This MCQ module is based on: Chapter 4 Exercises and Summary
TOPIC 15 OF 41
Chapter 4 Exercises and Summary
🎓 Class 6
Mathematics
CBSE
Theory
Ch 4 — Data Handling and Presentation
⏱ ~35 min
🌐 Language: [gtranslate]
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This mathematics assessment will be based on: Chapter 4 Exercises and Summary
Targeting Class 6 level in Statistics, with Basic difficulty.
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4.7 End-of-Chapter Exercises
Section 4.5 — Page 103, Figure it Out (consolidated). Solve each, then reveal the solution.
Q1. If you wanted to visually represent the data of the heights of the tallest persons in each class in your school, would you use a graph with vertical bars or horizontal bars? Why?
Vertical bars. Heights are naturally measured 'up and down', so vertical bars intuitively convey the idea. Class names as labels below each bar are short enough to fit.
Q2. If you were making a table of the lengths of the longest rivers on each continent and their lengths, would you prefer a table with vertical bars or with horizontal bars? Why? Try finding this information, and look for the corresponding table and graph! Which continents have the longest rivers?
Horizontal bars. Rivers flow horizontally — bars along the length feel natural. Continent names are long and fit better on the left axis. Longest rivers by continent (approx.):
Africa — Nile (~6,650 km); South America — Amazon (~6,400 km); Asia — Yangtze (~6,300 km); North America — Missouri/Mississippi (~6,275 km); Europe — Volga (~3,530 km); Australia — Murray (~2,508 km); Antarctica — Onyx (~32 km).
Africa — Nile (~6,650 km); South America — Amazon (~6,400 km); Asia — Yangtze (~6,300 km); North America — Missouri/Mississippi (~6,275 km); Europe — Volga (~3,530 km); Australia — Murray (~2,508 km); Antarctica — Onyx (~32 km).
Q3. Take data about 5 sports your class plays. Prepare a frequency table and bar graph.
Sample: Cricket 14, Football 10, Kabaddi 8, Kho-Kho 5, Badminton 3. Bar graph scale: 1 unit = 2 students. Bars of heights 7, 5, 4, 2.5, 1.5 units. (Your answer depends on your class.)
Q4. Design a pictograph showing favourite breakfast choices of students in your class: Idli 12, Dosa 9, Paratha 18, Poha 6, Bread-Butter 3.
Key: 1 symbol = 3 students. Symbols: Idli → 4, Dosa → 3, Paratha → 6, Poha → 2, Bread-Butter → 1. Total = 16 symbols representing 48 students.
Q5. Samantha's data — insects and critters in the garden (p. 93): Mites 6, Caterpillars 10, Beetles 5, Butterflies 3, Grasshoppers 2. Which bar is the tallest? What fraction of the total is made up of butterflies?
Tallest: Caterpillars (10). Total = 6 + 10 + 5 + 3 + 2 = 26. Butterflies share = 3/26.
Q6. Pooja's tickets data: Vidisha 24, Jabalpur 20, Seoni 16, Indore 28, Sagar 16. With scale 1 unit = 4 tickets, state bar heights.
Heights in units: 6, 5, 4, 7, 4 for Vidisha, Jabalpur, Seoni, Indore, Sagar respectively.
Q7. Chinu's transport data (9 a.m.–10 a.m.): Bike 13, Car 6, Bicycle 8, Auto Rickshaw 8, Scooter 9, Bus 4, Bullock Cart 2. (a) Total vehicles. (b) Which is least used? (c) What is the ratio of bikes to bullock carts?
(a) 13 + 6 + 8 + 8 + 9 + 4 + 2 = 50. (b) Bullock Cart (2). (c) 13 : 2.
Q8. Saplings planted: Mon 15, Tue 25, Wed 10, Thu 10, Fri 30, Sat 20, Sun 10. Which day has the greatest number? Make a bar graph using scale 1 unit = 5 saplings.
Greatest: Friday (30). Heights in units: 3, 5, 2, 2, 6, 4, 2. Draw vertical bars accordingly.
Q9. Free-time activities (120 students): Playing 45, Reading 30, Watching TV 20, Listening to music 10, Painting 15. Draw a bar graph using scale 1 unit = 5 students. Which activity is preferred by most students other than playing?
Heights: 9, 6, 4, 2, 3 units. Most preferred other than playing: Reading story books (30 students).
Q10. Mudhol Hounds (dogs) in villages A: 18, B: 36, C: 12, D: 48, E: 18, F: 24. Pictograph with suitable scale? Is the number of dogs in B + D more than the number in other 4 villages?
Scale 1 symbol = 6 dogs. Symbols: A 3, B 6, C 2, D 8, E 3, F 4.
B + D = 36 + 48 = 84. A + C + E + F = 18 + 12 + 18 + 24 = 72. Yes, 84 > 72.
B + D = 36 + 48 = 84. A + C + E + F = 18 + 12 + 18 + 24 = 72. Yes, 84 > 72.
Q11. Tigers in India: there are mistakes in the bars of 2006, 2010, 2014, 2018. Why were mistakes made? How can they be corrected?
Mistakes likely from (i) misreading census totals, (ii) inconsistent scaling, (iii) swapping years. Corrections: use the official census totals (2006: 1411; 2010: 1706; 2014: 2226; 2018: 2967; 2022: 3167), set a consistent scale (e.g. 1 unit = 200 tigers), and redraw bars monotonically rising.
Activity: Predict → Observe → Explain — Class data collection
Predict: Will pictograph or bar graph be chosen more often by your classmates as the "best" visualisation of a fruit-preference survey?
- Collect fruit-preference data from 20 classmates.
- Present the same data as a tally table, a pictograph, and a bar graph.
- Ask your classmates: which form was the clearest?
- Record results and discuss.
Observe: Most students prefer the bar graph for accurate comparisons, the pictograph for emotional appeal. Explain: Bar graphs are quicker to compare lengths; pictographs connect viewers with the subject visually — both have their place.
Competency-Based Questions
Scenario: A health worker surveys 50 children in a rural school about how many glasses of water they drink in a day: 2 glasses — 8 children, 3 glasses — 14, 4 glasses — 18, 5 glasses — 7, 6 glasses — 3.
Q1. Apply: Draw a suitable bar graph (describe bar heights) and find the most common water intake.
L3 ApplyScale 1 unit = 2 children. Heights: 4, 7, 9, 3.5, 1.5. Most common: 4 glasses (18 children).
Q2. Analyse: What percentage of children drink less than 4 glasses?
L4 AnalyseLess than 4 glasses = 2-glasses (8) + 3-glasses (14) = 22 children. Percentage = 22/50 × 100 = 44%.
Q3. Evaluate: The worker concludes "Most children drink enough water." Using 4 glasses/day as the recommended minimum, evaluate her claim.
L5 EvaluateChildren drinking ≥ 4 glasses = 18 + 7 + 3 = 28. 28/50 = 56%. The worker's claim is marginally correct — just above half meet the minimum — but 44% drink less than recommended, which is significant. The conclusion should be more careful.
Q4. Create a plan for a follow-up infographic poster the health worker can display in the school to promote better water intake. List (i) title, (ii) visual elements, (iii) key numbers, (iv) a call to action.
L6 Create(i) Title: "Drink Up: Water is Life!"
(ii) Visuals: Five glasses of blue water with percentages; a friendly cartoon child holding a water bottle.
(iii) Key numbers: 44% drink less than recommended; only 20% drink 5+ glasses; goal — at least 6 glasses/day.
(iv) Call to action: "Keep a water bottle handy. Refill it 3 times a day. Challenge a friend!"
(ii) Visuals: Five glasses of blue water with percentages; a friendly cartoon child holding a water bottle.
(iii) Key numbers: 44% drink less than recommended; only 20% drink 5+ glasses; goal — at least 6 glasses/day.
(iv) Call to action: "Keep a water bottle handy. Refill it 3 times a day. Challenge a friend!"
Assertion–Reason Questions
A: A frequency table is enough to distribute prizes by name to each student.
R: A frequency table stores total counts, not individual names.
R: A frequency table stores total counts, not individual names.
Answer: (d) — A is false; R is true and explains why A is false.
A: In a pictograph, two halves of the same symbol may represent the same number as one full symbol.
R: A half-symbol conventionally represents half the full-symbol value.
R: A half-symbol conventionally represents half the full-symbol value.
Answer: (a) — Two halves = one whole. R explains why halves work.
A: A bar graph of rainfall in mm for 5 cities shows Bhopal with the longest bar, so Bhopal received the most rainfall.
R: In a bar graph, the bar length is proportional to the quantity represented.
R: In a bar graph, the bar length is proportional to the quantity represented.
Answer: (a) — A follows directly from R.
Chapter 4 — Summary
Key Takeaways
- Data is any collection of facts, measurements, or observations that tell us something about the world.
- Data must be collected (surveys, observations, measurements) and then organised before it can answer questions.
- Tally marks are a fast, visual method of counting frequencies — grouped in fives for easy reading.
- A frequency table shows each category and how often it appears, but does not preserve individual identities.
- A pictograph uses pictures or symbols with a scale (key) to represent data amounts.
- A bar graph represents quantities as rectangles of equal width. The bar length is proportional to the value. Choose a scale that fits the largest bar and keeps smaller bars readable.
- Bar graphs can be vertical (good for heights, growth) or horizontal (good for long category labels and widths/lengths).
- An infographic combines charts, icons, and illustrations to convey data memorably and meaningfully.
- Good data presentation helps us draw inferences — trends, comparisons, surprises — and make better decisions.
- Always check a graph for: (i) a clear title, (ii) labelled axes, (iii) stated scale/key, (iv) accurate bar heights, (v) equal bar widths.
Frequently Asked Questions
What exercises are in Class 6 Ganita Prakash Chapter 4?
Chapter 4 exercises include organising raw data using tally marks, building frequency tables, drawing pictographs with a key, constructing bar graphs with a chosen scale, and interpreting given infographics. These reinforce all data handling concepts from NCERT Class 6 Ganita Prakash.
How do you solve a pictograph exercise?
Read the key first to know what each symbol represents. Multiply the number of symbols in each row by the key value to find the quantity for that category. For drawing, choose a suitable key and represent counts neatly. NCERT Class 6 Chapter 4 exercises follow this.
What is the main summary of Data Handling chapter?
Data Handling teaches four skills: collecting data with a clear question, organising it using tally marks and frequency tables, representing it with pictographs and bar graphs, and interpreting graphs and infographics. NCERT Class 6 Ganita Prakash Chapter 4 closes with these key ideas.
How do you check a bar graph exercise answer?
Verify the scale is written, bars have equal width, heights match the data values, axes are labelled, and the graph has a title. If interpreting, re-read each bar's height against the scale. NCERT Class 6 Chapter 4 emphasises these checks.
Why do Class 6 students study data handling?
Data handling builds early statistical literacy essential for science, social studies, and daily life. Students learn to ask questions, gather evidence, and communicate findings visually. NCERT Class 6 Ganita Prakash Chapter 4 lays this foundation.
How do data handling skills grow in later classes?
In Classes 7 and 8 students learn double bar graphs, mean, median, mode, and probability. Class 9 introduces histograms and frequency polygons. NCERT Class 6 Chapter 4 provides the groundwork for this progression.
Frequently Asked Questions — Data Handling and Presentation
What is Chapter 4 Exercises and Summary in NCERT Class 6 Mathematics?
Chapter 4 Exercises and Summary is a key concept covered in NCERT Class 6 Mathematics, Chapter 4: Data Handling and Presentation. This lesson builds the student's foundation in the chapter by explaining the core ideas with worked examples, definitions, and step-by-step methods aligned to the CBSE curriculum.
How do I solve problems on Chapter 4 Exercises and Summary step by step?
To solve problems on Chapter 4 Exercises and Summary, follow the NCERT method: identify the given quantities, choose the relevant formula or theorem, substitute values carefully, and simplify. Class 6 exercises gradually increase in difficulty — start with solved NCERT examples before attempting exercise questions, and always verify your answer by substitution or diagram.
What are the most important formulas for Chapter 4: Data Handling and Presentation?
The essential formulas of Chapter 4 (Data Handling and Presentation) are listed in the chapter summary and highlighted throughout the lesson in formula boxes. Memorise them and practise at least 2–3 problems per formula. CBSE board exams frequently test direct application as well as combined use of multiple formulas from this chapter.
Is Chapter 4 Exercises and Summary important for the Class 6 board exam?
Chapter 4 Exercises and Summary is part of the NCERT Class 6 Mathematics syllabus and appears in CBSE board exams. Questions typically include short-answer, long-answer, and competency-based items. Review the NCERT examples, exercise questions, and previous-year board problems on this topic to prepare confidently.
What mistakes should students avoid in Chapter 4 Exercises and Summary?
Common mistakes in Chapter 4 Exercises and Summary include skipping steps, misapplying formulas, sign errors, and losing track of units. Write each step clearly, double-check algebraic manipulations, and re-read the question after solving to verify that your answer matches what was asked.
Where can I find more NCERT practice questions on Chapter 4 Exercises and Summary?
End-of-chapter NCERT exercises for Chapter 4 Exercises and Summary cover all difficulty levels tested in CBSE exams. After completing them, try the examples again without looking at the solutions, attempt the NCERT Exemplar questions for Chapter 4, and solve at least one previous-year board paper to consolidate your understanding.
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