Chapter 4

NCERT Solutions - Class 6 Mathematics

Chapter 4: Data Handling and Presentation

Page No. 75

Section 4.1 — Figure it Out

Q1. What would you do to find the most popular game among Naresh's and Navya's classmates?[cite: 4]

Ans. One of the ways could be to arrange and organize the given data in a table. Think of some other ways.[cite: 4]

Q2. What is the most popular game in their class?[cite: 4]

Ans. Hockey (frequency - 8).[cite: 4]

Q4. Pari 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 (X) for the questions where she doesn't need to collect data. Discuss your answers in the classroom.[cite: 4]
a. What is the most popular TV show among her classmates?[cite: 4]
b. When did India get independence?[cite: 4]
c. How much water is getting wasted in her locality?[cite: 4]
d. What is the capital of India?[cite: 4]

Ans.
a. ✓[cite: 4]
b. X[cite: 4]
c. ✓[cite: 4]
d. X[cite: 4]

Page No. 76

Figure it Out

Q1. Complete the table to help Shri Nilesh to purchase the correct numbers of sweets:[cite: 4]
• How many students chose jalebi?[cite: 4]
• Barfi was chosen by ____ students?[cite: 4]
• How many students chose gujiya?[cite: 4]
• Rasgulla was chosen by ____ students?[cite: 4]
• How many students chose gulab jamun?[cite: 4]

Ans.
• Jalebi: 6[cite: 4]
• Barfi: 3[cite: 4]
• Gujiya: 13[cite: 4]
• Rasgulla: 7[cite: 4]
• Gulab Jamun: 9[cite: 4]

Q2. 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?[cite: 4]

Ans. No. It shows only the number of students who chose a particular sweet, and not about the sweet chosen by a particular student. One of the alternatives could be, students should be categorized according to their choice of sweet.[cite: 4]

Page No. 77

Figure it Out

Q1. Help her to figure out the following:[cite: 4]
• The largest shoe size in the class is ____[cite: 4]
• The smallest shoe size in the class is ____[cite: 4]
• There are ____ students who wear shoe size 5.[cite: 4]
• There are ____ students who wear shoe sizes larger than 4.[cite: 4]

Ans.
• Largest shoe size: 7[cite: 4]
• Smallest shoe size: 3[cite: 4]
• Wear shoe size 5: 10[cite: 4]
• Wear shoe sizes larger than 4: 15[cite: 4]

Q2. How did arranging the data in ascending order help to answer these questions?[cite: 4]

Ans. Ordered data is helpful because in this form, frequency of any data is easy to count and the given information can be used easily.[cite: 4]

Q3. Are there other ways to arrange the data?[cite: 4]

Ans. Yes, the data can be arranged in a frequency table.[cite: 4]

Page No. 83

Section 4.2 — Pictographs

Q. What could be the problems faced in preparing such a pictograph, if the total number of students present in a class is 33 or 27?[cite: 4]

Ans. Full symbol represents 10 students and half symbol represents 5 students. But to represent 3 or 7 students accurately by dividing these symbols is not possible.[cite: 4]

Q1. The pictograph shows the number of books borrowed by students, in a week, from the library of Middle School, Ginnori:[cite: 4]
a. On which day were the minimum number of books borrowed?[cite: 4]
b. What was the total number of books borrowed during the week?[cite: 4]
c. On which day were the maximum number of books borrowed? What may be the possible reason?[cite: 4]

Ans.
a. Thursday[cite: 4]
b. 24[cite: 4]
c. Saturday. One of the reasons could be that Sunday being a holiday students can read the borrowed books on Sunday.[cite: 4]

Q2. Magan Bhai sells kites at Jamnagar. Six shopkeepers from nearby villages come to purchase kites from him. Prepare a pictograph using the symbol = 100 kites and answer the following:[cite: 4]
a. How many symbols represent the kites that Rani purchased?[cite: 4]
b. Who purchased the maximum number of kites?[cite: 4]
c. Who purchased more kites, Jasmeet or Chaman?[cite: 4]
d. Rukhsana says Poonam Ben purchased more than double the number of kites that Rani purchased. Is she correct? Why?[cite: 4]

Ans.
a. 3 symbols[cite: 4]
b. Poonam Ben[cite: 4]
c. Jasmeet[cite: 4]
d. Yes. Number of kites purchased by Poonam Ben = 700 = 2 × 300 + 100[cite: 4]

Page No. 86

Section 4.3 — Attendance Analysis

Q1. In Class 2, ____ students were absent that day.[cite: 4]

Ans. 5[cite: 4]

Q2. In which class were the maximum number of students absent?[cite: 4]

Ans. Class 8[cite: 4]

Q3. Which class had full attendance that day?[cite: 4]

Ans. Class 5[cite: 4]

Page No. 88

Figure it Out

Q1. How many total cars passed through the crossing between 6 am and noon?[cite: 4]

Ans. 4450 cars[cite: 4]

Page No. 93

Section 4.4 — Expenditure & Data Representation

Q1. On which item does Imran's family spend the most and the second most?[cite: 4]

Ans. Imran's family spends the most on food and the second most on house rent.[cite: 4]

Q2. Is the cost of electricity about one-half the cost of education?[cite: 4]

Ans. Yes[cite: 4]

Q3. Is the cost of education less than one-fourth the cost of food?[cite: 4]

Ans. Yes. Cost of education = Rs. 800 and cost of food = Rs 3400 = 4 × Rs 850. So, cost of education = less than one-fourth of cost of food.[cite: 4]

Q. Samantha visited a tea garden and collected data of the insects and critters she saw there. Help her prepare a bar graph representing this data.[cite: 4]

Ans. Data points: Mites (6), Caterpillars (10), Beetles (5), Butterflies (3), Grasshoppers (2).[cite: 4]

Q2. Pooja collected data on the number of tickets sold at Bhopal railway station (Scale: 1 unit length = 4 tickets):[cite: 4]
a. Write the number of tickets sold for Vidisha above the bar.[cite: 4]
b. Write the number of tickets sold for Jabalpur above the bar.[cite: 4]
c. The bar for Vidisha is 6 unit lengths and the bar for Jabalpur is 5 unit lengths. What is the scale for this graph?[cite: 4]
d. Draw the correct bar for Sagar.[cite: 4]
e. Add the scale of the bar graph placing the correct numbers on the vertical axis.[cite: 4]
f. Are the bars for Seoni and Indore correct in this graph? If not, draw the correct bar(s).[cite: 4]

Ans.
a. 24[cite: 4]
b. 20[cite: 4]
c. 1 unit length = 4 tickets[cite: 4]
d. Bar of length representing 16 tickets.[cite: 4]
e. Vertical axis scale marked in increments of 4 (0, 4, 8, 12, 16, 20, 24, 28).[cite: 4]
f. The bar for Seoni is correct but for Indore is incorrect.[cite: 4]

Q3. Chinu listed the various means of transport that passed across the road in front of his house from 9 am to 10 am:[cite: 4]
a. Prepare a frequency distribution table for the data.[cite: 4]
b. Which means of transport was used the most?[cite: 4]
c. If you were there to collect this data, how could you do it? Write the steps or process.[cite: 4]

Ans.
a. Frequency Distribution Table: [cite: 4] [cite: 4] [cite: 4] [cite: 4] [cite: 4] [cite: 4] [cite: 4]

Means of Transport	Number
Bike	13
Car	6
Bicycle	8
Auto Rickshaw	8
Scooter	9
Bus	4
Bullock Cart	2

b. Bike[cite: 4]
c. Steps:
(i) Prepare a table with 2 columns (Means of transport & frequency).[cite: 4]
(ii) List the various means of transport as they pass across the road.[cite: 4]
(iii) Frequency should be presented using tally marks.[cite: 4]

Q5. Faiz prepared a frequency distribution table of data on the number of wickets taken by Jaspreet Bumrah in his last 30 matches:[cite: 4]
a. What information is this table giving?[cite: 4]
b. What may be the title of this table?[cite: 4]
c. What caught your attention in this table?[cite: 4]
d. In how many matches has Bumrah taken 4 wickets?[cite: 4]
e. Mayank 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 Mayank get the total number of wickets taken in this way? Why?[cite: 4]
f. How would you correctly figure out the total number of wickets taken by Bumrah in his last 30 matches, using this table?[cite: 4]

Ans.
a. This table gives information about different numbers of wickets taken by Jaspreet Bumrah across different matches.[cite: 4]
b. "Wickets Taken by Jaspreet Bumrah in Last 30 Matches".[cite: 4]
c. In 1 match, 7 wickets were taken by Jaspreet Bumrah.[cite: 4]
d. In 3 matches, Bumrah has taken 4 wickets.[cite: 4]
e. No, Mayank cannot get the total number this way. For example, 3 wickets per match were taken in 8 matches, which means a total of 24 wickets were taken.[cite: 4]
f. Prepare a 3rd column of "total wickets" (product of the two columns). Summing the 3rd column gives the total number of wickets = 90.[cite: 4]

Q6. The pictograph shows the number of tractors in five different villages:[cite: 4]
a. Which village has the smallest number of tractors?[cite: 4]
b. Which village has the most tractors?[cite: 4]
c. How many more tractors does Village C have than Village B?[cite: 4]
d. Komal says, "Village D has half the number of tractors as Village E." Is she right?[cite: 4]

Ans.
a. Village D[cite: 4]
b. Village C[cite: 4]
c. 3[cite: 4]
d. Yes[cite: 4]

Q7. The number of girl students in each class of a school is depicted by a pictograph:[cite: 4]
a. Which class has the least number of girl students?[cite: 4]
b. What is the difference between the number of girls in Class 5 and 6?[cite: 4]
c. If 2 more girls were admitted in Class 2, how would the graph change?[cite: 4]
d. How many girls are there in Class 7?[cite: 4]

Ans.
a. Class 8[cite: 4]
b. 6[cite: 4]
c. The last half symbol will be converted into a full symbol.[cite: 4]
d. 12[cite: 4]

Q8. Mudhol Hounds breed initiative data in 6 villages: Village A: 18, Village B: 36, Village C: 12, Village D: 48, Village E: 18, Village F: 24.[cite: 4]
a. What will be a useful scale or key to draw this pictograph?[cite: 4]
b. How many symbols will you use to represent the dogs in Village B?[cite: 4]
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? Give reasons.[cite: 4]

Ans.
a. Scale: 1 symbol = 6 dogs (since all quantities are multiples of 6).[cite: 4]
b. 6 symbols[cite: 4]
c. Yes, Kamini is right as Village B + Village D = 36 + 48 = 84, which is greater than the other 4 villages combined (18 + 12 + 18 + 24 = 72).[cite: 4]

Q9. A survey of 120 school students was conducted to find out which activity they preferred to do in their free time (Scale: 1 unit length = 5 students). Which activity is preferred by most students other than playing?[cite: 4]

Ans. Other than playing, reading story books is preferred by most students.[cite: 4]

Q10. Details of tree saplings planted:[cite: 4]
a. The total number of saplings planted on Wednesday and Thursday is ____[cite: 4]
b. The total number of saplings planted during the whole week is ____[cite: 4]
c. The greatest number of saplings were planted on ____ and the least number of saplings were planted on ____[cite: 4]

Ans.
a. 70[cite: 4]
b. 310[cite: 4]
c. Greatest: Saturday | Least: Wednesday[cite: 4]
Explanation: The variation in the number of saplings planted on different days may be because of the rainy season or different numbers of students present on different days.[cite: 4]

Q11. Mistakes in the Project Tiger bar graph (2006 to 2022).[cite: 4]

Ans. There are mistakes in the bars corresponding to the years 2006, 2010, 2014, and 2018.[cite: 4]

Page No. 103

Section 4.5 — Figure it Out

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?[cite: 4]

Ans. Vertical bar graph is useful because heights of persons can be compared easily with the vertical heights of the bars.[cite: 4]

Q2. 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?[cite: 4]

Ans. Horizontal bar graph is useful as length of a river is a horizontal feature, so lengths can be compared naturally with horizontal lengths of bars.[cite: 4]