

Data Handling and Presentation is a foundational chapter in CBSE Class 6 Mathematics that introduces students to the essential skill of making sense of numbers in everyday life. From reading election results to understanding sports statistics, this chapter builds visual and analytical thinking. This printable worksheet follows the NCERT curriculum exactly and offers varied question types to ensure thorough practice and conceptual clarity.

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Key takeaways

✓Complete practice coverage of pictographs, bar graphs, and frequency tables from NCERT Class 6 Mathematics Chapter 4
✓Graded question structure from basic MCQs to HOTS problems helps build confidence progressively
✓Real-world case study connects data handling concepts to everyday situations like school sports and elections
✓Answer key with step-by-step explanations enables self-assessment and independent learning
✓60-minute worksheet format mirrors CBSE exam patterns and helps develop time management skills
✓Printable PDF format allows repeated practice without internet dependency

Quick Chapter Recap: Data Handling and Presentation

Before attempting the worksheet, let us revisit the core concepts from NCERT Class 6 Mathematics Chapter 4. Data Handling involves collecting, organising, and presenting information in meaningful ways. The chapter introduces three main tools: frequency tables that count occurrences, pictographs that use symbols to represent data visually, and bar graphs that display quantities using rectangular bars of varying heights. Understanding scale is critical—in pictographs, one symbol might represent multiple units, while bar graphs require proper labelling of axes and uniform spacing. Students learn to read these representations to extract information and answer questions, developing skills that extend far beyond mathematics into science projects, social studies reports, and everyday decision-making.

Data: Information in the form of numbers, words, or measurements collected for a purpose
Frequency: The number of times a particular value or item occurs in a dataset
Pictograph: A visual representation using pictures or symbols where each symbol stands for a fixed number of items
Bar graph: A chart using rectangular bars of equal width and varying heights to compare different categories
Scale: The value that one picture or one unit length on a graph represents

Worksheet Instructions and Structure

This Data Handling and Presentation worksheet is designed for CBSE Class 6 students following the latest NCERT Mathematics syllabus. The difficulty level is Medium, suitable for regular practice and revision. Allocate 60 minutes to complete all sections under exam-like conditions. The worksheet is divided into six distinct sections: Section A contains 6 multiple-choice questions testing basic concepts; Section B has 5 fill-in-the-blank items for quick recall; Section C presents 5 matching or true-false statements; Section D includes 5 short-answer questions requiring 2-3 sentences each; Section E features 3 long-answer or HOTS (Higher Order Thinking Skills) questions demanding detailed working; and finally, one case-study question that applies multiple concepts to a real scenario. Write all answers neatly in your notebook or on separate sheets. A complete answer key with explanations follows the question sections, enabling self-assessment and learning from mistakes. Parents can use this worksheet for weekend practice, and teachers can photocopy it for classroom tests. For students who need extra help understanding any solution, CBSETUTOR.ai offers 24×7 AI tutoring with photo-upload problem solving at just ₹999 per month for all subjects and classes 6-12, with a 3-day free trial to get started.

Total time: 60 minutes
Total marks: 50 (indicative for self-assessment)
Materials needed: Ruler, pencil, eraser, and coloured pencils for graphs
Attempt all questions; marks are indicated for each section

Section A: Multiple Choice Questions (1 mark each)

Multiple-choice questions test your fundamental understanding of data handling concepts from Class 6 Mathematics Chapter 4. Read each question carefully, examine all four options, and select the most accurate answer. Avoid random guessing—eliminate obviously incorrect choices first, then decide between remaining options. Pay special attention to words like 'not', 'always', 'never', 'most', and 'least' as they change meaning significantly. When a question refers to a pictograph or bar graph, take a moment to understand the scale before choosing your answer. Remember that in CBSE examinations, negative marking is not applied for MCQs in Class 6, so always attempt every question even if you are unsure. These six questions cover the breadth of the chapter including data collection, pictographs, bar graphs, frequency tables, and interpretation skills.

Q1. Which of these is NOT a method of representing data? (a) Pictograph (b) Bar graph (c) Frequency table (d) Pie chart
Q2. In a pictograph, if one symbol represents 10 books, how many books do 7 symbols represent? (a) 7 (b) 17 (c) 70 (d) 700
Q3. The height of bars in a bar graph represents: (a) The category name (b) The frequency or value (c) The scale (d) The width of data
Q4. Tally marks are used to: (a) Decorate data (b) Count and record data systematically (c) Draw bar graphs (d) Calculate averages
Q5. In a bar graph showing marks of 5 students, which axis typically shows the students' names? (a) Vertical axis (b) Horizontal axis (c) Both axes (d) Neither axis
Q6. The main advantage of a pictograph over a simple list is that it: (a) Takes less time to make (b) Is more colourful (c) Helps compare data visually at a glance (d) Uses fewer numbers

Section B: Fill in the Blanks (1 mark each)

Fill-in-the-blank questions assess your recall of key terminology and concepts from Data Handling and Presentation. Write the most appropriate word or phrase in each blank space provided. Ensure correct spelling, as technical terms like 'frequency', 'pictograph', and 'horizontal' carry specific meanings in mathematics. Read the complete sentence before and after filling the blank to verify it makes logical sense. Some blanks may require numbers while others need vocabulary terms from the chapter. If you are unsure, think about the context—what topic is being discussed? Is it about pictographs, bar graphs, or data collection? This section reinforces the language of data handling that you will use throughout secondary school mathematics and science. All five items are drawn directly from NCERT Class 6 Mathematics Chapter 4 content, so revising your textbook definitions will help immensely.

Q7. A __________ is a table that shows how many times each item or value occurs in a dataset.
Q8. In a pictograph, each picture or symbol represents a fixed __________ of items.
Q9. The two axes in a bar graph are called the __________ axis and the vertical axis.
Q10. When collecting data through questions, we use a __________ to record responses.
Q11. The __________ of a bar graph tells us what one unit or division on the axis represents.

Section C: Match the Following / True or False (1 mark each)

This section sharpens your ability to connect concepts and verify statements about data handling. In matching questions, read all items in both columns before drawing connections, as some options might seem to fit multiple items at first glance. Look for the most precise and specific match. For true-false statements, do not guess—if even one part of a statement is incorrect, the entire statement is false. Pay attention to absolute words like 'always', 'never', 'all', and 'only', which often make statements false because they leave no room for exceptions. Data handling involves precise definitions, so a bar graph is different from a pictograph in specific ways, and mixing up these characteristics will lead to errors. This exercise builds your critical thinking and helps you distinguish between similar-looking concepts that have important differences. Scoring well here indicates you have moved beyond rote memorization to genuine understanding of Class 6 Mathematics Chapter 4 concepts.

Match Column A with Column B:
Column A: (i) Pictograph (ii) Bar graph (iii) Tally marks (iv) Frequency (v) Scale
Column B: (a) Number of times an item occurs (b) Uses symbols or pictures to show data (c) The value one unit represents (d) Quick way to count using groups of five (e) Uses bars of different heights

Section D: Short Answer Questions (2 marks each)

Short-answer questions require you to explain concepts or perform small calculations in 2 to 3 sentences or a few steps of working. Marks are awarded not just for the final answer but also for the method and reasoning you show, so always write your steps clearly. In data handling problems, this might mean explaining how you read a scale, showing your multiplication when interpreting a pictograph, or describing the steps to draw a bar graph. Use proper mathematical vocabulary from NCERT Class 6 Mathematics—terms like 'scale', 'frequency', 'horizontal axis', 'uniform width'—to demonstrate understanding. Neatness matters: if you draw a small bar graph or tally chart, use a ruler and label it properly. These five questions cover a mix of interpretation, drawing, and application of data concepts. Budget about 10-12 minutes for this section, spending roughly 2 minutes per question. If you get stuck on one question, move ahead and return to it later to maximise your score.

Q12. Draw a pictograph to show the number of books read by 4 friends: Amit-6, Priya-4, Rohan-8, Sneha-2. Use 📚 = 2 books. (2 marks)
Q13. The following data shows favourite colours of 20 students: Red-5, Blue-8, Green-4, Yellow-3. Make a frequency table for this data. (2 marks)
Q14. Look at the bar graph showing runs scored by 5 players: A-40, B-60, C-30, D-50, E-70. Who scored the highest and by how much more than the lowest scorer? (2 marks)
Q15. Why is a bar graph more suitable than a pictograph when dealing with large numbers? (2 marks)
Q16. Write any two differences between a pictograph and a bar graph. (2 marks)

Section E: Long Answer and HOTS Questions (4 marks each)

Long-answer and Higher Order Thinking Skills questions test your ability to apply Data Handling and Presentation concepts to complex, multi-step problems that mirror real-life situations. These questions typically require you to collect or organise data, draw a graph with proper labels and scale, interpret the graph, and answer follow-up questions based on your work. Marks distribution usually includes 1 mark for correct data organisation, 2 marks for accurate graph construction with all elements (title, axes labels, scale, bars or symbols), and 1 mark for interpretation or conclusion. Take your time with these—rushing leads to small errors in scale or labeling that cost marks. Use a ruler and pencil to ensure neat, proportional bars in bar graphs. When choosing a scale, pick one that fits your data range comfortably on the page; for example, if maximum frequency is 50, a scale of 1 cm = 10 units works better than 1 cm = 5 units. Read all parts of each question before starting so you understand the complete requirement. These three questions together assess whether you have truly mastered Class 6 Mathematics Chapter 4 or are merely memorising procedures. Students who struggle here often benefit from interactive AI tutoring—CBSETUTOR.ai offers step-by-step guidance for such complex problems through photo upload, available anytime at ₹999/month across all classes from 6 to 12.

Q17. The number of trees planted by 6 classes are: Class 6A-25, 6B-30, 6C-20, 6D-35, 6E-28, 6F-22. (a) Prepare a frequency table. (b) Draw a bar graph using scale 1 cm = 5 trees. (c) Which class planted the most trees and which planted the least? (4 marks)
Q18. In a survey of 40 students about their favourite sport, the following data was collected: Cricket-12, Football-10, Badminton-8, Tennis-6, Hockey-4. (a) Represent this data using a pictograph where one symbol 🏏 = 2 students. (b) How many symbols will you draw for Cricket? (c) Which sport is least popular? (4 marks)
Q19. Observe the given bar graph showing monthly rainfall (in cm) for five months: June-20, July-35, August-40, September-25, October-10. (a) In which month was rainfall maximum? (b) What is the difference between the highest and lowest rainfall? (c) If the average rainfall needed for good crops is 25 cm, in how many months was rainfall above average? (4 marks)

Case Study Question (5 marks)

The case-study question is a hallmark of modern CBSE assessment, integrating Data Handling and Presentation with real-world scenarios that Class 6 students encounter. You are presented with a paragraph describing a situation—a school event, a survey, a competition, or community data—followed by a data table or graph and 4 to 5 sub-questions. This format tests not just your mathematical skills but also your reading comprehension and ability to extract relevant information from text and visuals together. Marks are distributed across the sub-questions, usually 1 mark for direct reading from the graph, 1 mark for simple calculation, 2 marks for interpretation or comparison, and 1 mark for a conclusion or application. Approach it systematically: first, read the entire case carefully, underline key numbers and facts; second, study the data table or graph and note the scale and labels; third, read all sub-questions to understand what is being asked; fourth, answer them in order, showing all working. Case studies simulate how data is actually used—not in isolation, but to make decisions, compare options, or understand trends. Success here demonstrates you are ready for more advanced statistics in Classes 7 and 8. This question type also appears in CBSE board exams from Class 10 onwards, so building comfort now gives you a head start.

Q20. Case Study: School Election Results - A school conducted elections for Head Boy. Five candidates participated: Arjun, Meera, Kabir, Diya, and Sameer. Votes received by each are shown in the bar graph below (imagine graph): Arjun-80, Meera-120, Kabir-60, Diya-100, Sameer-90. Total votes polled: 450.
(a) Who won the election and by how many votes more than the runner-up? (1 mark)
(b) How many students voted for Kabir? (1 mark)
(c) What is the difference between the highest and lowest votes received? (1 mark)
(d) If 50 more students had voted for Sameer, would he have won? Justify your answer. (2 marks)

Answer Key with Explanations

This comprehensive answer key provides correct answers along with brief explanations or working steps for every question in the worksheet. Use it for self-assessment after completing the worksheet honestly without peeking. For MCQs and fill-in-the-blanks, check your answers directly; if you got any wrong, revisit that concept in your NCERT Class 6 Mathematics textbook Chapter 4. For short and long answers, compare your method with the one shown—there might be more than one correct approach, but your final answer and key steps should match. Award yourself marks honestly: give full marks only if your answer is complete and well-explained, partial marks if the method is right but you made a calculation slip or forgot a label. If your score is below 35 out of 50, revise the chapter thoroughly and attempt the worksheet again after a few days. Between 35 and 42 indicates good understanding with room for improvement in accuracy or speed. Above 42 means you have mastered Data Handling and Presentation concepts at the Class 6 level. Keep this answer key handy for quick revision before school tests. Parents can use these explanations to guide their children without needing to recall the mathematics themselves—simply read the explanation aloud and work through it together. For students who need deeper conceptual clarity, remember that CBSETUOR.ai provides unlimited question-solving support with detailed step-by-step explanations at ₹999/month for all classes 6-12, with the convenience of uploading photos of worksheet questions directly from your phone or tablet for instant AI tutor responses, available 24×7 including late-night study sessions and weekends.

Section A Answers: 1(d), 2(c), 3(b), 4(b), 5(b), 6(c)
Section B Answers: 7-Frequency table, 8-Number/quantity, 9-Horizontal, 10-Questionnaire/tally sheet, 11-Scale
Section C Answers: (i)-(b), (ii)-(e), (iii)-(d), (iv)-(a), (v)-(c)
Detailed explanations for Sections D, E, and Case Study follow below

Detailed Solutions for Short Answer Questions (Section D)

Q12 Solution: Create a pictograph with four rows. Row 1: Amit | 📚📚📚 (since 6 books ÷ 2 = 3 symbols). Row 2: Priya | 📚📚 (4 ÷ 2 = 2 symbols). Row 3: Rohan | 📚📚📚📚 (8 ÷ 2 = 4 symbols). Row 4: Sneha | 📚 (2 ÷ 2 = 1 symbol). Write title 'Books Read by Friends' and mention scale: 📚 = 2 books. Award yourself 1 mark for correct symbols and 1 mark for proper title and scale. Q13 Solution: Draw a table with two columns: 'Colour' and 'Frequency'. List Red-5, Blue-8, Green-4, Yellow-3. Check that total is 5+8+4+3=20 students as given. 1 mark for correct table structure, 1 mark for accurate numbers. Q14 Solution: From the bar graph, highest scorer is E with 70 runs, lowest scorer is C with 30 runs. Difference = 70 - 30 = 40 runs. Answer: E scored the highest, 40 runs more than C. 1 mark for identifying E and C, 1 mark for correct difference calculation. Q15 Solution: A bar graph is more suitable for large numbers because drawing many symbols in a pictograph becomes time-consuming and cluttered. For example, if a category has 500 items and each symbol represents 10 items, you would need to draw 50 symbols, which is tedious. A bar graph simply shows a tall bar, making it quicker and clearer. 1 mark for mentioning time/space efficiency, 1 mark for a valid reason or example. Q16 Solution: Two differences: (i) A pictograph uses pictures or symbols, while a bar graph uses rectangular bars. (ii) In a pictograph, we count symbols and multiply by scale to find value; in a bar graph, we read the height of the bar directly from the axis. 1 mark per difference, properly explained.

Detailed Solutions for Long Answer and HOTS Questions (Section E)

Q17 Solution: (a) Frequency Table - Create a two-column table: 'Class' (6A, 6B, 6C, 6D, 6E, 6F) and 'Number of Trees' (25, 30, 20, 35, 28, 22). (1 mark for correct table). (b) Bar Graph - Draw horizontal axis and label it 'Class'. Draw vertical axis and label it 'Number of Trees'. Since maximum is 35, choose scale 1 cm = 5 trees, so axis goes 0, 5, 10, 15, 20, 25, 30, 35. Draw six bars of equal width with heights corresponding to 25, 30, 20, 35, 28, 22. Use a ruler for straight lines. Add title 'Trees Planted by Each Class'. (2 marks: 1 for scale and axes, 1 for accurate bars and title). (c) Class 6D planted the most trees (35), and Class 6C planted the least (20). (1 mark for both correct identifications). Q18 Solution: (a) Pictograph - Since 🏏 = 2 students, Cricket (12 students) needs 12÷2 = 6 symbols, Football (10) needs 5 symbols, Badminton (8) needs 4 symbols, Tennis (6) needs 3 symbols, Hockey (4) needs 2 symbols. Draw five rows with sport names and corresponding symbols. Write title 'Favourite Sports of Students' and scale 🏏 = 2 students. (2 marks for correct pictograph with scale). (b) For Cricket, number of symbols = 12 ÷ 2 = 6 symbols. (1 mark). (c) Hockey is the least popular sport with only 4 students. (1 mark). Q19 Solution: (a) Maximum rainfall was in August at 40 cm. (1 mark). (b) Highest = 40 cm (August), Lowest = 10 cm (October). Difference = 40 - 10 = 30 cm. (1 mark). (c) Months with rainfall above 25 cm average: July (35 cm), August (40 cm). That is 2 months. June has exactly 25 cm, so depending on interpretation, you might include it or not; typically 'above' means strictly greater than, so answer is 2 months. (2 marks: 1 for correct identification, 1 for count).

Detailed Solution for Case Study Question

Q20 Case Study Solution: (a) Winner and margin - Reading the bar graph, Meera received the highest votes (120). The runner-up is Diya with 100 votes. Meera won by 120 - 100 = 20 votes. (1 mark for correct answer with calculation). (b) Votes for Kabir - From the graph, Kabir received 60 votes. (1 mark for direct reading). (c) Difference between highest and lowest - Highest votes = 120 (Meera), Lowest votes = 60 (Kabir). Difference = 120 - 60 = 60 votes. (1 mark for correct calculation). (d) Hypothetical scenario - Originally Sameer got 90 votes. If 50 more students voted for him, new total = 90 + 50 = 140 votes. Meera still has 120 votes (unchanged). Since 140 > 120, yes, Sameer would have won the election. Justification: 140 votes is 20 more than Meera's 120, making him the new winner. (2 marks: 1 for correct new total calculation, 1 for proper comparison and conclusion). Key learning: This case study tests your ability to read data, perform arithmetic, and reason logically about 'what if' situations—skills useful far beyond the mathematics classroom. Always show your working clearly; even if the final answer is wrong due to a slip, you can earn partial marks for correct method.

Frequently asked questions

What is the difference between a pictograph and a bar graph in Class 6 Data Handling?+

A pictograph uses pictures or symbols to represent data, where each symbol stands for a fixed number of items, making it visually appealing and easy to understand for small datasets. A bar graph uses rectangular bars of uniform width and varying heights to show quantities, making it more suitable for larger numbers and precise comparisons. Both are covered in NCERT Class 6 Mathematics Chapter 4.

How do I choose the right scale when drawing a bar graph in CBSE Class 6?+

Select a scale that fits your data range comfortably on the page. Find the maximum value in your data; if it is 50, a scale of 1 cm = 10 units works well. If the maximum is 100, use 1 cm = 20 units. The scale should make the graph neither too cramped nor too spread out. Always write the scale clearly near the axis.

Why are tally marks used in data collection for Class 6 Mathematics?+

Tally marks provide a quick, systematic way to count items as you collect data. Grouping them in fives (four vertical lines crossed by a diagonal fifth line) makes counting faster and reduces errors. This method is especially useful during surveys or observations where you record data in real time, as taught in NCERT Class 6 Mathematics Chapter 4.

What are the common mistakes students make in Data Handling worksheets?+

Common errors include forgetting to write the scale in pictographs and bar graphs, drawing bars of unequal width, not labeling axes properly, incorrect multiplication when reading pictographs (adding instead of multiplying), and choosing an awkward scale that makes the graph hard to read. Always double-check labels, titles, and calculations before finalising your answer.

How can I improve my speed in solving Data Handling questions for CBSE exams?+

Practice drawing graphs with a ruler regularly to build speed and neatness. Memorise the steps: read data, choose scale, label axes, draw bars or symbols, write title. For interpretation questions, first locate the relevant bars or symbols, then perform calculations. Attempting worksheets under timed conditions, like this 60-minute exercise, builds exam confidence and time management skills.

Is it necessary to use colours in bar graphs for Class 6 Mathematics?+

No, using colours is not mandatory in CBSE Class 6 Mathematics exams. While colours make graphs more attractive and easier to distinguish, you can draw perfectly acceptable bar graphs using only a pencil. Just ensure bars are clearly separated, properly labeled, and neatly drawn with a ruler. Colours are a visual aid, not a requirement for marks.

How does CBSETUTOR.ai help with Data Handling and Presentation practice?+

CBSETUTOR.ai offers 24×7 AI tutoring where students can upload photos of any worksheet question, including graphs and pictographs, and receive step-by-step solutions instantly. The platform covers all NCERT Class 6 Mathematics chapters at a flat ₹999 per month for classes 6-12, with a 3-day free trial. It acts as a personal tutor available anytime, especially helpful for HOTS and case-study questions.

What is a frequency table and when do we use it in Class 6?+

A frequency table is a two-column table that lists each item or value in one column and the number of times it occurs (frequency) in the other column. It organises raw data neatly, making it easy to see patterns and compare values. We use it as a first step before drawing pictographs or bar graphs, as explained in NCERT Class 6 Mathematics Chapter 4.

Can I draw half symbols in a pictograph if the number does not divide evenly?+

Yes, if the scale is 1 symbol = 2 items and you have 5 items, you can draw 2 full symbols and half a symbol. However, NCERT Class 6 typically uses data that divides evenly to avoid confusion. If you need to draw half symbols, mention it clearly in your pictograph, for example, 'Half symbol = 1 item'. Always check the question to see if partial symbols are expected.

How many marks is Chapter 4 Data Handling usually worth in CBSE Class 6 exams?+

In the CBSE Class 6 Mathematics annual exam (80 marks), Data Handling and Presentation typically carries 6 to 8 marks. Questions may include one 2-mark interpretation question, one 3-mark graph-drawing question, and one or two 1-mark objective questions. Scoring well here is important because these are straightforward marks if you practice drawing and reading graphs regularly using worksheets like this one.

Related resources

Important Questions: CBSE Class 6 Mathematics Chapter 4 Data Handling and Presentation Class 6 Mathematics Chapter 4 Data Handling and Presentation — Formulas & Key Points NCERT Solutions for CBSE Class 6 Mathematics Chapter 4: Data Handling and Presentation CBSE Class 6 Mathematics Chapter 4 Data Handling and Presentation — Notes AI Tutor for Class 6: The Smart Alternative to Tuition AI Tutor for Class 6 Maths: Learn Faster with Instant Help NCERT Solutions for Class 9 Mathematics Chapter 1: Number Systems – Complete Guide CBSE Class 9 Mathematics Chapter 1 Number Systems Worksheet with Answers

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