This MCQ module is based on: Pictographs and Bar Graphs
TOPIC 13 OF 41
Pictographs and Bar Graphs
🎓 Class 6
Mathematics
CBSE
Theory
Ch 4 — Data Handling and Presentation
⏱ ~35 min
🌐 Language: [gtranslate]
🧠 AI-Powered MCQ Assessment
▲
📐 Maths Assessment
▲
This mathematics assessment will be based on: Pictographs and Bar Graphs
Targeting Class 6 level in Statistics, with Basic difficulty.
Upload images, PDFs, or Word documents to include their content in assessment generation.
4.2 Pictographs
A pictograph? uses pictures or symbols to represent data. It is a friendly, visually appealing way to present frequencies.
Key terms
A scale or key tells you how many units each picture represents (for example, ☺ = 5 students).A pictograph can be horizontal or vertical. In a category with large frequencies, it is useful to let one symbol stand for multiple units.
Imagine showing "favourite colours" data using a pictograph with ☺ = 5 students. If 35 students chose blue, you would draw 7 smiley faces in the "blue" row (since 35 ÷ 5 = 7).
Example — Books borrowed in a week (Shri Nilesh's library, p. 83)
| Class | Books borrowed | Pictograph (📕 = 5 books) |
|---|---|---|
| Class 5 | 15 | 📕📕📕 |
| Class 6 | 25 | 📕📕📕📕📕 |
| Class 7 | 40 | 📕📕📕📕📕📕📕📕 |
| Class 8 | 30 | 📕📕📕📕📕📕 |
Figure it Out — Library pictograph (p. 83)
Q1. The following pictograph shows the number of books borrowed by students in a week from the library. If each book symbol represents 5 books:
(a) Which class borrowed the most?
(b) Which class borrowed the least?
(c) Total books borrowed.
(a) Class 7 (40 books). (b) Class 5 (15 books). (c) Total = 15 + 25 + 40 + 30 = 110 books.
Q2. Figure it Out (p. 85) — Number of cars passing through a crossing between 6 a.m. and noon. Data: 6–7 am: 36, 7–8 am: 44, 8–9 am: 54, 9–10 am: 68, 10–11 am: 84, 11 am–12 noon: 102.
(a) Total cars between 6 am and noon.
(b) Why so little traffic 6–7 am vs. 7–8 am?
(c) Why heaviest between 7–8 am?
(d) Why less traffic from 8 a.m. onwards until noon?
(a) 36 + 44 + 54 + 68 + 84 + 102 = 388 cars.
(Note: the NCERT graph actually shows rising traffic through 11 am–noon in this example — answers below match that.)
(b) Fewer people commute so early. Shops and schools are still closed.
(c) Peak rush for schools/offices is between 7–8 am.
(d) After peak, movement continues but spreads out; fewer concentrated surges.
(Note: the NCERT graph actually shows rising traffic through 11 am–noon in this example — answers below match that.)
(b) Fewer people commute so early. Shops and schools are still closed.
(c) Peak rush for schools/offices is between 7–8 am.
(d) After peak, movement continues but spreads out; fewer concentrated surges.
4.3 Bar Graphs
A bar graph? represents categories using rectangular bars of equal width. The length (or height) of each bar is proportional to the frequency or value it represents.
Parts of a bar graph
- Axes: horizontal (x-axis) and vertical (y-axis).
- Scale: e.g. 1 unit length = 10 students.
- Bars: drawn at equal gaps; each of same width.
- Title & labels: describe what the graph shows.
Example — Population of India in crores (p. 86)
| Year | 1951 | 1961 | 1971 | 1981 | 1991 | 2001 |
|---|---|---|---|---|---|---|
| Population (crore) | 36 | 44 | 54 | 68 | 84 | 102 |
Bar graph: Population of India (in crore) for each decade 1951–2001. Scale: 1 unit length = 10 crore.
Figure it Out — Bar graph reading (p. 87)
Q1. In which decade did the population increase the most?
Differences: 1961−1951 = 8; 1971−1961 = 10; 1981−1971 = 14; 1991−1981 = 16; 2001−1991 = 18. 1991 to 2001 (18 crore).
Q2. By how much did the population of India increase from 1951 to 2001?
102 − 36 = 66 crore.
Q3 (p. 90). Imran's monthly family expenses (₹): Food 2000, Rent 1500, Transport 600, Electricity 300, Education 1200, Others 400. Bar graph scale: 1 unit = ₹200.
(a) On which item does Imran's family spend the most and the second most?
(b) Is the cost of electricity about one-half the cost of education?
(c) Is the cost of education less than one-fourth the cost of food?
(a) Most: Food (₹2000). Second most: Rent (₹1500).
(b) Electricity 300, Education 1200. 300/1200 = 1/4 — so Electricity is one-fourth of Education, not one-half.
(c) Food 2000, Education 1200. 2000 ÷ 4 = 500. Education 1200 > 500 — No, Education is more than one-fourth the cost of food.
(b) Electricity 300, Education 1200. 300/1200 = 1/4 — so Electricity is one-fourth of Education, not one-half.
(c) Food 2000, Education 1200. 2000 ÷ 4 = 500. Education 1200 > 500 — No, Education is more than one-fourth the cost of food.
Samantha's tea-garden data (p. 90)
Samantha recorded insects and critters: Mites 6, Caterpillars 10, Beetles 5, Butterflies 3, Grasshoppers 2.
Bar graph: Insects and critters in Samantha's tea garden.
Q2 (p. 93). Pooja's ticket-sale data for Bhopal railway station over 2 months in 5 cities of Madhya Pradesh: Vidisha 24, Jabalpur 20, Seoni 16, Indore 28, Sagar 16.
Prepare a bar graph. Someone erased a portion. (f) Bar for Seoni is correct but for Indore is incorrect. One unit length = 4 tickets.
With scale 1 unit = 4 tickets:
Vidisha → 6 units (24), Jabalpur → 5 units (20), Seoni → 4 units (16), Indore → 7 units (28), Sagar → 4 units (16). Draw rectangles of heights 6, 5, 4, 7, 4 units respectively. Correct the Indore bar height to 7 units.
Vidisha → 6 units (24), Jabalpur → 5 units (20), Seoni → 4 units (16), Indore → 7 units (28), Sagar → 4 units (16). Draw rectangles of heights 6, 5, 4, 7, 4 units respectively. Correct the Indore bar height to 7 units.
Q3. Chinu listed means of transport crossing the road from 9 a.m. to 10 a.m.:
Bike 13, Car 6, Bicycle 8, Auto Rickshaw 8, Scooter 9, Bus 4, Bullock Cart 2.
(a) Frequency table. (b) Most used. (c) Data-collection process.
(a) Frequency table as given.
(b) Bike (13) most used.
(c) Prepare a 2-column table (transport | tally), observe road from 9–10 a.m., add a tally mark each time a vehicle passes.
(b) Bike (13) most used.
(c) Prepare a 2-column table (transport | tally), observe road from 9–10 a.m., add a tally mark each time a vehicle passes.
Activity: Predict → Observe → Explain — Pictograph vs. Bar graph
Predict: For a class-strength comparison across 5 classes, which presentation (pictograph or bar graph) will let classmates read the values faster?
- Collect class strengths (5 classes): 28, 32, 30, 35, 27.
- Draw both a pictograph (☺ = 4 students) and a bar graph (scale 1 unit = 5 students).
- Ask 10 classmates to read off each class's strength from both. Time them.
Observe: Most students read bar graphs faster, especially when values are not exact multiples of the pictograph unit. Explain: Bar graphs convey continuous magnitudes; pictographs force rounding when values aren't multiples of the key.
Competency-Based Questions
Scenario: A library records books issued in 5 days (Mon–Fri): 20, 40, 25, 35, 50. The librarian wants to display the data on a 3 × 2 notice board.
Q1. Draw a pictograph with key 📕 = 5 books.
L3 ApplyMon: 📕📕📕📕 (4 symbols = 20)
Tue: 📕📕📕📕📕📕📕📕 (8 = 40)
Wed: 📕📕📕📕📕 (5 = 25)
Thu: 📕📕📕📕📕📕📕 (7 = 35)
Fri: 📕📕📕📕📕📕📕📕📕📕 (10 = 50).
Tue: 📕📕📕📕📕📕📕📕 (8 = 40)
Wed: 📕📕📕📕📕 (5 = 25)
Thu: 📕📕📕📕📕📕📕 (7 = 35)
Fri: 📕📕📕📕📕📕📕📕📕📕 (10 = 50).
Q2. Analyse: The librarian draws a bar graph with scale 1 unit = 10 books. What height must each bar be?
L4 AnalyseDivide each frequency by 10: Mon 2, Tue 4, Wed 2.5, Thu 3.5, Fri 5 units. Using 0.5 unit steps, bars are drawn to these heights.
Q3. Evaluate: A student says "Pictographs are always better because pictures attract attention." Evaluate.
L5 EvaluatePartly true. Pictographs are visually appealing for small, whole-number multiples. But for odd or precise values, bar graphs are faster to read. For very large datasets, bar graphs and numerical summaries work better.
Q4. Create a bar graph showing the hypothetical marks of 6 students in a maths test (out of 50): Ayaan 38, Priya 45, Karan 30, Meera 48, Rohan 27, Sara 42. Choose an appropriate scale and explain why.
L6 CreateMaximum value = 48, so a scale of 1 unit = 5 marks gives bars between 5.4 and 9.6 units high — fitting comfortably. Draw rectangles on x-axis for each name with heights 7.6, 9, 6, 9.6, 5.4, 8.4 units. Label axes "Student" and "Marks". This scale avoids both tiny bars (scale too big) and bars that don't fit (scale too small).
Assertion–Reason Questions
A: In a bar graph, the width of each bar must be the same.
R: Only the length of the bar represents the data value; keeping widths equal prevents visual bias.
R: Only the length of the bar represents the data value; keeping widths equal prevents visual bias.
Answer: (a) — Equal width ensures visual comparison is fair.
A: A pictograph key (e.g. ☺ = 10) is not necessary if the data values are small.
R: Without a key, the reader cannot determine what one symbol represents.
R: Without a key, the reader cannot determine what one symbol represents.
Answer: (d) — A is false (key always needed). R is correct — it explains why A is false.
A: The scale on the y-axis of a bar graph can be chosen freely.
R: The scale must be chosen so that the largest bar fits within the drawing area and smaller bars remain readable.
R: The scale must be chosen so that the largest bar fits within the drawing area and smaller bars remain readable.
Answer: (d) — A is partly misleading (scale is not free — it must be sensible). R correctly states the rule.
Frequently Asked Questions
What is a pictograph in Class 6 Maths?
A pictograph is a chart that uses pictures or symbols to represent data. Each symbol stands for a fixed number of items. NCERT Class 6 Ganita Prakash Chapter 4 teaches students to read and draw pictographs with a clear key or scale.
What is a bar graph?
A bar graph uses rectangular bars of equal width whose heights or lengths represent data values. Taller bars mean larger quantities. NCERT Class 6 Ganita Prakash Chapter 4 introduces bar graphs as a precise way to compare categories.
How do you choose a scale for a bar graph?
Pick a scale so all bars fit neatly on the graph paper while making differences visible. For values up to 50, a scale of 1 unit = 5 is useful. For large values, try 1 unit = 10 or 100. NCERT Class 6 Chapter 4 discusses scale selection.
What is the key in a pictograph?
The key explains how many items each picture or symbol represents. For example, if one apple symbol means 5 apples, a row of 4 symbols means 20 apples. Without a key, a pictograph cannot be interpreted correctly. NCERT Class 6 Chapter 4 emphasises this.
What is the difference between a pictograph and a bar graph?
A pictograph uses pictures with a key to show quantities, best for small or simple data. A bar graph uses bars on axes with a numerical scale, better for precise comparisons and larger values. Both are covered in NCERT Class 6 Ganita Prakash Chapter 4.
How do you draw a bar graph step by step?
Step 1: Draw two perpendicular axes. Step 2: Label the horizontal axis with categories, the vertical axis with values and a scale. Step 3: Draw equal-width bars for each category with the correct height. Step 4: Add a title and key. NCERT Class 6 Chapter 4 walks through this.
Frequently Asked Questions — Data Handling and Presentation
What is Pictographs and Bar Graphs in NCERT Class 6 Mathematics?
Pictographs and Bar Graphs 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 Pictographs and Bar Graphs step by step?
To solve problems on Pictographs and Bar Graphs, 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 Pictographs and Bar Graphs important for the Class 6 board exam?
Pictographs and Bar Graphs 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 Pictographs and Bar Graphs?
Common mistakes in Pictographs and Bar Graphs 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 Pictographs and Bar Graphs?
End-of-chapter NCERT exercises for Pictographs and Bar Graphs 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.
AI Tutor
Mathematics Class 6 — Ganita Prakash
Ready