Page 176
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To figure out the most popular game in their class, what should Navya and Naresh do? Can you help them?
Navya and Naresh should ask each classmate their favourite game, record the responses in a list, and then organize the data into a frequency table with tally marks to count how many students chose each game.
Page 178
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1. What would you do to find the most popular game among Naresh's and Navya's classmates?
Count the number of students who chose each sport from Table 1 and prepare a frequency table.
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2. What is the most popular game in their class?
Counting from Table 1:
- Hockey: 8 students (Aadya, Leela, Afshan, Yasodha, Gurpreet, Rehana, Sanvi, Harsha)
- Kabaddi: 6 students (Karthik, Simran, Ankita, Teja, Ananya, Mohan)
- Cricket: 6 students (Neeraja, Tahira, Sankar, Bhavya, Yadaiah, Jyothi)
- Football: 5 students (Monika, Pushkar, Janvi, Yuvraj, Rajesh, Thara → 6 students)
- Badminton: 5 students (Bhaskar, Nandu, Densy, Kushal, Johnpal)
The most popular game is Hockey (chosen by 8 students). -
3. Try to find out the most popular game among your classmates.
Conduct a classroom survey by asking all classmates to name their favourite game, count the votes for each game, and identify the game with the highest frequency (e.g., Cricket or Badminton).
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4. Haritha wants to respond to the questions given below. Put a tick (✓) for the questions where she needs to carry out data collection and put a cross (✗) for the questions where she doesn't need to collect data.
a. What is the most popular TV show among her classmates?
b. When did India get independence?
c. How much water is getting wasted in her locality?
d. What is the capital of India?a. What is the most popular TV show among her classmates? → [✓] (Needs Data Collection)
b. When did India get independence? → [✗] (Fixed historical fact)
c. How much water is getting wasted in her locality? → [✓] (Needs Data Collection)
d. What is the capital of India? → [✗] (Fixed geographical fact)
Page 180
Table 2: Frequency Distribution of Sweets
| Sweets | Tally Marks | No. of Students |
|---|---|---|
| Jilebi | 卌 | | 6 |
| Gulab jamun | 卌 |||| | 9 |
| Laddu | 卌 卌 ||| | 13 |
| Barfi | ||| | 3 |
| Rasgulla | 卌 || | 7 |
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1. Complete the table to help Nilesh sir to purchase the correct numbers of sweets:
a. How many students chose jilebi?
b. Barfi was chosen by ___ students.
c. How many students chose Laddu?
d. Rasgulla was chosen by ___ students.
e. How many students chose gulab jamun?a. 6 students chose jilebi.
b. Barfi was chosen by 3 students.
c. 13 students chose Laddu.
d. Rasgulla was chosen by 7 students.
e. 9 students chose gulab jamun. -
2. Is the above table sufficient to distribute each type of sweet to the correct student? Explain. If it is not sufficient, what is the alternative?
No, the frequency table gives only the total quantity of each sweet needed, but does not list individual student names with their choices. To distribute correctly, the teacher needs the original list containing each student's name alongside their chosen sweet.
Page 182
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1. Help Sandhya madam to figure out the following from the ascending order list (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):
a. The largest shoe size in the class is ___
b. The smallest shoe size in the class is ___
c. There are ___ students who wear shoe size 5.
d. There are ___ students who wear shoe sizes larger than 4.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 (ten 5s + four 6s + one 7 = 15). -
2. How did arranging the data in ascending order help to answer these questions?
Arranging in ascending order grouped identical sizes together and placed the smallest value at the beginning and the largest value at the end, making counting and comparing instant and error-free.
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3. Are there other ways to arrange the data?
Yes, data can also be arranged in descending order (from largest to smallest) or represented as a frequency distribution table using tally marks.
Page 184
Project Work-2
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Count the occurrences of letters in an English news clipping and analyze:
a. The letter found the most number of times is ___
b. The letter found the least number of times is ___
c. List the five letters 'c', 'e', 'i', 'r', 'x' in ascending order of frequency. Why do you think this is the case?a. The letter found the most number of times is e.
b. The letter found the least number of times is x.
c. Ascending order of frequency: x < c < r < i < e.
Reason: In the English language, vowels like 'e' and 'i' and consonants like 'r' and 'c' are used very frequently in everyday words, while 'x' is one of the rarest letters used in vocabulary.
Figure it Out - 4.1 (Page 186)
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1. Chinnu listed the vehicles passing across the road from 9 a.m. to 10 a.m.
a. Prepare a frequency distribution table for the data.
b. Which means of transport was used the most?
c. If you were there to collect this data, how could you do it? Write the steps or process.a. Frequency Distribution Table:
b. Bike was used the most (15 times).Means of Transport Tally Marks Frequency Bike 卌 卌 卌 15 Scooter 卌 卌 10 Bicycle 卌 ||| 8 Auto 卌 || 7 Car 卌 | 6 Bus |||| 4 Tricycle || 2 Total 52
c. Process:
1. Sit safely by the roadside with a notebook and pen.
2. Draw a table with vehicle categories.
3. Put a tally mark against the corresponding vehicle type as soon as it passes by.
4. Bundle tally marks into groups of 5 and sum them up after 10 a.m. -
3. Swapna prepared a frequency distribution table of wickets taken by Jaspreet Bumrah in 30 matches:
a. What information is this table giving?
b. What may be the title of this table?
c. What caught your attention in this table?
d. In how many matches has Bumrah taken 4 wickets?
e. Siva says, "If we want to know the total number of wickets he has taken in his last 30 matches, we have to add the numbers 0, 1, 2, 3 up to 7." Can Siva get the total number of wickets taken in this way? Give Reason.
f. How would you correctly figure out the total number of wickets taken by Bumrah in his last 30 matches, using this table?a. The table gives the frequency of matches in which Jaspreet Bumrah took specific numbers of wickets (0 to 7 wickets) across 30 matches.
b. Title: "Number of Wickets Taken by Jaspreet Bumrah in 30 Matches".
c. In most matches (8 matches), he took 3 wickets, and in only 2 matches did he go wicketless (0 wickets).
d. Bumrah has taken 4 wickets in 3 matches.
e. No, Siva cannot get the total wickets this way. Simply adding 0 to 7 ignores how many times (frequency) each wicket count occurred.
f. Correct Method: Multiply each wicket count by its respective number of matches and sum the products:
$\text{Total Wickets} = (0 \times 2) + (1 \times 4) + (2 \times 6) + (3 \times 8) + (4 \times 3) + (5 \times 5) + (6 \times 1) + (7 \times 1)$
$= 0 + 4 + 12 + 24 + 12 + 25 + 6 + 7 = \mathbf{90\text{ wickets}}$.
Page 188
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Answer based on Modes of Travelling pictograph:
- Which mode of travel is used by the most number of students?
- Which mode of travel is used by the least number of students?- School Bus is used by the most number of students.
- Private Car / Cycle is used by the least number of students.
Page 190
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Using Nanda Kishore's sleep response pictograph (where 1 symbol = 10 Children):
1. What is the number of children who always slept at least 9 hours at night?
2. How many children sometimes slept at least 9 hours at night?
3. How many children always slept less than 9 hours each night? Explain how you got your answer.1. Always: 5 full symbols → $5 \times 10 =$ 50 children.
2. Sometimes: 2 full symbols + 1 half symbol → $20 + 5 =$ 25 children.
3. Never (Always less than 9 hours): 4 full symbols → $4 \times 10 =$ 40 children.
Figure it Out - 4.2 (Page 196)
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1. The pictograph shows library books borrowed in a week (where 1 symbol = 1 Book):
a. On which day were the minimum number of books borrowed?
b. What was the total number of books borrowed during the week?
c. On which day were the maximum number of books borrowed? What may be the possible reason?a. Tuesday (only 1 book was borrowed).
b. $\text{Total books} = 5 + 1 + 3 + 4 + 7 + 8 =$ 28 books.
c. Saturday (8 books were borrowed). Reason: Students borrow more storybooks on weekends/Saturday to read over the Sunday holiday.
Page 198
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2. Anil sells kites to six shopkeepers: Chandu (250), Rani (300), Rukhsana (450), Arjun (200), Mary (250), Poonam (700). Prepare a pictograph (1 symbol = 100 kites) and answer:
a. How many symbols represent the kites that Rani purchased?
b. Who purchased the maximum number of kites?
c. Who purchased more kites, Arjun or Chandu?
d. Rukhsana says Poonam purchased more than double the number of kites that Rani purchased. Is she correct? Why?Pictograph Representation:
a. 3 symbols represent Rani's purchase.Shopkeeper Kites Sold (1 symbol = 100 kites) Total Kites Chandu ◆◆ ◇ (2.5 symbols) 250 Rani ◆◆◆ (3 symbols) 300 Rukhsana ◆◆◆◆ ◇ (4.5 symbols) 450 Arjun ◆◆ (2 symbols) 200 Mary ◆◆ ◇ (2.5 symbols) 250 Poonam ◆◆◆◆◆◆◆ (7 symbols) 700
b. Poonam purchased the maximum number of kites (700 kites).
c. Chandu purchased more kites (250 > 200).
d. Yes, Rukhsana is correct. Double of Rani's purchase $= 2 \times 300 = 600$ kites. Poonam purchased 700 kites, which is strictly greater than 600.
Page 200
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3. Tractors in five villages (where 1 icon = 1 Tractor): Village A (6), Village B (8), Village C (12), Village D (3), Village E (6). Answer:
a. Which village has the least number of tractors?
b. Which village has the most number of tractors?
c. How many more tractors does Village C have than Village B?
d. Kamala says, "Village D has half the number of tractors as Village E." Is she right?a. Village D has the least number of tractors (3 tractors).
b. Village C has the most number of tractors (12 tractors).
c. $12 - 8 =$ 4 more tractors.
d. Yes, Kamala is right. Half of Village E $= 6 \div 2 = 3$, which equals Village D. -
4. Indian Pariah dogs in Tirupati district: Village A: 18, Village B: 36, Village C: 12, Village D: 48, Village E: 18, Village F: 24.
a. What will be a useful scale or key to draw this pictograph?
b. How many symbols will you use to represent the dogs in Village B?
c. Harika said that the number of these dogs in Village B and Village D together will be more than the number of these dogs in the other 4 villages. Is she right? Give reasons.a. A useful scale is 1 symbol = 6 dogs (since all values are exact multiples of 6).
b. For Village B (36 dogs): $36 \div 6 =$ 6 symbols.
c. Yes, Harika is right.
- Village B + Village D $= 36 + 48 = 84\text{ dogs}$.
- Remaining 4 villages (A + C + E + F) $= 18 + 12 + 18 + 24 = 72\text{ dogs}$.
Since $84 > 72$, her statement is correct.
Page 202
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5. Number of girl students in each class (where 1 icon = 4 Girls):
- Class 1: 6 icons = 24 girls
- Class 2: 4.5 icons = 18 girls
- Class 3: 5 icons = 20 girls
- Class 4: 3.5 icons = 14 girls
- Class 5: 2.5 icons = 10 girls
- Class 6: 4 icons = 16 girls
- Class 7: 3 icons = 12 girls
- Class 8: 1.5 icons = 6 girls
a. Which class has the least number of girl students?
b. What is the difference between the number of girls in Class 5 and 6?
c. If two more girls were admitted in Class 2, how would the graph change?
d. How many girls are there in Class 7?a. Class 8 has the least number of girl students (6 girls).
b. Difference $= 16 - 10 =$ 6 girls.
c. Adding 2 girls makes Class 2 total $= 18 + 2 = 20$ girls, changing the representation from 4.5 icons to exactly 5 complete icons.
d. Class 7 has 3 complete icons → $3 \times 4 =$ 12 girls.
Page 206
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Answer from Bar Graph-1 (Absent students):
1. In Class 2, ___ students were absent that day.
2. In which class were the maximum number of students absent?
3. Which class had full attendance that day?1. In Class 2, 5 students were absent that day.
2. Maximum students were absent in Class 8 (7 students).
3. Class 5 had full attendance (0 students absent).
Page 208
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Answer from Bar Graph-2 (Vehicular traffic):
1. How many total cars/vehicles passed through the crossing between 6 a.m. and 12 noon?
2. Why do you think so little traffic occurred during the hour of 6-7 a.m.?
3. Why do you think the traffic was the heaviest between 7-8 a.m.?
4. Why do you think the traffic was lesser and lesser each hour after 8 a.m. all the way until 12 noon?1. $\text{Total} = 150 + 1200 + 1000 + 800 + 700 + 600 =$ 4,450 vehicles.
2. Early morning (6–7 a.m.) is before offices, schools, and markets open, so few commuters are on the road.
3. 7–8 a.m. is peak morning rush hour when school buses, workers, and commuters travel simultaneously.
4. Most people have already reached their schools and workplaces by 8–9 a.m., so fewer new trips are made between 9 a.m. and 12 noon. -
Questions from Bar Graph-3 (India's Population):
- How much did the population of India increase over 50 years (1951 to 2001)?
- How much did the population increase in each decade?- Total 50-year increase: $102 - 36 =$ 66 crores.
- Decadal Increases:
* 1951–1961: $44 - 36 = 8\text{ crores}$
* 1961–1971: $54 - 44 = 10\text{ crores}$
* 1971–1981: $68 - 54 = 14\text{ crores}$
* 1981–1991: $84 - 68 = 16\text{ crores}$
* 1991–2001: $102 - 84 = 18\text{ crores}$
Page 218
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Use Bar Graph-6 (Imran's family monthly expenditure) to answer:
1. On which item does Imran's family spend the most and the 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: Food (₹3,400); Second most: House rent (₹3,000).
2. Yes. Electricity (₹400) is exactly half of Education (₹800).
3. Yes. One-fourth of Food $= 3400 \div 4 = \text{\rupee}850$. Since Education is ₹800 (< ₹850), it is less than one-fourth of the food cost.
Figure it Out - 4.3 (Page 220)
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1. Samantha collected insect data: Mites (6), Caterpillars (10), Beetles (5), Butterflies (3), Grasshoppers (2). Help her prepare a bar graph.
- Horizontal Axis: Insect categories (Mites, Caterpillars, Beetles, Butterflies, Grasshoppers).
- Vertical Axis: Number of insects (Scale: 1 unit length = 1 insect, marked from 0 to 12).
- Heights of bars: Mites = 6, Caterpillars = 10, Beetles = 5, Butterflies = 3, Grasshoppers = 2. -
2. Tickets sold at Tirupati railway station: Chennai (24), Bangalore (20), Hyderabad (16), Delhi (28), Vijayawada (16).
a. Write the number of tickets sold for Chennai above the bar.
b. Write the number of tickets sold for Delhi above the bar.
c. The bar for Chennai is 6 unit lengths and the bar for Hyderabad is 4 unit lengths. What is the scale for this graph?
d. Draw the correct bar for Bangalore.
e. Add the scale of the bar graph by placing the correct numbers on the vertical axis.
f. Are the bars for Chennai and Delhi correct in this graph?a. Number above Chennai bar = 24.
b. Number above Delhi bar = 28.
c. $\text{Scale} = 24 \div 6 = 4 \implies$ 1 unit length = 4 tickets.
d. Height for Bangalore bar $= 20 \div 4 =$ 5 unit lengths.
e. Vertical axis markings: 0, 4, 8, 12, 16, 20, 24, 28, 32.
f. Yes, Chennai has height 6 units ($6 \times 4 = 24$) and Delhi has height 7 units ($7 \times 4 = 28$), which are both correct. -
3. Survey of 120 students' free-time activities: Playing (45), Reading story books (30), Watching TV (20), Listening to music (10), Painting (15). Which activity is preferred by most students other than playing?
Reading story books (preferred by 30 students) is the most popular activity other than playing.
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4. Saplings planted during the first week of July (Monday: 52, Tuesday: 40, Wednesday: 30, Thursday: 40, Friday: 50, Saturday: 60, Sunday: 40):
a. The total number of saplings planted on Wednesday and Thursday is ___
b. The total number of saplings planted during the whole week is ___
c. The greatest number of saplings were planted on ___ and the least number of saplings were planted on ___a. Wednesday + Thursday $= 30 + 40 =$ 70 saplings.
b. Whole week total $= 52 + 40 + 30 + 40 + 50 + 60 + 40 =$ 312 saplings.
c. The greatest number were planted on Saturday (60) and the least on Wednesday (30).
Reason: Saturdays allow more free volunteer time for community plantation drives, while mid-week days have regular academic workload. -
5. Project Tiger Bar Graph Correction (2006: 1400, 2010: 1700, 2014: 2200, 2018: 3000, 2022: 3700):
What are the mistakes in the given graph and how to fix them?1. Year 2006: Bar drawn at approx 800 → Fix: Extend bar to 1400.
2. Year 2010: Bar drawn at 1500 → Fix: Extend bar to 1700.
3. Year 2014: Bar drawn at 2900 → Fix: Shorten bar to 2200.
4. Year 2018: Bar drawn at 2200 → Fix: Extend bar to 3000.
Let's Explore (Page 230)
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1. 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?
I would use a vertical bar (column) graph because physical height is measured upwards against gravity from the ground, making vertical bars naturally intuitive.
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2. If you were making a table of the longest rivers on each continent and their lengths, would you prefer to use a bar graph with vertical bars or with horizontal bars? Why?
I would prefer a horizontal bar graph because river lengths flow horizontally across the landscape parallel to the Earth's surface.
CHAPTER MASTERY (Page 234)
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I. Answer the following questions:
1. Using tally marks which one of the following represents the number 7?Answer: a) 卌 || -
2. The marks (out of 10) obtained by 15 students in a mathematics test are: 8, 0, 5, 8, 3, 0, 8, 10, 10, 3, 4, 8, 7, 8, 9. The number of students who obtained marks more than or equal to 8 is:
Marks ≥ 8 are: 8, 8, 8, 10, 10, 8, 8, 9 (total 8 students).
Answer: b) 8 -
3. Fill the following table which represents shirt size of 40 students in a school:
Shirt size Tally Marks Number of students 30 ||| 3 32 卌 5 34 卌 ||| 8 36 卌 || 7 38 卌 卌 10 40 卌 || 7 Total 40
Page 236
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II. True or False:
Statement Ans 4. In a pictograph, if a symbol represents 20 flowers in a basket then 1.5 symbols stand for 30 flowers. True 5. In a bar graph, the width of bars may be unequal. False 6. In a bar graph, the gap between two consecutive bars may not be the same. False -
7. In an examination, the grades achieved by 30 students are: 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 these grades in a table using tally marks:
Grade Tally Marks Number of Students A ||| 3 B 卌 || 7 C 卌 卌 10 D 卌 | 6 E |||| 4 Total 30 -
8. Subject popularity survey (where 1 icon = 50 students): Hindi (5.5 icons = 275), English (4 icons = 200), Mathematics (7 icons = 350), Science (6 icons = 300), Social Studies (4 icons = 200).
a) Which subject is most popular among the students?
b) How many students like Mathematics?
c) Find the number of students who like subjects other than Mathematics and Science.a) Mathematics is the most popular subject.
b) $7 \times 50 =$ 350 students like Mathematics.
c) Hindi (275) + English (200) + Social Studies (200) $= 275 + 200 + 200 =$ 675 students.
Page 238
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9. Approximate length of National Highways (Scale: 1 unit length = 200 km):
N.H. 10 (450 km), N.H. 9 (900 km), N.H. 8 (1400 km), N.H. 3 (1200 km), N.H. 2 (1500 km).
(a) Which National Highway is the longest among the above?
(b) Which National Highway is the shortest among the above?
(c) What is the length of National Highway 9?
(d) Length of which National Highway is about three times the National Highway 10?(a) N.H. 2 is the longest (approx. 1500 km).
(b) N.H. 10 is the shortest (approx. 450 km).
(c) The length of N.H. 9 is 900 km.
(d) $3 \times 450\text{ km} = 1350\text{ km} \approx$ N.H. 8 (1400 km). -
10. Area of land for different crops: Rice (50), Wheat (30), Pulses (20), Sugarcane (25), Cotton (10). Find what is wrong in Babji's bar graph and correct it.
- Error 1: The bar for Sugarcane is drawn up to approx 28 instead of exactly 25.
- Error 2: The bar for Cotton is drawn up to approx 15 instead of exactly 10.
- Correction: Reduce the sugarcane bar height to midway between 20 and 30 (25), and reduce the cotton bar height to exactly 10.
Page 240
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11. Number of ATMs in a city: HDFC Bank (5), Union Bank (15), Indian Bank (20), State Bank of India (25), Canara Bank (10). Draw a bar graph.
- Horizontal Axis: Banks (HDFC Bank, Union Bank, Indian Bank, SBI, Canara Bank).
- Vertical Axis: Number of ATMs.
- Scale: 1 unit length = 5 ATMs (marked at 0, 5, 10, 15, 20, 25, 30).
- Bar Heights:
* HDFC Bank = 1 unit (5 ATMs)
* Union Bank = 3 units (15 ATMs)
* Indian Bank = 4 units (20 ATMs)
* State Bank of India = 5 units (25 ATMs)
* Canara Bank = 2 units (10 ATMs)
