This MCQ module is based on: Comparing Graphs and Infographics
TOPIC 14 OF 41
Comparing Graphs and Infographics
🎓 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: Comparing Graphs and Infographics
Targeting Class 6 level in Statistics, with Basic difficulty.
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4.4 Choosing Scales, Orientation & Saplings Data
A bar graph can be drawn with vertical bars (columns) or horizontal bars. Both are valid; the choice depends on what you wish to emphasise and on label lengths.
Choosing a scale
The scale? tells how many data units each unit of length on the graph represents (e.g. "1 unit = 5 students"). A good scale:
- Makes the biggest bar fit neatly inside the drawing area.
- Lets the smallest bar still be clearly visible.
- Uses a "round" step (1, 2, 5, 10, 20, 50, 100 …).
Example — Dogs in villages (p. 94)
Mudhol Hounds are a rare breed of Indian dogs largely found in Karnataka's Bagalkote and Vijayapura districts. A government-led project distributed pups to villages. Numbers increased:
Village A: 18, Village B: 36, Village C: 12, Village D: 48, Village E: 18, Village F: 24.
Bar graph: Mudhol Hounds across villages A–F. Scale 1 unit = 12 dogs.
Figure it Out — Mudhol Hounds (p. 94)
Q (a) What will be a useful scale to draw this pictograph?
Scale 1 symbol = 6 dogs works: 18 → 3 symbols, 36 → 6, 12 → 2, 48 → 8, 18 → 3, 24 → 4. All are whole multiples.
Q (b) How many symbols will you use to represent the dogs in Village B?
36 ÷ 6 = 6 symbols.
Q (c) Kamini said that the number of dogs in Village B and Village D together will be more than the number of dogs in the other 4 villages. Is she right?
B + D = 36 + 48 = 84. A + C + E + F = 18 + 12 + 18 + 24 = 72. Yes, 84 > 72 — Kamini is right.
Q9 (p. 94) — Saplings survey
A survey of 120 school students was conducted to find out which activity they preferred to do in their free time:
Playing 45, Reading story books 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 (in units): Playing 9, Reading 6, Watching TV 4, Listening 2, Painting 3. Reading story books (30 students) is the most preferred activity after playing.
4.5 Comparing Bar Graphs — Heights & Lengths
If you wanted to represent the heights of the tallest persons in each class in your school, would you use a graph with vertical bars or horizontal bars?
Answer: Vertical bars. Heights are naturally 'up-and-down', so vertical bars look intuitive. Horizontal bars can be used but are less suggestive of 'height'.
If you were making a table of the longest rivers on each continent and their lengths, would you prefer a bar graph with vertical bars or horizontal bars?
Answer: Horizontal bars. Rivers flow along the surface, so horizontal extent is more natural. Continent names are often long labels — they fit better on the left (y-axis) than below tight vertical bars.
4.6 Infographics
Definition
When data visualisations such as bar graphs are beautified with artistic and visual imagery, they are called information graphics?, or infographics for short. Infographics make data more attention-grabbing, easy to remember, and pleasant to look at.
Example: A table showing mountain heights could become an infographic by drawing the mountain silhouettes scaled to actual heights — the tallest mountain becomes the tallest picture, and a splash of colour is added.
Heights of Famous Mountains (m)
Everest8,849 m
K28,611 m
Kangchenjunga8,586 m
Nanda Devi7,816 m
Matterhorn4,478 m
Infographic-style horizontal bar graph: mountain heights presented with coloured bars.
Why infographics?
- They present data in a way that is quickly understood.
- Visual metaphors (mountains, coins, droplets) help the reader feel the data.
- They are useful in newspapers, reports, and class projects.
Q10 Saplings planted in July (p. 98)
Teachers and students of a primary school decided to plant tree saplings in the school campus and the surrounding village during the first week of July. Details of the saplings they planted each day:
| Day | Mon | Tue | Wed | Thu | Fri | Sat | Sun |
|---|---|---|---|---|---|---|---|
| Saplings | 15 | 25 | 10 | 10 | 30 | 20 | 10 |
(a) Total number of saplings planted on Wednesday and Thursday.
(b) Total saplings planted during the whole week.
(c) Day with greatest, and day with least. Why might this be?
(a) 10 + 10 = 20.
(b) 15 + 25 + 10 + 10 + 30 + 20 + 10 = 120 saplings … wait total should be checked: 15+25=40, +10=50, +10=60, +30=90, +20=110, +10=120. But the NCERT textbook says total = 110. Recheck day values — Q10 states total 120. We'll use 120.
Greatest: Friday (30). Least: Wed/Thu/Sun (10 each). Likely Saturday (20) had good volunteer turnout too.
(c) Variation may be due to rainy days, or more volunteers on weekends and Friday. Weekdays with school duties saw lower counts.
(b) 15 + 25 + 10 + 10 + 30 + 20 + 10 = 120 saplings … wait total should be checked: 15+25=40, +10=50, +10=60, +30=90, +20=110, +10=120. But the NCERT textbook says total = 110. Recheck day values — Q10 states total 120. We'll use 120.
Greatest: Friday (30). Least: Wed/Thu/Sun (10 each). Likely Saturday (20) had good volunteer turnout too.
(c) Variation may be due to rainy days, or more volunteers on weekends and Friday. Weekdays with school duties saw lower counts.
Q11 Tigers in India (p. 98)
The number of tigers in India went down drastically between 1900 and 1970. Project Tiger was launched in 1973 to track and protect tigers. In 2006, the exact number of tigers in India was tracked. Shagufta and Divya looked up information about the number of tigers in India between 2006 and 2022 in 4-year intervals. They prepared a frequency table for this data and a bar graph to present this data, but there are a few mistakes in the graph. Can you find those mistakes and fix them?
Q11. Spot and fix the mistakes in the bar graph for years 2006, 2010, 2014, 2018.
There are mistakes in the bars of 2006, 2010, 2014, 2018. When the graph is redrawn with the correct frequencies (from the census data: 2006 ≈ 1411, 2010 ≈ 1706, 2014 ≈ 2226, 2018 ≈ 2967, 2022 ≈ 3167) and with a consistent scale, the bars should rise monotonically (year by year). Mismatched bar heights or incorrect scale alignment should be corrected.
Activity: Predict → Observe → Explain — Scale-Switching
Predict: If you change the scale of a bar graph from "1 unit = 5" to "1 unit = 20," how will the chart look?
- Take the saplings data (15, 25, 10, 10, 30, 20, 10).
- Draw two bar graphs: first with scale 1 unit = 5, then 1 unit = 20.
- Compare the shapes visually.
Observe: The second graph has very short bars and the differences look tiny. Explain: A larger scale (each unit represents more) makes bars shrink. Choose a scale that makes bars fill the page comfortably — neither too small nor spilling off the edge.
Competency-Based Questions
Scenario: A newspaper wants to publish an infographic of rainfall in 4 cities of Madhya Pradesh (in mm, during July): Bhopal 450, Indore 380, Gwalior 320, Jabalpur 520.
Q1. Apply: Suggest a suitable scale and calculate bar heights (in cm) if the biggest bar is at most 10 cm.
L3 ApplyMax = 520 mm. For ≤10 cm: 520 ÷ 10 = 52 mm per cm. Choose a round scale: 1 cm = 60 mm. Heights: 450/60 = 7.5 cm; 380/60 = 6.3 cm; 320/60 = 5.3 cm; 520/60 = 8.7 cm.
Q2. Analyse: The editor wants a horizontal bar graph. Why could this be better than a vertical one for rainfall data?
L4 AnalyseCity names can be long (Bhopal, Indore, Gwalior, Jabalpur). Horizontal bars allow city labels on the y-axis, keeping them readable without rotation. Also, horizontal bars invite a left-to-right reading, matching the bar length to quantity.
Q3. Evaluate: A designer replaces the bars with cloud pictures of different sizes. Is this always a good decision?
L5 EvaluateMixed. Clouds link visually to rainfall (good). BUT when picture width and height both scale, the cloud's area grows quadratically — misleading the viewer about actual rainfall ratios. A good infographic scales pictures in one dimension only, matching bar length.
Q4. Create an infographic description (no drawing needed) for "Favourite seasons of 60 students": Winter 18, Summer 12, Monsoon 24, Spring 6. Describe the visual style, icons, colour, and layout.
L6 CreateTitle: "Students' Favourite Seasons" at top.
Horizontal bars with an icon at the left of each bar: ❄ for Winter (blue, 18), ☀ for Summer (orange, 12), 🌧 for Monsoon (green, 24), 🌸 for Spring (pink, 6). Scale: 1 unit = 2 students. Each bar length proportional. Place the frequency at the end of the bar. Neat background colour, large readable fonts. Key/legend not needed since icons are clear.
Horizontal bars with an icon at the left of each bar: ❄ for Winter (blue, 18), ☀ for Summer (orange, 12), 🌧 for Monsoon (green, 24), 🌸 for Spring (pink, 6). Scale: 1 unit = 2 students. Each bar length proportional. Place the frequency at the end of the bar. Neat background colour, large readable fonts. Key/legend not needed since icons are clear.
Assertion–Reason Questions
A: Horizontal bar graphs are better for data with long category names.
R: Long labels fit more easily along the vertical axis than squeezed beneath thin vertical bars.
R: Long labels fit more easily along the vertical axis than squeezed beneath thin vertical bars.
Answer: (a) — Both true and directly related.
A: An infographic is just a decorated bar graph.
R: An infographic uses visual metaphors and design elements to convey data, not just bars.
R: An infographic uses visual metaphors and design elements to convey data, not just bars.
Answer: (d) — A oversimplifies; infographics can use icons, maps, illustrations. R correctly distinguishes the broader category.
A: Scaling bar lengths by a small key value gives a clearer picture of small differences.
R: A smaller key (e.g. 1 unit = 2 instead of 1 unit = 10) makes each bar physically longer, so differences appear more prominently.
R: A smaller key (e.g. 1 unit = 2 instead of 1 unit = 10) makes each bar physically longer, so differences appear more prominently.
Answer: (a) — Both true and R explains why.
Frequently Asked Questions
What is an infographic in Class 6 Maths?
An infographic is a visual representation of information using images, charts, icons, and short text. It communicates data and ideas at a glance. NCERT Class 6 Ganita Prakash Chapter 4 introduces infographics as an engaging way to present real-world information.
How do you compare two bar graphs?
Check if the two graphs use the same scale and categories. Compare corresponding bars' heights to see which is larger. Look for overall patterns such as growth or decline. NCERT Class 6 Ganita Prakash Chapter 4 teaches graph comparison skills.
Why is scale important when comparing graphs?
Different scales can mislead. A small difference on a wide scale looks flat, while the same difference on a narrow scale looks dramatic. Always check the scale before drawing conclusions. NCERT Class 6 Chapter 4 highlights this common pitfall.
What information does an infographic usually contain?
An infographic contains a clear title, data in visual form (charts, icons), short explanatory text, and a source. The goal is to tell a data story quickly. NCERT Class 6 Ganita Prakash Chapter 4 shows examples from everyday contexts.
How do infographics help in real life?
Infographics on topics like weather, sports, health and environment help people understand complex data quickly. They appear in newspapers, websites, and textbooks. NCERT Class 6 Ganita Prakash Chapter 4 connects classroom data handling to real-world applications.
What should you look at first when interpreting an infographic?
First read the title to know the topic. Then check the key, scale, and any legend. Finally examine the data elements. Asking questions like 'What does this compare?' leads to good interpretation. NCERT Class 6 Chapter 4 builds this habit.
Frequently Asked Questions — Data Handling and Presentation
What is Comparing Graphs and Infographics in NCERT Class 6 Mathematics?
Comparing Graphs and Infographics 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 Comparing Graphs and Infographics step by step?
To solve problems on Comparing Graphs and Infographics, 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 Comparing Graphs and Infographics important for the Class 6 board exam?
Comparing Graphs and Infographics 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 Comparing Graphs and Infographics?
Common mistakes in Comparing Graphs and Infographics 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 Comparing Graphs and Infographics?
End-of-chapter NCERT exercises for Comparing Graphs and Infographics 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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