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NCERT Solutions for Class 6 maths Chapter 4: Data Handling and Presentation

40 Solved Questions & Exercises19 min estimated readingUpdated 2026-09-16
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NCERT Solutions • Class 6 Mathematics (Ganita Prakash)
Chapter 4: Data Handling and Presentation
Latest Rationalised Syllabus (NEP 2026-27)

Get the simplifiedClass 6 Maths NCERT Solutionsof Ganita Prakash Chapter 4 Data Handling and Presentation textbook exercise questions with complete explanations.

Ganita Prakash Class 6 Maths Chapter 4 Solutions Data Handling and Presentation

Question 1 (4)

1 Collecting and Organising Data Figure it Out (Page No. 75 – 76)

Question 1


What would you do to find the most popular game among Naresh’s and Navya’s classmates?

Solution:
To find the most popular game, we should create a table with two columns, one for the game name and one for the number of students who choose each game. By referring the Naresh’s and Navya’s list, for each game count how many students selected it and record that number in the table. The game with the highest count will be the most popular game.
Question 2


What is the most popular game in their class?
Solution:
After looking the data, we can see that Hockey is mentioned the most times.
Specifically, there are 8 students who have listed Hockey as their favourite game.

Question 3


Try to find out the most popular game among your classmates.
Answer:
The most popular game in my class is cricket.

Question 4


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 (✗) for the questions where
she doesn’t need to collect data. Discuss your answers in the classroom.
(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?
Solution:
Do it yourself.

Question 2 (4)

1 Collecting and Organising Data Figure it Out (Page No. 76 – 77)

Question 1


Shri Nilesh is a teacher. He decided to bring weets to the class to celebrate the new year. The sweets shop nearby hasjalebi, gulab jamun, gujiya, barfi, and rasgulla. He wanted to know the choices of the children. He wrote the names of the sweets on the board and asked each child to tell him their preference. He put a tally mark ‘ | ’ for each student and when the count reached 5, he put a line through the previous four and marked it as

(i) Complete the table to help Shri Nilesh to purchase the correct numbers of sweets:
(a) How many students chose jalebi?
(b) Barfi was chosen by students?
(c) How many students chose gujiya?
(d) Rasgulla was chosen by students?
(e) How many students chose gulabjamun?

Solution:

(a) It is clear from the table, 6 students chose Jalebi.
(b) From the table, we can say that Barfi was chosen by 3 students;
(c) 13 students chose the gujiya.
(d) Rasgulla was chosen by 7 students.
(e) 9 students chose gulab jamun.

Data Handling and Presentation Diagram 1

Data Handling and Presentation Diagram 2

Question 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?
Solution:
No, it is not sufficient.
Shri Nilesh should have also written children’s names against each sweet item. Only then he could have given the right sweet to the right child.

Question 3 (4)

1 Collecting and Organising Data Figure it Out (Page No. 77 – 79)

Question 1


Help her to figure out the following-

Sushri Sandhya asked her asked her students about the sizes of the shoes they wear. She noted the data on the board-

She then arranged the shoe sizes of the students 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

Data Handling and Presentation Diagram 3

Solution:
Question 2


How did arranging the data in ascending order help to answer these questions?
Solution:
Arrangement of data in ascending order enables us to •find the smallest shoe size, the largest shoe size and the shoe sizes lying between them.

Question 3


Are there other ways to arrange the data?
Solution:
Yes. The data can also be arranged in descending order.

Question 4


Write the names of a few trees you see around you. When you observe a tree on the way from your home to school (or while walking from one place to another place), record the data and fill in the following table:

(a) Which tree was found in the greatest number?
(b) Which tree was found in the smallest number?
(c) Were there any two trees found in the same numbers?
Solution:
Do it yourself.

Data Handling and Presentation Diagram 4

Question 5


Take a blank piece of paper and paste any small news item from a newspaper. Each student may use a different article. Now, prepare a table on the piece of paper as given below. Count the number of each of the letters ‘c’, ‘e’, ‘i’, ‘r’, and ‘x’ in the words of the news article, and fill in the table.

(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. Now, compare the order of your list with that of your classmates. Is your order the same or nearly the same as theirs? (Almost everyone is likely to get the order ‘x, c, r, i, e’). Why do you think this is the case?
(d) Write the process you followed to complete this task.
(e) Discuss with your friends the processes they followed.
(f) If you do this task with another news item, what process would you follow?
Solution:
Do it yourself.

Data Handling and Presentation Diagram 5

Question 4 (4)

2 Pictographs Figure it Out (Page No. 83 – 84)

Question 1


The following pictograph shows the number of books borrowed by students, in a week, from the library of Middle School, Ginnori

(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?

Solution:
(a) The minimum number of books were borrowed on the day with the shortest bar or the fewest symbols in the pictograph. It is clear that number of Books borrowed on Thursday is zero.
(b) To find the total number of books borrowed during this week, add up the number of books represented by the symbol for each day.
Here, total number of books = 24
(c) The maximum number of books were borrowed on Saturday because Saturday has the maximum number of symbols in the pictograph.

Data Handling and Presentation Diagram 6

Question 2


Magan Bhai sells kites at Jamnagar. Six shopkeepers from nearby villages come to purchase kites from him. The number of kites he sold to these six shopkeepers is given below-

Prepare a pictograph using the symbol to represent 100 kites.
Answer the following questions:
(a) How many symbols represent the kites that Rani purchased?
(b) Who purchased the maximum number of kites?
(c) Who purchased more kites, Jasmeet or Chaman?
(d) Rukhsana says Poonam Ben purchased more than double the number of kites that Rani purchased. Is she correct? Why?
Solution:
Let’s draw the pictograph = 100 kites

(a) Three symbols
(b) Poonam Ben
(c) Jasmeet
(d) Yes.
Kites purchased by Rani = 300
Kites purchased by Poonam Ben = 700
Hence Poonam Ben purchased more than double.

Data Handling and Presentation Diagram 7

Data Handling and Presentation Diagram 8

Data Handling and Presentation Diagram 9

Data Handling and Presentation Diagram 10

Question 5 (4)

3 Bar Graphs Figure it Out (Page No. 88)

Data Handling and Presentation Diagram 11

Question 1


How many total cars passed through the crossing between 6 am and noon?

Solution:
Total number of cars which passed through the crossing between 6 am and noon = 150 + 1200 + 1000 + 820 + 700 + 600 = 4470 (Refer the bar graph on page 87)
Question 2


Why do you think so little traffic occurred during the hour of 6-7 am, as compared to the other hours from 7 am-noon?
Solution:
During 6-7 am time duration, little traffic occured as compared to other hours from 7 am-noon, because during 6-7 am, there were less people going to their work.

Question 3


Why do you think the traffic was the heaviest between 7 am and 8 am?
Solution:
7-8 am is the hour when the maximum number of factory officers and workers use their cars and parents use their cars to drop their children at school.

Question 4


Why do you think the traffic was lesser and lesser each hour after 8 am until noon?
Solution:
Because, most of the schools start at 8 am – and many factories also start at 8 am and hence less traffic between 8 am-9 am. Most offices start at 9 am and shops start at 10 am and hence less traffic between 9 am-10 am.

Question 6 (4)

4 Drawing a Bar Graph Figure it Out (Page No. 93-99)

Question 1


Samantha visited a tea garden and collected data of the insects and critters she saw there. Here is the data she collected

Help her prepare a bar graph representing this data.

Solution:
To prepare a bar graph representing the given data, follow the point given below.
(i) Draw a horizontal axis (X-axis) labeled, ‘Insects/critters’ with each type of insect or critter evenly spaced
(ii) Draw a vertical axis (Y-axis) labeled ‘Number seen’ with numbers starting from 0 up to the maximum number seen (in this case, 10) evenly spaced.
(iii) For each insect or critter, draw a bar that rises to the number seen. For example, the bar of caterpillars should reach up to 2.

Data Handling and Presentation Diagram 12

Required bar graph is given below.

Data Handling and Presentation Diagram 13

Question 2


Pooja collected data on the number of tickets sold at the Bhopal railway station for a few different cities in Madhya Pradesh over 2 hours.

She used this data and prepared a bar graph on the board to discuss the data with her students, but someone erased a portion of the graph.

(a) Write the number of tickets sold for Vidisha above the bar.
(b) Write the number of tickets sold for Jabalpur above the bar.
(c) The bar for Vidisha is 6 units in length and the bar for Jabalpur is 5 units in length. What is the scale for this graph?
(d) Draw the correct bar for Sagar.
(e) Add the scale of the bar graph placing the correct numbers on the vertical axis.
(f) Are the bars for Seoni and Indore correct in this graph? If not, draw the correct bar(s).
Answer:

(c) The number of tickets sold for Jabalpur above the bar is 20.
(d) The bar for Vidisha is 6 units in length and 24 tickets are sold so (24 ÷ 6 = 4) 4 tickets represent each unit and the bar for Jabalpur is 5 units in length and 20 tickets are sold so (20 ÷ 5 = 4) 4 tickets represent each unit. Therefore, the scale is 1 unit length = 4 tickets
(d) The correct bar for Sagar is as follows:

(e) Number on scale are as: 4, 8, 12, 16,…

(f) The bars for Seoni is correct but that of Indore is wrong.

Data Handling and Presentation Diagram 14

Data Handling and Presentation Diagram 15

Data Handling and Presentation Diagram 16

Data Handling and Presentation Diagram 17

Data Handling and Presentation Diagram 18

Data Handling and Presentation Diagram 19

Question 3


Chinu listed the various means of transport that passed across the road in front of his house from 9 am to 10 am:

(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.
Solution:
(a) Frequency Distribution Table

(b) Bike
(c) Step 1: Note down the name of various means of transport in the notebook.
Step 2: Between 9 am to 10 am, watch the different means of transport passing in front of the house.
Step 3: Write the number of different means of transport in front of their name.

Data Handling and Presentation Diagram 20

Data Handling and Presentation Diagram 21

Question 4


Roll a die 30 times and record the number you obtain each time. Prepare a frequency distribution table using tally marks. Find the number that appeared:
(a) The minimum number of times.
(b) The maximum number of times.
(c) Find numbers that appeared an equal number of times.
Answer:
Do it by yourself.

Question 5


Faiz prepared a frequency distribution table of data on the number of wickets taken by Jaspreet Bumrah in his last 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) 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?
(f) How would you correctly figure out the total number of wickets taken by Bumrah in his last 30 matches, using this table?
Answer:
(a) This table shows a frequency distribution of data on the number of wickets taken by Jaspreet Bumrah in his last 30 matches.
(b) Number of wickets taken by Jaspreet Bumrah in his last 30 matches.
(c) The thing that caught my attention is that Jaspreet Bumrah has taken 3 wickets in most of his matches.
(d) In 3 matches Bumrah has taken 4 wickets.
(e) No, Mayank cannot get the total number of wickets just by adding the numbers 0, 1, 2, 3…up to 7 because he needs to multiply the number by its corresponding frequency first.
(f) By multiplying the number of wickets with its frequency and then adding the product.

Data Handling and Presentation Diagram 22

Question 6

The following pictograph shows the number of tractors in five different villages.

Observe the pictograph and answer the following questions—
(a) Which village has the smallest number of tractors?
Solution:
Village D has the smallest number of tractors.

Data Handling and Presentation Diagram 23

(b) Which village has the most tractors?
Solution:
Village C has the most tractors.

(c) How many more tractors does Village C have than Village B?
Solution:
Number of tractors village C has = 8
Number of tractors village B has = 5
Difference = 8 – 5 = 3
So, village C has 3 more tractors than village B.

(d) Komal says, “Village D has half the number of tractors as Village E.” Is she right?
Solution:
Number of tractors village D has = 3
Number of tractors village E has = 6
Clearly, village D has half the number of tractors as village E.
Hence, Komal is right.

Question 7


The number of girl students in each class of a school is depicted by a pictograph:

Observe this pictograph and answer the following questions:
(a) Which class has the least number of girl students?
Solution:
Class 8 has the least number of girl students.

Data Handling and Presentation Diagram 24

(b) What is the difference between the number of girls in Class 5 and 6?
Solution:
Number of girls in class 5 = 4 + 4 + 2 = 10
Number of girls in class 6 = 4 + 4 + 4 + 4= 16
∴ Difference = 16 – 10 = 6

(c) If 2 more girls were admitted in Class 2, how would the graph change?
Solution:
Number of girls in class 2 = 4 + 4 + 4 + 4 + 2 = 18
If 2 more girls are added, then,
Number of girls in class 2 = 18 + 2 = 20
Therefore, new graph would be:

Data Handling and Presentation Diagram 25

(d) How many girls are there in Class 7?
Solution:
Number of girls in class 7 = 4 + 4 + 4 = 12

Question 8


Mudhol Hounds (a type of breed of Indian dogs) are largely found in North Karnataka’s Bagalkote and Vijaypura districts. The government took an initiative to protect this breed by providing support to those who adopted these dogs. Due to this initiative, the number of these dogs increased. The number of Mudhol dogs in six villages of Karnataka are as follows
Village A: 18, Village B : 36, Village C : 12, Village D : 48, Village E : 18, Village F: 24
Prepare a pictograph and answer the following questions:
(i) What will be a useful scale or key to draw this pictograph?
(ii) How many symbols will you use to represent the dogs in village 6?
(iii) Kamini said that the number of 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 for your response.
Solution:
(i) A useful scale would be 1 symbol = 6 dogs.
This scale is a good choice because it divides evenly into the numbers provided (e.g. 18 dogs would be 3 symbols, 36 dogs would be 6 symbols)

(ii) Since, each symbol represents 6 dogs.
∴ Village B has 36 dogs.
∴ =6 symbols 6
H Hence, 6 symbols will be used to represent the dogs in village B.

(iii) Yes, Kamini is correct. The combined total number of dogs in village B and village D is (36 + 48) = 84 dogs.
∴ The total for other four villages is 72 dogs. Therefore, 84 is greater than 72.
So, Kamini is right.

Question 9


A survey of 120 school students was conducted to find out which activity they preferred to do in their free time.

Draw a bar graph to illustrate the above data taking the scale of 1 unit length = 5 students. Which activity is preferred by most students other than playing?
Answer:
Reading book story is preferred by most students other than playing.

Data Handling and Presentation Diagram 26

Data Handling and Presentation Diagram 27

Question 10


Students and teachers of a primary school decided to plant tree saplings in the school campus and in the surrounding village during the first week of July. Details of the saplings they planted are as follows:

(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 _________.
Why do you think that is the case? Why were more saplings planted on certain days of the week and less on others? Can you think of possible explanations or reasons? How could you try and figure out whether your explanations are correct?
Solution:
(a) The total number of saplings planted on Wednesday and Thursday is 30 + 40 = 70.
(b) The total number of saplings planted during the whole week is
52 + 40 + 30 + 40 + 50 + 60 + 40
= 312
(c) Do it yourself.

Data Handling and Presentation Diagram 28

Question 11


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 India. Starting 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 were a few mistakes in the graph. Can you find those mistakes and fix them?

Answer:

Data Handling and Presentation Diagram 29

Data Handling and Presentation Diagram 30

Question 7 (4)

5 Artistic and Aesthetic Considerations Figure it Out (Page 103)

Question 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?

Solution:
Do it by yourself.
Question 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 horizontal bars? Why? Try finding out this information, and then make the corresponding table and bar graph! Which continents have the, longest rivers?
Solution:
Graph with horizontal bars, because rivers flow on land horizontally.

Intext Questions

Solution:
the following questions using the bar graph. (Page No. 86)

Data Handling and Presentation Diagram 31

Question 1


In Class 2, ____________ students were absent that day.
Solution:
5 students

Question 2


In which class were the maximum number of students absent? ____________
Solution:
Class 8

Question 3


Which class had full attendance that day? ____________
Solution:
Class 5

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