CLASS 6 MATHEMATICS | CHAPTER 4
DATA HANDLING AND PRESENTATION
Complete Answer Key with Solved Questions, Figure it Out & Chapter Mastery
Looking for the Class 6 Maths Chapter 4 Data Handling and Presentation solutions based on the APSCERT and CBSE syllabus? This complete answer key covers every question, "Figure it Out" exercise, Project Work, and Chapter Mastery question from the chapter — including collecting and organising data, frequency distribution tables, tally marks, pictographs, bar graphs, and infographics. Ideal for Class 6 students, parents helping with homework, and teachers preparing worksheets, these page-by-page solved answers make revision quick and exam-ready. Keywords: Class 6 Maths Chapter 4 answers, Data Handling and Presentation solutions, SCERT Class 6 Maths, pictograph and bar graph worksheet, frequency distribution table Class 6.
AP 6th Maths Unit 4 Data Handling and Presentation Answers
📖 Page 174
4.0 Introduction
Learning Outcomes: Collect and organise data, tabulate and represent it visually, compare different types of data interpretation, select appropriate scales, and connect data handling with other subjects like Science, Social Science and Sports.
Key Idea: Any collection of facts, numbers, measures or observations that gives information about something is called data. This chapter explores different ways to collect, organise and present data — through tables, tally marks, pictographs and bar graphs.
Key Idea: Any collection of facts, numbers, measures or observations that gives information about something is called data. This chapter explores different ways to collect, organise and present data — through tables, tally marks, pictographs and bar graphs.
4.1 Collecting and Organising Data
📖 Page 176-178
Navya and Naresh want to find the most popular game in their class. They collect data by asking each student their favourite game and prepare Table 1 listing 31 students and their favourite games (Kabaddi, Football, Hockey, Badminton, Cricket).
❀ Answer the following from Table.1
- What would you do to find the most popular game among Naresh's and Navya's classmates?
- What is the most popular game in their class?
- Try to find out the most popular game among your classmates.
- Haritha wants to respond to the questions given below. Put a tick (✓) where she needs to collect data, and a cross (✗) where she doesn't.
- What is the most popular TV show among her classmates?
- When did India get independence?
- How much water is getting wasted in her locality?
- What is the capital of India?
✔ Answers:
- We should count how many students chose each game from the list, and the game chosen by the most students is the most popular one.
- Counting the list: Kabaddi = 6, Hockey = 8, Badminton = 5, Cricket = 6, Football = 6. So Hockey is the most popular game (chosen by 8 students).
- Students should go around their own class, ask each classmate their favourite game, note it down, and then count to find the most popular one. (Answers will vary based on real classroom data.)
-
Question Needs Data Collection? a. Most popular TV show among classmates ✓ Tick b. When did India get independence ✗ Cross (fixed fact — 15 Aug 1947) c. How much water is wasted in her locality ✓ Tick d. What is the capital of India ✗ Cross (fixed fact — New Delhi)
📖 Page 178-180
Nilesh sir wants to know sweet preferences of his class using tally marks. He prepares Table 2:
| Sweets | Tally Marks | No. of Students |
|---|---|---|
| Jilebi | 𝍫 | | 6 |
| Gulab Jamun | 𝍫 |||| | 9 |
| Laddu | 𝍫 𝍫 ||| | 13 |
| Barfi | ||| | 3 |
| Rasgulla | 𝍫 || | 7 |
❀ Answer the following from Table.2
- Complete the table: a. Jilebi? b. Barfi chosen by? c. Laddu? d. Rasgulla chosen by? e. Gulab jamun?
- Is the table sufficient to distribute the correct sweet to the correct student? Explain. If not, what is the alternative?
✔ Answers:
- a. Jilebi = 6 students b. Barfi = 3 students c. Laddu = 13 students d. Rasgulla = 7 students e. Gulab jamun = 9 students
- No, this table is not sufficient to distribute sweets to the correct student, because it only shows the total count of students who like each sweet — it does not tell us which student chose which sweet. The alternative is to make a list with each student's name written next to their sweet choice (like the original list Nilesh sir collected), so each sweet can be given to the right person.
📌 Key Term — Frequency: Frequency is the number of times a specific value or item appears in a data set. The table showing frequencies of each category is called a Frequency Distribution Table.
📖 Page 182
Sandhya madam noted the shoe sizes of 27 students and arranged them in ascending order:
3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7
❀ Answer the following from the ascending order
- Help her figure out: a. Largest shoe size? b. Smallest shoe size? c. Students who wear size 5? d. Students who wear sizes larger than 4?
- How did arranging the data in ascending order help answer these questions?
- Are there other ways to arrange the data?
✔ Answers:
- a. The largest shoe size in the class is 7.
b. The smallest shoe size in the class is 3.
c. There are 10 students who wear shoe size 5.
d. There are 15 students who wear shoe sizes larger than 4 (10 of size 5 + 4 of size 6 + 1 of size 7 = 15). - Arranging data in ascending order groups the same numbers together, so we can quickly count how many times each value appears and easily spot the smallest and largest values without searching through the whole list.
- Yes — data can also be arranged in descending order, grouped in a frequency/tally table, or organised in a bar graph or pictograph.
🛠️ Project Work – 1
Collect and write the names of a few flowers you see around. Record the data in a table:
| Flower | No. of Flowers |
|---|---|
| Rose | |
| Jasmin | |
| … |
✔ Guidance for students: This is a hands-on data collection activity — go around your home or school garden, count each type of flower you see, and fill in the table yourself. Then answer: (a) the flower with the greatest count is your most-seen flower; (b) the flower with the smallest count is your least-seen flower; (c) compare your counts to see if any two flower types have the same number. Every student's table and answers will be different based on their own observations.
📖 Page 184
🛠️ Project Work – 2
Paste a small news item from a newspaper. Count the number of letters 'c', 'e', 'i', 'r', 'x' in it and fill the table:
| Letter | c | e | i | r | x |
|---|---|---|---|---|---|
| No. of times found |
✔ Guidance: a. The letter found most often is usually 'e' (it is the most common letter in English text). b. The letter found least often is usually 'x' (it is rarely used in English words). c. In ascending order of frequency, most students find the order close to: x, c, r, i, e. This happens because in English, some letters like 'e' naturally occur very often in common words, while letters like 'x' occur rarely — this pattern stays roughly the same across different pieces of writing.
Example (Solved): Anjali collected data on how students travel to school. Prepare a frequency distribution table.
| Transport | Tally Marks | Frequency |
|---|---|---|
| Walk | 𝍫𝍫 ||| | 13 |
| Bus | 𝍫 || | 7 |
| Bicycle | |||| | 4 |
| Auto | 𝍫 | 5 |
| Tricycle | | | 1 |
📖 Page 186-188
✏️ Figure it Out – 4.1
Q1. Chinnu listed the means of transport passing his house from 9-10 a.m.: bike, car, bike, bus, bike, bike, bike, auto, bicycle, tricycle, bicycle, auto, car, scooter, car, auto, bicycle, bike, car, auto, bike, scooter, bike, car, bicycle, scooter, bicycle, scooter, bike, bus, auto, auto, bike, bicycle, bus, bike, bicycle, scooter, bus, scooter, auto, bike, scooter, bicycle, bike, tricycle, auto, scooter, car, scooter.
- Prepare a frequency distribution table for the data.
- Which means of transport was used the most?
- If you were there to collect this data, how could you do it? Write the steps.
✔ Answer:
b. Bike was used the most (13 times).
c. Steps to collect this data: (1) Sit at a spot where you can see the road clearly. (2) Note down every vehicle that passes, one by one, in a list or using tally marks. (3) Continue for the full time period (9-10 a.m.). (4) Count the tally marks for each type of vehicle to get the frequency table.
| Transport | Frequency |
|---|---|
| Bike | 13 |
| Scooter | 9 |
| Auto | 8 |
| Bicycle | 8 |
| Car | 6 |
| Bus | 4 |
| Tricycle | 2 |
c. Steps to collect this data: (1) Sit at a spot where you can see the road clearly. (2) Note down every vehicle that passes, one by one, in a list or using tally marks. (3) Continue for the full time period (9-10 a.m.). (4) Count the tally marks for each type of vehicle to get the frequency table.
Q2. Roll a die 15 times and record the number each time. Prepare a frequency distribution table using tally marks. Find: a. minimum number of times, b. maximum number of times, c. numbers that appeared an equal number of times.
✔ Answer (Sample activity): This is a hands-on experiment — actually roll a die 15 times and tally the results yourself, since every attempt gives different numbers. As a model example, if you rolled and got: 2,4,6,1,3,2,5,6,4,2,1,6,3,5,2 → the frequency table would be: 1→2, 2→4, 3→2, 4→2, 5→2, 6→3 (total=15). Here, the minimum number of times any number appeared is 2 (for 1, 3, 4, 5), the maximum is 4 (for number 2), and numbers 1, 3, 4 and 5 appeared an equal number of times (2 each). Repeat this experiment with your own die roll and fill in your own real results.
Q3. Swapna prepared a frequency table of wickets taken by Jaspreet Bumrah in his last 30 matches:
a. What information is this table giving? b. What may be the title? c. What caught your attention? d. In how many matches has Bumrah taken 4 wickets? e. Siva says adding 0,1,2,...,7 gives the total wickets — can he get it this way? f. How would you correctly figure out the total wickets taken?
| Wickets Taken | Number of Matches |
|---|---|
| 0 | 2 |
| 1 | 4 |
| 2 | 6 |
| 3 | 8 |
| 4 | 3 |
| 5 | 5 |
| 6 | 1 |
| 7 | 1 |
✔ Answer:
a. The table shows how many matches (out of his last 30) Bumrah took each specific number of wickets in.
b. A suitable title: "Wickets Taken by Jaspreet Bumrah in his Last 30 Matches".
c. Sample observation: He most often takes exactly 3 wickets — this happened in 8 matches, more than any other count.
d. Bumrah has taken 4 wickets in 3 matches.
e. No, Siva cannot get the total this way. Simply adding 0+1+2+3+4+5+6+7 only adds each wicket-value once — it ignores how many matches had that many wickets, so it does not give the true total.
f. Step-wise Solution:
Given: Number of matches for each wicket count (0 to 7 wickets).
Task: Find the total wickets taken across all 30 matches.
Method: Multiply each wicket count by the number of matches with that count, then add all the products.
(0×2) + (1×4) + (2×6) + (3×8) + (4×3) + (5×5) + (6×1) + (7×1)
= 0 + 4 + 12 + 24 + 12 + 25 + 6 + 7 = 90
So Bumrah took a total of 90 wickets in his last 30 matches.
b. A suitable title: "Wickets Taken by Jaspreet Bumrah in his Last 30 Matches".
c. Sample observation: He most often takes exactly 3 wickets — this happened in 8 matches, more than any other count.
d. Bumrah has taken 4 wickets in 3 matches.
e. No, Siva cannot get the total this way. Simply adding 0+1+2+3+4+5+6+7 only adds each wicket-value once — it ignores how many matches had that many wickets, so it does not give the true total.
f. Step-wise Solution:
Given: Number of matches for each wicket count (0 to 7 wickets).
Task: Find the total wickets taken across all 30 matches.
Method: Multiply each wicket count by the number of matches with that count, then add all the products.
(0×2) + (1×4) + (2×6) + (3×8) + (4×3) + (5×5) + (6×1) + (7×1)
= 0 + 4 + 12 + 24 + 12 + 25 + 6 + 7 = 90
So Bumrah took a total of 90 wickets in his last 30 matches.
4.2 Pictographs
📖 Page 188-190
A pictograph represents data through pictures. Table showing "Modes of Travelling" (1 student = 😊): Private Car (4), Public Bus (5), School Bus (10), Cycle (3), Walking (7).
Which mode of travel is used by the most / least number of students? | Example: Nanda Kishore's pictograph on sleep habits (1 △ = 10 children): Always = 5△, Sometimes = 2△+half△, Never = 4△.
1. Children who always slept ≥9 hrs? 2. Children who sometimes slept ≥9 hrs? 3. Children who always slept <9 hrs?
1. Children who always slept ≥9 hrs? 2. Children who sometimes slept ≥9 hrs? 3. Children who always slept <9 hrs?
✔ Answers: Most used mode = School Bus (10 students); Least used = Cycle (3 students).
Sleep pictograph: 1. Always ≥9 hrs = 5 × 10 = 50 children. 2. Sometimes = (2×10) + 5 (half) = 25 children. 3. Never (i.e., always <9 hrs) = 4 × 10 = 40 children.
Sleep pictograph: 1. Always ≥9 hrs = 5 × 10 = 50 children. 2. Sometimes = (2×10) + 5 (half) = 25 children. 3. Never (i.e., always <9 hrs) = 4 × 10 = 40 children.
📖 Page 192-196 — 4.2.1 Drawing a Pictograph
Vijay recorded absent students by class (I–VIII): 3,5,4,2,0,1,5,7 and drew Pictograph-1 using 1 😊 = 1 student. Fhiredouse & Sangita recorded present students: 30,35,20,25,30,25,30,20. Fhiredouse used 1 😊 = 5 students (Pictograph-2); Sangita used 1 😊 = 10 students with a half-symbol for 5 (Pictograph-3).
💬 Math Talk: What problems arise while making a pictograph if the total in a class is 33 or 27 (not a clean multiple of the scale)?
✔ Answer: When a number isn't an exact multiple of the scale (e.g., scale=10 but value=33), we can't draw whole symbols only — we need to draw a partial symbol (like ⅓ of a picture) to represent the remainder, which can be tricky to draw accurately and read precisely.
✔ Answer: When a number isn't an exact multiple of the scale (e.g., scale=10 but value=33), we can't draw whole symbols only — we need to draw a partial symbol (like ⅓ of a picture) to represent the remainder, which can be tricky to draw accurately and read precisely.
✏️ Figure it Out – 4.2
📖 Page 196-198
Q1. Pictograph of books borrowed from a library (📖📖 = 1 book): Monday=5, Tuesday=4, Wednesday=2, Thursday=0, Friday=5, Saturday=8.
- On which day were the minimum books borrowed?
- Total books borrowed during the week?
- On which day were the maximum books borrowed? Possible reason?
✔ Answer: a. Minimum borrowed on Thursday (0 books). b. Total = 5+4+2+0+5+8 = 24 books. c. Maximum borrowed on Saturday (8 books) — likely because it's a weekend/holiday and students have more free time to read and borrow books.
Q2. Kites sold by Anil: Chandu=250, Rani=300, Rukhsana=100, Arjun=450, Mary=250, Poonam=700. Prepare a pictograph using 🪁=100 kites.
- Symbols for Rani?
- Who purchased the maximum kites?
- Who purchased more — Arjun or Chandu?
- Rukhsana says Poonam purchased more than double Rani's kites. Is she correct?
✔ Answer:
a. Rani's kites (300) = 3 symbols.
b. Poonam purchased the maximum kites (700).
c. Arjun purchased more kites than Chandu (450 > 250).
d. Rani = 300, so double Rani = 600. Poonam purchased 700, which is more than 600. So yes, Rukhsana is correct — Poonam purchased more than double what Rani purchased.
| Shopkeeper | Symbols (🪁=100) |
|---|---|
| Chandu | 🪁🪁½ (2.5) |
| Rani | 🪁🪁🪁 (3) |
| Rukhsana | 🪁 (1) |
| Arjun | 🪁🪁🪁🪁½ (4.5) |
| Mary | 🪁🪁½ (2.5) |
| Poonam | 🪁🪁🪁🪁🪁🪁🪁 (7) |
b. Poonam purchased the maximum kites (700).
c. Arjun purchased more kites than Chandu (450 > 250).
d. Rani = 300, so double Rani = 600. Poonam purchased 700, which is more than 600. So yes, Rukhsana is correct — Poonam purchased more than double what Rani purchased.
📖 Page 200
Q3. Pictograph of tractors (🚜=1 tractor) in 5 villages: A=6, B=5, C=8, D=3, E=6.
- Least tractors?
- Most tractors?
- How many more tractors does C have than B?
- Kamala says Village D has half the tractors of Village E — is she right?
✔ Answer: a. Least = Village D (3). b. Most = Village C (8). c. C − B = 8 − 5 = 3 more tractors. d. Village E = 6, half of E = 3, and Village D = 3. So yes, Kamala is right — Village D has exactly half the tractors of Village E.
Q4. Indian Pariah dogs in six villages: A=18, B=36, C=12, D=48, E=18, F=24. Prepare a pictograph and answer:
- Useful scale or key?
- How many symbols for Village B?
- Harika says B+D together will be more than the other 4 villages combined. Is she right?
✔ Answer: a. Since all values (18,36,12,48,18,24) are multiples of 6, a useful scale is 1 🐕 symbol = 6 dogs. This gives whole numbers of symbols for every village: A=3, B=6, C=2, D=8, E=3, F=4.
b. Village B = 36 ÷ 6 = 6 symbols.
c. B + D = 36 + 48 = 84. Other 4 villages (A+C+E+F) = 18+12+18+24 = 72. Since 84 > 72, yes, Harika is right — Village B and D together have more dogs than the other four villages combined.
b. Village B = 36 ÷ 6 = 6 symbols.
c. B + D = 36 + 48 = 84. Other 4 villages (A+C+E+F) = 18+12+18+24 = 72. Since 84 > 72, yes, Harika is right — Village B and D together have more dogs than the other four villages combined.
📖 Page 202
Q5. Girl students pictograph (👧 icon = 4 girls) for Classes 1-8. Observe and answer:
- Which class has the least number of girl students?
- Difference between girls in Class 5 and Class 6?
- If two more girls join Class 2, how would the graph change?
- How many girls are there in Class 7?
✔ Answer (based on the icons shown): Class 1=24, Class 2=18, Class 3=16, Class 4=14, Class 5=10, Class 6=16, Class 7=12, Class 8=6 girls (approx., reading full icon=4 girls, half icon=2 girls).
a. Least girls = Class 8 (6 girls).
b. Difference between Class 5 (10) and Class 6 (16) = 6 girls.
c. Class 2 currently has 18 girls; adding 2 more makes it 20, which is exactly 20 ÷ 4 = 5 full icons (instead of 4 full icons + 1 half icon).
d. Class 7 has 12 girls.
a. Least girls = Class 8 (6 girls).
b. Difference between Class 5 (10) and Class 6 (16) = 6 girls.
c. Class 2 currently has 18 girls; adding 2 more makes it 20, which is exactly 20 ÷ 4 = 5 full icons (instead of 4 full icons + 1 half icon).
d. Class 7 has 12 girls.
4.3 Bar Graphs
📖 Page 204-206
Bar graphs help us quickly compare categories using bars of uniform width. Vijay's data of students absent by class (I-VIII: 3,5,4,2,0,1,5,7) is shown as Bar Graph-1 using scale 1 unit = 1 student.
1. In Class 2, ______ students were absent. 2. In which class were the maximum absent? 3. Which class had full attendance?
1. In Class 2, 5 students were absent. 2. Maximum absent in Class VIII (7 students). 3. Class V had full attendance (0 absent).
📖 Page 206-208
Traffic data at Amaravathi crossing (6 a.m.-12 noon), 1 unit=100 vehicles — Bar Graph-2: 6-7=150, 7-8=1200, 8-9=1000, 9-10=800, 10-11=700, 11-12=600.
Answer the following from bar graph.2:
- How many total cars passed between 6 a.m. and 12 noon?
- Why so little traffic during 6-7 a.m.?
- Why was traffic heaviest between 7-8 a.m.?
- Why was traffic lesser each hour after 8 a.m. until 12 noon?
✔ Answer:
1. Step-wise solution:
Given: Vehicles per hour — 150, 1200, 1000, 800, 700, 600.
Task: Find total vehicles between 6 a.m. and 12 noon.
Solution: 150 + 1200 + 1000 + 800 + 700 + 600 = 4450 vehicles passed through the crossing.
2. Very early morning (6-7 a.m.) has little traffic because most people are still at home, and schools/offices haven't started yet.
3. Traffic is heaviest at 7-8 a.m. because that is peak time when students go to school and adults leave for work.
4. Traffic reduces after 8 a.m. because most people have already reached their schools/workplaces, so fewer vehicles are still travelling.
1. Step-wise solution:
Given: Vehicles per hour — 150, 1200, 1000, 800, 700, 600.
Task: Find total vehicles between 6 a.m. and 12 noon.
Solution: 150 + 1200 + 1000 + 800 + 700 + 600 = 4450 vehicles passed through the crossing.
2. Very early morning (6-7 a.m.) has little traffic because most people are still at home, and schools/offices haven't started yet.
3. Traffic is heaviest at 7-8 a.m. because that is peak time when students go to school and adults leave for work.
4. Traffic reduces after 8 a.m. because most people have already reached their schools/workplaces, so fewer vehicles are still travelling.
📖 Page 208-218 — 4.3.1 Drawing a Bar Graph
Using Nilesh sir's sweet frequency table (Jilebi=6, Gulab jamun=9, Laddu=13, Barfi=3, Rasgulla=7), Bar Graph-4 is drawn with scale 1 unit=1 student. For Smruti's runs (80,50,10,100,90,0,90,50 across 8 matches), scale 1 unit=10 runs is used (Bar Graph-5). For Imran's family expenditure, scale 1 unit=₹200 is used:
| Item | Expenditure (₹) | Bar Height (units) |
|---|---|---|
| House rent | 3000 | 15 |
| Food | 3400 | 17 |
| Education | 800 | 4 |
| Electricity | 400 | 2 |
| Transport | 600 | 3 |
| Miscellaneous | 1200 | 6 |
📖 Page 218
Use Bar Graph-6 to answer: 1. On which item does Imran's family spend the most and second most? 2. Is the cost of electricity about one-half the cost of education? 3. Is the cost of education less than one-fourth the cost of food?
1. Most spent on Food (₹3400); second most on House rent (₹3000).
2. Education = ₹800, half of it = ₹400. Electricity = ₹400. So yes, electricity cost is exactly one-half the cost of education.
3. One-fourth of Food (3400) = 850. Education = ₹800, which is less than ₹850. So yes, education cost is less than one-fourth the cost of food.
2. Education = ₹800, half of it = ₹400. Electricity = ₹400. So yes, electricity cost is exactly one-half the cost of education.
3. One-fourth of Food (3400) = 850. Education = ₹800, which is less than ₹850. So yes, education cost is less than one-fourth the cost of food.
📌 Summary: Bar graphs use equally-spaced, equal-width bars whose length/height shows the frequency of each category. Choosing the right scale (based on minimum and maximum values) makes the graph fit well and look clear. Bar markings must always start from zero.
✏️ Figure it Out – 4.3
📖 Page 220
Q1. Samantha's tea garden data — Mites=6, Caterpillars=10, Beetles=5, Butterflies=3, Grasshoppers=2. Help her prepare a bar graph.
✔ Bar Graph (scale: 1 unit = 1 insect):
Caterpillars have the tallest bar (10) — the most commonly seen insect in the tea garden.
Mites
6
6
Caterpillars
10
10
Beetles
5
5
Butterflies
3
3
Grasshoppers
2
2
📖 Page 220-222
Q2. Tickets sold: Chennai=24, Bangalore=20, Hyderabad=16, Delhi=28, Vijayawada=16. Bar for Chennai=6 units, Hyderabad=4 units. A portion of the graph was erased.
- Write tickets sold for Chennai above the bar.
- Write tickets sold for Delhi above the bar.
- What is the scale for this graph?
- Draw the correct bar for Bangalore.
- Add the scale on the vertical axis.
- Are the bars for Chennai and Delhi correct? If not, draw the correct bar(s).
✔ Answer: a. Chennai = 24. b. Delhi = 28.
c. Step-wise: Chennai bar = 6 units = 24 tickets, so 1 unit = 24÷6 = 4 tickets. Check with Hyderabad: 4 units × 4 = 16 ✓ matches. So scale = 1 unit length = 4 tickets.
d. Bangalore = 20 tickets ÷ 4 = 5 unit bar.
e. Vertical axis labels: 0, 4, 8, 12, 16, 20, 24, 28 (in steps of 4).
f. Chennai (6 units = 24 ✓) and Delhi (7 units = 28 ✓) bars are correct as drawn — only the scale numbers on the axis were erased and need to be added back.
c. Step-wise: Chennai bar = 6 units = 24 tickets, so 1 unit = 24÷6 = 4 tickets. Check with Hyderabad: 4 units × 4 = 16 ✓ matches. So scale = 1 unit length = 4 tickets.
d. Bangalore = 20 tickets ÷ 4 = 5 unit bar.
e. Vertical axis labels: 0, 4, 8, 12, 16, 20, 24, 28 (in steps of 4).
f. Chennai (6 units = 24 ✓) and Delhi (7 units = 28 ✓) bars are correct as drawn — only the scale numbers on the axis were erased and need to be added back.
Q3. Survey of 120 students on preferred free-time activity: 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 most other than playing?
✔ Answer: Bar heights (÷5): Playing=9 units, Reading=6 units, Watching TV=4 units, Listening=2 units, Painting=3 units.
Other than playing, Reading story books (30 students) is preferred the most.
Playing
45
45
Reading
30
30
TV
20
20
Music
10
10
Painting
15
15
📖 Page 222-224
Q4. Tree saplings planted during the first week of July (bar graph): Monday=50, Tuesday=40, Wednesday=30, Thursday=40, Friday=50, Saturday=60, Sunday=40.
- Total saplings planted on Wednesday and Thursday?
- Total saplings planted during the whole week?
- Greatest and least number planted — on which days, and why?
✔ Answer:
a. Wednesday + Thursday = 30 + 40 = 70 saplings.
b. Step-wise: 50+40+30+40+50+60+40 = 310 saplings planted during the whole week.
c. Greatest planted on Saturday (60) — likely a holiday, so more students and teachers could join. Least planted on Wednesday (30) — probably a regular school day with normal classes and less time for outdoor activity.
a. Wednesday + Thursday = 30 + 40 = 70 saplings.
b. Step-wise: 50+40+30+40+50+60+40 = 310 saplings planted during the whole week.
c. Greatest planted on Saturday (60) — likely a holiday, so more students and teachers could join. Least planted on Wednesday (30) — probably a regular school day with normal classes and less time for outdoor activity.
📖 Page 224-226
Q5. Project Tiger data (2006-2022): 2006=1400, 2010=1700, 2014=2200, 2018=3000, 2022=3700. Murthy and Divya's bar graph has a few mistakes. Find and fix them.
✔ Answer: Comparing the drawn bars with the table, some bar lengths don't match their correct values on the scale (for example, the bars for 2014 and 2018 need to be checked carefully against the axis). To fix this, each bar's length must be redrawn so it exactly matches its table value using a consistent scale — the corrected bar graph should show bars increasing steadily in length as: 2006 (shortest) → 2010 → 2014 → 2018 → 2022 (longest, 3700), since the number of tigers has been rising every four years.
4.4 Artistic and Aesthetic Considerations
📖 Page 226-232
Tallest mountains on each continent — Everest (Asia, 8848m), Aconcagua (S. America, 6962m), Denali (N. America, 6194m), Kilimanjaro (Africa, 5895m), Elbrus (Europe, 5642m), Vinson Massif (Antarctica, 4892m), Koscuiszko (Australia, 2228m). This data is shown as a horizontal bar graph, then rotated into a vertical column graph, and finally as a colourful mountain-shaped infographic — though the infographic (with taller triangles also drawn wider) can be slightly misleading since it implies taller mountains are also "bigger," not just taller.
🧮 Quick Maths: What is 5642 × 2?
✔ Step-wise Solution: Given: 5642 × 2. Task: Multiply. Solution: 5642 × 2 = 11,284.
✔ Step-wise Solution: Given: 5642 × 2. Task: Multiply. Solution: 5642 × 2 = 11,284.
🔍 Let's Explore
- If you wanted to visually represent heights of the tallest persons in each class, would you use vertical or horizontal bars? Why?
- For the longest rivers on each continent, would you prefer vertical or horizontal bars? Why? Which continents have the longest rivers?
✔ Answers:
1. Vertical bars would be better, because height is naturally measured upward from the ground, so vertical bars visually match the idea of "tallness" more intuitively.
2. Horizontal bars would be better, because river lengths run across land (like horizontal distances), similar to how distances are usually shown. Based on general knowledge, the Nile (Africa) and the Amazon (South America) are among the world's longest rivers, while the Yangtze (Asia) is Asia's longest river.
1. Vertical bars would be better, because height is naturally measured upward from the ground, so vertical bars visually match the idea of "tallness" more intuitively.
2. Horizontal bars would be better, because river lengths run across land (like horizontal distances), similar to how distances are usually shown. Based on general knowledge, the Nile (Africa) and the Amazon (South America) are among the world's longest rivers, while the Yangtze (Asia) is Asia's longest river.
📌 Infographics Note: Infographics combine data with artistic visuals to make information more engaging. However, we must be careful — if pictures are not drawn to accurate proportion (e.g., making bars both taller and wider), they can accidentally mislead the reader about the real data.
🏆 CHAPTER MASTERY
📖 Page 232-240
I. Answer the following questions
- Using tally marks, which one represents the number 7? a) 𝍫𝍫 b) mixed slashes c) (||||) || d) 𝍫 ||
- Marks (out of 10) by 15 students: 8,0,5,8,3,0,8,10,10,3,4,8,7,8,9. Number of students who scored ≥8 is: a) 5 b) 8 c) 6 d) 7
- Fill the table (shirt sizes of 40 students):
Shirt Size Tally Marks No. of Students 30 ||| 3 32 𝍫 5 34 𝍫 ||| 8 36 𝍫 || 7 38 𝍫 𝍫 10 40 𝍫 || 7
✔ Answers:
Q1. Answer: (d) — a proper tally group of 5 (𝍫) plus 2 more single strokes correctly shows 7.
Q2. Step-wise: Marks ≥ 8 from the list are: 8, 8, 8, 10, 10, 8, 8, 9 → that is 8 students. Answer: (b) 8.
Q3. Missing values filled above: Size 32 → 5 students; Size 34 → 𝍫 ||| (5+3); Size 36 → 7 students; Size 38 → 𝍫𝍫 (5+5); Size 40 → 𝍫 || (5+2). Check: 3+5+8+7+10+7 = 40 ✓
Q1. Answer: (d) — a proper tally group of 5 (𝍫) plus 2 more single strokes correctly shows 7.
Q2. Step-wise: Marks ≥ 8 from the list are: 8, 8, 8, 10, 10, 8, 8, 9 → that is 8 students. Answer: (b) 8.
Q3. Missing values filled above: Size 32 → 5 students; Size 34 → 𝍫 ||| (5+3); Size 36 → 7 students; Size 38 → 𝍫𝍫 (5+5); Size 40 → 𝍫 || (5+2). Check: 3+5+8+7+10+7 = 40 ✓
II. True or False
- In a pictograph, if a symbol 🍀 represents 20 flowers in a basket then 🍀🍀🍀 stands for 30 flowers.
- In a bar graph, the width of bars may be unequal.
- In a bar graph, the gap between two consecutive bars may not be the same.
Q4. False — 3 symbols × 20 = 60 flowers, not 30.
Q5. False — all bars in a bar graph must have equal (uniform) width.
Q6. False — the gap between consecutive bars must always be the same (uniform spacing).
Q5. False — all bars in a bar graph must have equal (uniform) width.
Q6. False — the gap between consecutive bars must always be the same (uniform spacing).
III. Solve the following
- Grades of 30 students: B,C,C,E,A,C,B,B,D,D,D,D,B,C,C,C,A,C,B,E,A,D,C,B,E,C,B,E,C,D. Arrange in a table using tally marks.
- Pictograph (📘=50 students) of subject popularity: Hindi (4 icons), English (3 icons), Mathematics (4 icons), Science (2 icons), Social Studies (2 icons).
- Which subject is most popular?
- How many students like Mathematics?
- Find the number of students who like subjects other than Mathematics and Science.
✔ Q7 Answer:
Total = 3+7+10+6+4 = 30 ✓
✔ Q8 Answer: Number of students per subject (icon × 50): Hindi=200, English=150, Mathematics=200, Science=100, Social Studies=100.
a. Most popular subjects: Hindi and Mathematics (200 students each — tied for most popular).
b. Students who like Mathematics = 200.
c. Step-wise: Subjects other than Maths and Science = Hindi + English + Social Studies = 200 + 150 + 100 = 450 students.
| Grade | Tally Marks | Frequency |
|---|---|---|
| A | ||| | 3 |
| B | 𝍫 || | 7 |
| C | 𝍫 𝍫 | 10 |
| D | 𝍫 | | 6 |
| E | |||| | 4 |
✔ Q8 Answer: Number of students per subject (icon × 50): Hindi=200, English=150, Mathematics=200, Science=100, Social Studies=100.
a. Most popular subjects: Hindi and Mathematics (200 students each — tied for most popular).
b. Students who like Mathematics = 200.
c. Step-wise: Subjects other than Maths and Science = Hindi + English + Social Studies = 200 + 150 + 100 = 450 students.
📖 Page 238-240
- Bar graph of National Highway lengths (1 unit=200 km): N.H.10, N.H.9, N.H.8, N.H.3, N.H.2.
- Longest N.H. among these?
- Shortest N.H. among these?
- Length of N.H.9?
- Which N.H.'s length is about 3 times N.H.10's length?
- Land area (sq. units) for crops: Rice=50, Wheat=30, Pulses=20, Sugarcane=25, Cotton=10. Babji's bar graph has an error — find and correct it.
✔ Q9 Answer (reading bar lengths against the scale 1 unit=200 km): N.H.2≈1500km, N.H.3≈1200km, N.H.8≈1400km, N.H.9≈900km, N.H.10≈300km.
a. Longest = N.H.2 (1500 km). b. Shortest = N.H.10 (300 km). c. N.H.9 length = 900 km.
d. Step-wise: 3 × N.H.10 = 3 × 300 = 900 km, which matches N.H.9's length. So N.H.9 is about 3 times the length of N.H.10.
✔ Q10 Answer: Comparing Babji's graph to the table, the Sugarcane bar is drawn too tall (shown close to 28 instead of 25) and the Cotton bar is drawn too tall (shown close to 15 instead of 10). Also, the chart has no proper title — "Chart Title" should be replaced with something meaningful like "Area of Land Used for Different Crops." Correcting these: Sugarcane bar should reach exactly 25, and Cotton bar should reach exactly 10, matching the table.
a. Longest = N.H.2 (1500 km). b. Shortest = N.H.10 (300 km). c. N.H.9 length = 900 km.
d. Step-wise: 3 × N.H.10 = 3 × 300 = 900 km, which matches N.H.9's length. So N.H.9 is about 3 times the length of N.H.10.
✔ Q10 Answer: Comparing Babji's graph to the table, the Sugarcane bar is drawn too tall (shown close to 28 instead of 25) and the Cotton bar is drawn too tall (shown close to 15 instead of 10). Also, the chart has no proper title — "Chart Title" should be replaced with something meaningful like "Area of Land Used for Different Crops." Correcting these: Sugarcane bar should reach exactly 25, and Cotton bar should reach exactly 10, matching the table.
- ATMs of different banks in a city: HDFC=5, Union=15, Indian=20, SBI=25, Canara=10. Draw a bar graph using a suitable scale.
✔ Answer: Using scale 1 unit = 5 ATMs, bar heights: HDFC=1 unit, Union=3 units, Indian=4 units, SBI=5 units, Canara=2 units.
HDFC
5
5
Union
15
15
Indian
20
20
SBI
25
25
Canara
10
10
📖 Page 240
📋 SUMMARY
- Data can be organised in a tabular form using tally marks for easy analysis and interpretation.
- Frequency is the count of occurrences of values, measures or observations.
- Pictographs represent data using pictures/objects — each picture represents a frequency (a scale), which must always be specified.
- Bar graphs use bars of uniform width; their length/height indicates the frequency. The scale used must be specified.
- Choosing an appropriate scale is important to accurately and effectively represent data and make it visually appealing.
- Artistic and aesthetic aspects (colours, pictures, orientation) add visual appeal, but data presentation must always remain accurate and not misleading — this careful balance is part of data handling and presentation.
📚 Class 6 Mathematics — Chapter 4: Data Handling and Presentation | Complete SCERT/CBSE Answer Key
