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

NCERT Solutions for Class 6 Maths Chapter 4

Data Handling Class 6 Maths Chapter 4 is an important chapter that helps students understand how information is collected, organised, and interpreted in daily life. In NCERT Class 6 Maths Chapter 4, students learn the basics of data handling through simple and practical examples, making maths more interesting and useful.

This chapter introduces students to data collection, where information is gathered through surveys, observations, or questions. After collecting data, students learn how to organise it using tables and tally marks, which makes large sets of information easy to understand. One of the key topics in Chapter 4 Class 6 Maths is pictographs, where data is represented using pictures or symbols. Students also learn bar graphs, a visual way to compare data quickly.

Practising data handling questions for Class 6 helps students improve logical thinking and analytical skills. Data Handling Class 6 questions with answers included in NCERT focus on reading graphs, counting frequencies, and answering real-life based problems. These questions build a strong foundation for higher classes.

Overall, NCERT Solutions for Class 6 Maths Chapter 4 makes students confident in working with data. With regular practice, students can easily score well in exams and apply data handling concepts in everyday situations like analysing scores, surveys, and reports.

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Data Handling Class 6 Questions with Answers

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:

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.

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.

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

• The largest shoe size in the class is _____________

• The smallest shoe size in the class is _____________

• There are _____________ students who wear shoe size 5.

• There are _____________ students who wear shoe sizes larger than 4.

Answer:

• The largest shoe size in the class is 7.

• The smallest shoe size in the class is 3.

• There are 10 students who wear shoe size 5.

• There are 15 students who wear shoe sizes larger than 4.

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:

Sample Tree Observation Table

(a) Which tree was found in the greatest number?
→ Neem (6 trees)

(b) Which tree was found in the smallest number?
→ Banyan (2 trees)

(c) Were there any two trees found in the same numbers?
→ Yes, Mango and Gulmohar were both seen 5 times.

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:

a. The letter found the most number of times is: e
b. The letter found the least number of times is: x
c. Letters in ascending order of frequency: x, c, t, i, r, e

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.

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 symbolto 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.

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.

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.

Question 2.
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:

Sample 30 Dice Rolls
(Randomly simulated)
4, 2, 6, 3, 5, 1, 4, 6, 2, 5, 3, 6, 2, 1, 5, 6, 4, 3, 4, 2, 5, 3, 1, 4, 6, 2, 5, 3, 1, 6

(a) The number that appeared the least number of times:
→ 1 (appeared 3 times)

(b) The number that appeared the most number of times:
→ 6 (appeared 8 times)

(c) Numbers that appeared an equal number of times:
→ 3, 4, and 5 (each appeared 5 times)

Question 3.
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.

Question 4.

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.

(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 5.
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.

(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:

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

Question 6.
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.
∴ 

36

6

 =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 7.
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.

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?
Answer:

I would use a graph with vertical bars to represent the heights of the tallest persons in each class.

Why?

Heights are naturally measured upwards from the ground.

Vertical bars visually suggest an increase in height, making it easier to compare who is taller or shorter.

A column graph (vertical bars) clearly shows the difference in height, as each bar rises according to the value.

Read More: Pictograph

Mastering Basic Geometrical Ideas Class 6 and Data Representation

When students of class 6 maths chapter 4, they go from simple numbers to the world of managing data. This chapter, which is often called "Data Handling and Presentation," covers a few main skills. Students must focus on basic geometrical ideas for class 6 to do well, such as making sure the axes are orthogonal and the bars are the same width while making graphs.

Doing basic geometry class 6 problems together with data activities helps you learn about the space needs of a bar graph. For example, when working on basic geometrical ideas class 6 extra questions, you might realise that you need to know a lot about lines and angles to draw a clear horizontal or vertical axis. Using expert basic geometrical ideas class 6 solutions, students may make sure that their charts are not only mathematically correct but also easy to read.

Detailed Guide to Data Handling and Presentation

Data handling is the process of collecting, organizing, and studying information to learn something new. It allows us to turn a messy list of numbers into a clear, visual representation. Below is a breakdown of the key methods found in the NCERT solutions.

1. Gathering and putting together information
   The first thing you need to do when you want to learn more about maths is to get information. For instance, Shri Nilesh, the instructor, must ask each pupil which of the following sweets they would like: Jalebi, Gulab Jamun, Gujiya, Barfi, or Rasgulla.

• Tally Marks: We make a vertical line '|' for each student's decision in this system. We put a diagonal line between the previous four numbers when the count reaches five to show that there are five numbers.

• Tables of Frequencies: We count the tally marks and write down the overall "frequency" for each group after we have them. The frequency is 13 if 13 students picked Gujiya.

2. Using Pictographs
   A pictograph uses drawings or symbols to show information. The scale tells you how many items each symbol stands for.

• How to Read a Pictograph: Think about a library where one book symbol stands for ten real books. If there are five symbols for Monday, then that means that 50 books were borrowed.

• How to Draw a Pictograph: Always pick a scale that is beneficial while making one. For instance, if you want to keep track of how many Mudhol Hounds live in different villages (for example, 18, 36, 12, and 48), a scale of 1 star equals 6 dogs works well.
  
  Important Example from NCERT:
  Students write down the number of trees and their names as they count them on the walk to school. They can readily see which tree was found the most and the least by putting the data in order from smallest to largest.

3. How to Read and Make Bar Graphs
   
   Bar graphs are a type of chart that uses equal-width rectangular bars to show data. The height of vertical graphs and the length of horizontal graphs show how often something happens.

• Vertical vs. Horizontal:

• Vertical Bars: Use them to compare the heights of individuals or things that are tall, like pillars.

• Horizontal Bars: These are often used for objects that flow or are flat, such rivers that are long.

• How to Understand Traffic Data: One common concern is looking at traffic at a crossing between 6 am and noon. There are fewer people going to work between 6 and 7 a.m. and more people going to school and work between 7 and 8 a.m.

4. How to Draw a Bar the Right Way Graph

• Draw the Axes: Make a horizontal X-axis for groups (such names of bugs or cities) and a vertical Y-axis for numbers.

• Give Everything a Name: It is important that each axis has a visible label.

• Pick a Scale: Figure out what "1 unit length" means. For instance, 1 unit is equal to 4 tickets sold.

• Draw Bars: Make sure that all of the bars are the same width and are spaced out evenly. If you notice two caterpillars in a garden, the bar on the Y-axis goes up to the "2" mark.

5. Artistic and aesthetic factors
   Data isn't just numbers; it's also about talking to each other. Exercise 4.5 is all about how graphs look and feel. Important parts are:

• Colour Choice: Using colours to tell the difference between groups.

• Spacing: Making sure the bars are far enough apart so that people don't get confused.

• Correctness: Fixing errors, like when a graph mistakenly portrays the tiger population in 2006 (1400) as being lower than it really was.

Read More: 

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