NCERT Solutions for Class 6 Maths Chapter 4 - Data Handling and Presentation

We are surrounded by data from all sides. Be it numbers, surveys, or the height and weight of our medical examinations, all have certain figures in them. But we never wondered what is actually that collection of facts and figures or why we are doing it. In this chapter, we will learn about basic concepts regarding data management, how to present data, the various techniques involved, and much more. The NCERT Solutions for Class 6 Maths provide the step-by-step solutions for all the questions in each chapter in the Class 6 book.

These NCERT Solutions help the students in exam preparation by practising many questions and checking the answers. This way of preparation helps students know their weaker points, so that they can focus more on their weaknesses. These NCERT Solutions for Class 6 are a reliable resource as they are created with respect to the NCERT Syllabus by the subject matter experts at Careers360.

NCERT Solutions for Class 6 Maths Chapter 4 Exercise

Q1. 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 will first arrange the table of games according to their frequency or repetition in the table. The game with the highest frequency will be the most popular game among students.

Q2. What is the most popular game in their class?

Solution: As you can see from the table, the most popular game in the class is Hockey with the highest frequency, i.e. 8.

Q3. Try to find out the most popular game among your classmates.

Solution: Do it Yourself [DIY] {Hint: Prepare a table and find the game with the highest frequency.}

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 (×) 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:
a. Yes, she needs to collect the data to form a table showing the frequency of each show.

b. 15th August 1947. (No data collection is required)

c. Yes, she needs to collect the data from her neighbourhood to form a table showing the amount of water wasted.

d. New Delhi. (No data collection is required)

Q1. Complete the table to help Shri Nilesh purchase the correct number 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 gulab jamun? ◻

Shri Nilesh requested one of the staff members to bring the sweets as given in the table. The above table helped him to purchase the correct number of sweets.

Solution: According to the given data in the table. Count the lines of the Tally mark to find the number of students.

a. 6
b. 3
c. 13
d. 7
e. 9

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?

Solution: No, the table is not sufficient for the distribution of each type of sweet. With this table, you need a list with the names of students according to their choice.

Sushri Sandhya 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

Q1. Help her figure out the following:

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.

Solution:
a. 7
b. 3
c. 10
d. 15

Q2. How did arranging the data in ascending order help to answer these questions?

Solution: Arranging the data helped us to find the smallest size and the largest size. Also enabled us to find the frequency of the sizes.

Q3. Are there other ways to arrange the data?

Solution: Yes, by arranging the data in decreasing order or using the Tally Mark Table.
For example:

Descending order:
7, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 4, 3, 3, 3

Q4. 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:
You can solve these questions by following the given steps:
(1) Write down the names of the trees.
(2) Write the count of each tree in front of the tree.
Now, you will be able to answer the given questions.

Q5. 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 [DIY Time]

Q1. 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 was the minimum number of books borrowed?

b. What was the total number of books borrowed during the week?

c. On which day was the maximum number of books borrowed? What may be the possible reason?

Solution:
a. Thursday (0 books)
b. 5 + 4 + 2 + 0 + 5 + 8 = 24
c. Saturday (8 books), it may be possible due to the free periods, as it is the last day of the week and the next day is Sunday, so that students may get time to read.

Q2. 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:

a. 3
b. Poonam Ben
c. Jasmeet
d. Yes, Rani bought 300 kites whereas Poonam Ben bought 700 kites, which is more than the double of Rani.

Q1. How many total cars passed through the crossing between 6 a.m. and noon?

Q2. Why do you think so little traffic occurred during the hour of 6-7 a.m., as compared to the other hours from 7 a.m. to noon?

Q3. Why do you think the traffic was the heaviest between 7−8 a.m.?

Q4. Why do you think the traffic was less and less each hour after 8 a.m. until noon?

Solution:

1. 4470

2. It is because fewer people go to work.

3. It is because all the adults and children start going to their places.

4. It is because the number of school-going children is reducing.

Q1. Samantha visited a tea garden and collected data on the insects and critters she saw there. Here is the data she collected:

Help her prepare a bar graph representing this data.

Solution:

Q2. Pooja collected data on the number of tickets sold at the Bhopal railway station for a few different cities of Madhya Pradesh over two 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 unit lengths, and the bar for Jabalpur is 5 unit lengths. What is the scale for this graph?

d. Draw the correct bar for Sagar.

e. Add the scale of the bar graph by 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).

Solution:

(a and b).

c. Vidisha 6 units = 24 tickets

∴ Vidisha 1 unit = 246⇒4

Jabalpur 5 units = 20 tickets

∴ Jabalpur 1 unit = 205⇒4

Hence, 1 unit = 4 tickets

(d, e).

f. The graph of Seoni was correct, but the graph of Indore was not. So, the correct graph is

Q3. Chinu listed the various means of transport that passed across the road in front of his house 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.

Solution:
a.

b. Bike (13 times)
c.
Step 1: Write down the mode of transport in the first column.
Step 2: Counting the vehicles passing between 9 am to 10 am.
Step 3: Write down the number of vehicles of each type in front of the vehicle.
Step 4: Draw a bar graph to represent the data.

Q4. 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.

Solution: DIY [Take a reference from solution 3 (a)]

Q5. 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?

Solution:

a. The table gives information about the number of wickets taken by Jasprit Bumrah in a number of matches.

b. The title of the table can be given as “Distribution of Wickets taken by Jaspreet Bumrah per match”.

c. In this table, the most eye-catching thing is the consistent performance by Jasprit Bumrah that he took 5 wickets in 5 matches.

d. 3 Matches

e. No, by adding all the wickets, we can’t find the total number of wickets taken by Bumrah. To find the total number of wickets, we need to multiply the number of matches by the number of wickets in each row and then we need to add the results of each row.

f. To find the total number of wickets, we need to multiply the number of matches by the number of wickets.
So, total wickets taken by Bumrah = 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

Q6. 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?

b. Which village has the most tractors?

c. How many more tractors does Village C have than Village B?

d. Komal says, "Village D has half the number of tractors as Village E." Is she right?

Solution:

a. Village D (3 tractors)

b. Village C (8 tractors)

c. The difference in the number of tractors of Village C and Village B= Village C - Village B = 8 - 5 = 3

d. Village E has 6 tractors, whereas Village D has 3 tractors. So, yes, Village D has exactly half the number of tractors as Village E.

Q7. The number of girl students in each class of a school is depicted by the pictograph:

Observe this pictograph and answer the following questions:

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?

Solution:
a. Class 8 has the least number of girls.
b. Number of girls in Class 6 -Number of girls in Class 5 = 16 - 10 = 6
c. Then Class 2 will have 20 students with 5 symbols in the table.
d. Class 7 has 3 complete symbols, i.e. it has 12 girls.

Q8. Mudhol Hounds (a type of breed of Indian dogs) are largely found in North Karnataka's Bagalkote and Vijayapura 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 is 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:

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. Kamini 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 for your response.

Solution:

a. One symbol of a dog = 6 dogs in number

b. 6 Symbols are used to depict the number of dogs in Village B.

c. Village B + Village D = 14 symbols.

∴ it is more than the number of dogs in other villages.

Q9. 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?

Solution:

Reading storybooks is the other most preferred activity than playing.

Q10. 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 was planted on ______ and the least was planted on __________. Why do you think that is the case? Why were more saplings planted on certain days of the week and fewer on others? Can you think of possible explanations or reasons? How are your explanations correct?

Solutions:

a. Wednesday + Thursday = 30 + 40 = 70
b. 52 + 40 + 30 + 40 + 50 + 60 + 40 = 312
c. The greatest number of saplings was planted on Saturday, and the least was planted on Wednesday. In most of the schools, Saturdays have less number of classes and the next day is a holiday. So, most saplings are done on Saturdays.
The reasoning may differ according to the schools and their curriculum.

Q11. The number of tigers in India went down drastically between 1900 and 1970. Project Tiger was launched in 1973 to track and protect the 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 four-year intervals. They prepared a frequency table for this data and a bar graph to present this data, but there are a few mistakes in the graph. Can you find those mistakes and fix them?

Solution: Yes, in the bar graph data is not represented in the correct manner. ∴ the correct graph is:

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?

Solution: A bar graph featuring vertical bars is utilised to visually depict the height data of the tallest individuals in each class. It is more intuitive and visually attractive to display heights measured from the ground using bar graphs with vertical bars.

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? Try finding out this information, and then make the corresponding table and bar graph! Which continents have the longest rivers?

Solution: To prepare a table listing the longest rivers on each continent, along with their lengths, a horizontal bar graph is utilised. This is because lengths parallel to the ground are typically best represented using bar graphs with horizontal bars.

Data Handling and Presentation Class 6 Maths Chapter 4 - Topics:

Here, Students can find all the topics that are discussed in this chapter, Data Handling and Presentation, class 6:

• Collecting and Organising Data
• Pictographs
• Bar Graphs
• Artistic and Aesthetic Considerations

NCERT Solutions for Class 6 Maths Chapter 4 Data Handling and Presentation - Notes

Here are the detailed and useful notes for class 6 chapter 4, Data Handling and Presentation, which will help the students understand the chapter easily and effectively:

Data: Data can be defined as any collection of facts, numbers, measures, observations or other descriptions of things that convey information about those things in particular. Data is a collection of similar pieces of information. For example, if we go around our class and collect information about the favourite subject of every student, it is data.

Representation of Data: The data is represented in various ways, like tally marks, pictographs and bar graphs.
Tally marks: Tally marks are a set of lines that are used to represent the data.

Pictographs: Pictographs are a pictorial representation of data using symbols and pictures. These are a visual and suggestive way to represent data without writing any numbers.

NCERT Solutions for Class 6 Maths Chapter 4 Data Handling and Presentation - Points to Remember

Given below are some important points to remember about Class 6 Chapter 4, Data Handling and Presentation:

Data: Data is a collection of similar pieces of information.

Tally marks: Tally marks are a set of lines that are used to represent the occurrence of data.

Pictographs: Pictographs are a pictorial representation of data using symbols and pictures.

Bar Graphs: Bar graphs are a graphical representation of data using vertical or horizontal bars.

NCERT Solutions for Class 6 Maths Chapter Wise

Students can find chapter-wise solutions of class 6 Maths below:

NCERT Solutions for Class 6 Subject Wise

The NCERT Solutions give step-by-step, comprehensive solutions to all the exercise questions in each chapter, which is of great help during exam preparations. Students can refer to the subject-wise solutions for Class 6 in the links below.

• NCERT Solutions for Class 6 Maths
• NCERT Solutions for Class 6 Science

Students can also check the NCERT Books and the NCERT Syllabus for Class 6 here:

• NCERT Syllabus Class 6 Maths
• NCERT Books Class 6
• NCERT Syllabus Class 6