NCERT Solutions for Class 6 Maths Ganita Prakash Chapter 4 – Data Handling and Presentation
NCERT Solutions for Class 6 Maths Ganita Prakash Chapter 4 – Data Handling and Presentation are given here in easy, step-by-step form. NCERT stands for National Council of Educational Research and Training, the body that makes your textbook. Ganita Prakash is the new Class 6 Maths book. Data means any collection of facts, numbers or observations. This chapter teaches how to collect data, organise it neatly with tally marks and tables, and then show it in pictures using pictographs and bar graphs so that it is easy to read and understand.
The chapter is made of “Figure it Out” activity boxes and some in-text questions. All of them are solved below, section by section, in simple language, with clear graphs. Students can use this page for homework and revision, parents can use it to check the work at home, and teachers can use it in class. A free printable PDF is also available for offline study.
NCERT Solutions for Class 6 Maths Ganita Prakash Chapter 4 – Data Handling and Presentation
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| Year | Number of Tigers (approx.) |
2006 | 1400 |
2010 | 1700 |
2014 | 2200 |
2018 | 3000 |
2022 | 3700 |
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NCERT Solutions for Class 6 Maths Ganita Prakash Chapter 4 – Data Handling and Presentation
4.1 Collecting and Organising Data Figure it Out (Page No. 75 – 76)
1. What would you do to find the most popular game among Naresh’s and Navya’s classmates?
Answer:
To find the most popular game, we should create a table with two columns: the name of the game and the number of students who chose it. By referring to Naresh’s and Navya’s lists, we can count how many students selected each game and record the totals in the table. The game with the highest number of students will be the most popular game.
2. What is the most popular game in their class?
Answer:
After reviewing the data, we can see that Hockey is the most frequently mentioned game. In total, 8 students have listed Hockey as their favourite game.
3. Try to find out the most popular game among your classmates.
Answer:
Cricket is the most popular game in my class.
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?
Answer:
(a) What is the most popular TV show among her classmates? (✓)
(b) When did India gain independence? (✗)
(c) How much water is being wasted in her locality? (✓)
(d) What is the capital city of India? (✗)
4.1 Collecting and Organising Data Figure it Out (Page No. 76 – 77)
1. 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 gulab jamun?
Answer:
(a) The table shows that 6 students chose Jalebi.
(b) According to the table, 3 students chose Barfi.
(c) A total of 13 students chose Gujiya.
(d) The table shows that 7 students chose Rasgulla.
(e) A total of 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?
Answer:
No, the table is not enough to distribute each type of sweet to the correct student. It only shows the total number of students who like each sweet and does not tell us which sweet each student prefers. To distribute the sweets correctly, we need a detailed list that includes each student’s name and their preferred sweet.
4.1 Collecting and Organising Data Figure it Out (Page No. 77 – 79)
1. Help her to 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.
Answer:
(a) The largest shoe size in the class is 7.
(b) The smallest shoe size in the class is 3.
(c) A total of 10 students wear shoe size 5.
(d) A total of 15 students wear shoe sizes larger than 4.
2. How did arranging the data in ascending order help to answer these questions?
Answer:
Let’s arrange the data 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
Finding the answers from this list takes a little more time compared to using a frequency table.
3. Are there other ways to arrange the data?
Answer:
Yes, data can be arranged in descending order to find the largest values quickly. It can also be grouped by frequency to identify the most common values easily. Another useful method is to group the data into ranges, which helps us understand patterns and distributions more clearly and makes the data easier to analyse.
In-Text Questions (Page 80)
Q. Which mode of travel is used by the most number of students?
Answer:
In the table on Page 79, the school bus has the highest number of symbols. Therefore, the school bus is the most common mode of travel among the students.
4.2 Pictographs Figure it Out (Page No. 83 – 84)
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?
Answer:
(a) The minimum number of books were borrowed on Thursday, as it has the shortest bar or the fewest symbols in the pictograph. The number of books borrowed on Thursday was zero.
(b) To find the total number of books borrowed during the week, we add the number of books represented for each day.
Total number of books borrowed = 24
(c) The maximum number of books were borrowed on Saturday because it has the highest number of symbols in the pictograph.
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 are 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?
Answer:
Pictograph
(a) Rani purchased 3 kites, as shown by the 3 symbols in the pictograph.
(b) Poonam Ben purchased the maximum number of kites.
(c) The pictograph shows more symbols for Jasmeet than for Chaman. Therefore, Jasmeet purchased more kites than Chaman.
(d) Yes, Rukhsana is correct.
Poonam Ben purchased 700 kites, while Rani purchased 300 kites. Double of 300 is 600.
Since 700 is greater than 600, Poonam Ben purchased more than double the number of kites purchased by Rani.
In-Text Questions (Page 86)
Answer the following questions using the bar graph:
1. In Class 2, _____ students were absent that day.
Answer:
There were 5 students absent from Class 2 that day.
2. In which class were the maximum number of students absent?
Answer:
The bar for Class 8 is the highest. Therefore, Class 8 had the maximum number of absent students.
3. Which class had full attendance that day?
Answer:
There is no bar for Class 5, which means that the number of absent students was zero. Therefore, all students in Class 5 were present that day.
4.3 Bar Graphs Figure it Out (Page No. 88)
1. How many total cars passed through the crossing between 6 am and noon?
Answer:
Total cars passed = 600 + 700 + 800 + 1000 + 1200 + 150 = 4450 cars
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?
Answer:
There was less traffic between 6–7 a.m. compared to the hours from 7 a.m. to noon because fewer people were travelling to work during this time.
3. Why do you think the traffic was the heaviest between 7 am and 8 am?
Answer:
7–8 a.m. is the time when the maximum number of factory officers and workers use their cars, and parents use their cars to drop their children at school.
4. Why do you think the traffic was lesser and lesser each hour after 8 am until noon?
Answer:
There is less traffic between 8–9 a.m. because most schools and many factories start at around 8 a.m. Similarly, traffic is lower between 9–10 a.m. because most offices start at 9 a.m., while many shops open around 10 a.m.
In-Text Questions (Page 93)
Use the bar graph to answer the following questions:
1. On which item does Imran’s family spend the most and the second most?
Answer:
The highest bar represents food, followed by house rent. Therefore, Imran’s family spends the most on food and the second-highest amount on house rent.
2. Is the cost of electricity about one-half the cost of education?
Answer:
In the bar graph, the height of the bar for electricity is 400, while the height of the bar for education is 800.
Therefore, the cost of electricity is one-half of the cost of education.
3. Is the cost of education less than one-fourth the cost of food?
Answer:
In the bar graph, the height of the bar for food (3400) is more than four times the height of the bar for education (800).
Therefore, the cost of education is less than one-fourth of the cost of food.
4.4 Drawing a Bar Graph Figure it Out (Page No. 93-99)
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.
Answer:
To prepare a bar graph representing the given data, follow the steps given below:
(i) Draw a horizontal axis (X-axis) and label it ‘Insects/Critters’. Write the names of the different insects or critters at equal intervals.
(ii) Draw a vertical axis (Y-axis) and label it ‘Number Seen’. Mark the numbers from 0 to the maximum number seen, which is 10, at equal intervals.
(iii) Draw a bar for each insect or critter. The height of each bar should represent the number seen. For example, the bar for caterpillars should reach up to 2.
The required bar graph is given below.
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:
(a) The number of tickets sold for Vidisha is 24.
(b) The data shows that 20 tickets were sold for Jabalpur. This number should be written above the corresponding bar on the graph.
Hence, the number of tickets sold for Jabalpur is 20.
(c) The bar for Vidisha represents 24 tickets and is 6 units long. Therefore, each unit represents:
24 ÷ 6 = 4 tickets
Similarly, the bar for Jabalpur represents 20 tickets and is 5 units long:
20 ÷ 5 = 4 tickets per unit
Hence, the scale of the graph is 4 tickets per unit length.
(d) The bar for Sagar should be drawn with a height of 4 units because 16 tickets were sold for Sagar and the scale is 4 tickets per unit.
(e) The scale should be marked on the vertical axis, with each unit representing 4 tickets.
The numbers should be marked as 4, 8, 12, 16, 20, 24, 28, and so on.
(f) Seoni sold 16 tickets, so its bar should be 4 units high, which is correct. Indore sold 28 tickets, so its bar should be 7 units high.
Therefore, the given bar for Indore is not correct.
The correct bar for Indore is given below.
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.
Answer:
(a) Frequency Distribution Table
(b) Bike
(c) Observation Timeframe
I will choose a specific time, such as 9 a.m. to 10 a.m., to observe the traffic on the road.
Recording Data
I will use a tally chart or a counting app to record the different types of vehicles passing by during that hour.
Categorisation
I will organise the collected data into categories such as bikes, cars, scooters, buses, etc.
Final Count
After the observation period, I will count the total number of vehicles in each category.
Analysis
Finally, I will prepare a frequency distribution table based on the recorded data for analysis.
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:
Let the outcomes of 30 times roll of a die be
6, 2, 3, 5, 6, 4, 1, 1, 2, 5
3, 4, 1, 1, 3, 5, 2, 2, 1, 1
6, 2, 3, 5, 1, 2, 2, 3, 4, 2
(a) The minimum number of times: 3 times
(b) The maximum number of times: 8 times
(c) The numbers that appeared an equal number of times: 4 and 6, each appearing 3 times.
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?
Answer:
The table shows the frequency of the different numbers of wickets taken by Jasprit Bumrah in his last 30 matches.
(b) What may be the title of this table?
Answer:
“Number of wickets taken by Jasprit Bumrah in his last 30 matches” could be used as the title of this table
(c) What caught your attention in this table?
Answer:
It is interesting to see the number of wickets Jasprit Bumrah has taken most frequently in his recent matches. The most notable finding is that he took 3 wickets in 8 matches, making it his most frequent wicket tally.
(d) In how many matches has Bumrah taken 4 wickets?
Answer:
Bumrah claimed four wickets in three matches.
(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?
Answer:
No, Mayank cannot calculate the total number of wickets simply by adding 0, 1, 2, 3, and so on up to 7. He first needs to multiply each number of wickets by its corresponding frequency and then add all the resulting values.
(f) How would you correctly figure out the total number of wickets taken by Bumrah in his last 30 matches, using this table?
Answer:
To Find the Total Number of Wickets
- Multiply the number of wickets by the corresponding number of matches for each row.
- Add all the resulting products together.
For example:
(0 × 2) + (1 × 4) + (2 × 6) + (3 × 8) + (4 × 3) + (5 × 5) + (6 × 1) + (7 × 1) = 90
Therefore, the total number of wickets taken across all 30 matches is 90.
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?
Answer:
Village D has the smallest number of tractors.
(b) Which village has the most tractors?
Answer:
Village C has the most tractors.
(c) How many more tractors does Village C have than Village B?
Answer:
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?
Answer:
Number of tractors in Village D = 3
Number of tractors in Village E = 6
Clearly, Village D has half as many tractors as Village E.
Therefore, Komal is correct.
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?
Answer:
Class 8 has the fewest number of girl students.
(b) What is the difference between the number of girls in Class 5 and 6?
Answer:
Number of girls in Class 5 = 4 + 4 + 2 = 10
Number of girls in Class 6 = 4 + 4 + 4 + 4 = 16
Therefore, the difference = 16 − 10 = 6
(c) If 2 more girls were admitted in Class 2, how would the graph change?
Answer:
Number of girls in Class 2 = 4 + 4 + 4 + 4 + 2 = 18
If 2 more girls are added, then:
New number of girls in Class 2 = 18 + 2 = 20
Therefore, the new graph will be:
(d) How many girls are there in Class 7?
Answer:
Number of girls in Class 7 = 4 + 4 + 4 = 12
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:
(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 6?
(c) 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.
Answer:
Pictograph
Mudhol Hounds, a breed of Indian dogs, are mainly found in the Bagalkote and Vijayapura districts of North Karnataka.
(i) The appropriate scale for the pictograph is 6 dogs = 1 symbol.
(ii) The pictograph will contain 6 symbols.
(iii) Yes, Kamini is correct.
The total number of dogs in Villages B and D is:
36 + 48 = 84 dogs
The total number of dogs in the other four villages is:
18 + 12 + 18 + 24 = 72 dogs
Since 84 > 72, Villages B and D together have more dogs than the other four villages combined.
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:
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?
Answer:
(a) The total number of saplings planted on Wednesday and Thursday is:
30 + 40 = 70 saplings
(b) The total number of saplings planted throughout the week is:
52 + 40 + 30 + 40 + 50 + 60 + 40 = 312 saplings
(c) The days on which the highest number of saplings were planted are Saturday and Wednesday.
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 are a few mistakes in the graph. Can you find those mistakes and fix them?
Answer:
4.5 Artistic and Aesthetic Considerations Figure it Out (Page 103)
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:
To visually represent the heights of the tallest persons in each class, a bar graph with vertical bars is used. This makes the data more intuitive and visually appealing, as height is measured vertically upward from the ground.
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? Try finding out this information, and then make the corresponding table and bar graph! Which continents have the longest- rivers?
Answer:
To represent the data on the longest rivers in each continent and their lengths, a bar graph with horizontal bars is used. This is because river lengths are measured horizontally along the ground, making horizontal bars a more intuitive way t
Related Links
- Chapter 1 Patterns in Mathematics
- Chapter 2 Lines and Angles
- Chapter 3 Number Play
- Chapter 5 Prime Time
- Chapter 6 Perimeter and Area
- Chapter 7 Fractions
- Chapter 8 Playing with Constructions
- Chapter 9 Symmetry
- Chapter 10 The Other Side of Zero