By using Ganita Prakash Book Class 6 Solutions and Chapter 4 Data Handling and Presentation Class 6 NCERT Solutions Question Answer, students can improve their problem-solving skills.
Class 6 Maths Chapter 4 Data Handling and Presentation Solutions
Data Handling and Presentation Class 6 Solutions Questions and Answers
4.1 Collecting and Organising Data Figure it Out (Page No. 75 – 76)
Question 1.
Naresh and Navya decided to go to each student in the class and ask what their favourite game is. Then, they prepared a list.
Navya is showing the list.
She says (happily), “I have collected the data. I can figure out the most popular game now!”
A few other children are looking at the and wondering, “We can’t yet see the most popular game. How can we get, it from this list?”
(i) What would you do to find the most popular game among Naresh’s and Navya’s classmates?
Solution:
To find the most popular game among Nareshs and S Navya’s classmates, we make the following table using the given data.
From the above table, it is clear that game Hockey liked by 8 students.
Hence, the most popular game among Naresh’s and Navya’s classmates is Hockey.
(ii) 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.
(iii) Try to find out the most popular game among your classmates.
Solution:
Hockey
(iv) 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.
(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 yourself
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.
(ii) 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:
The table provided lists the number of students who chose each type of sweet but it does not include the names of the students who made those choices.
Therefore, while the table is sufficient for knowing how many sweets to buy. It is not sufficient for distributing each type of sweet to the correct student because it does not specify which student chose which sweet.
Alternative To distribute the sweets accurately to each student, you would need a list that not only includes the number of students for each sweet but also records the name of the students along with their preferred sweets. This way can be ensure that each student receives the sweet they specifically required.
4.1 Collecting and Organising Data Figure it Out (Page No. 77 – 79)
Question 1.
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
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.
Solution:
(a) The largest shoe size in the class is 7.
(b) The smallest shoe size in the class is 3.
(c) There are 10 students who wear shoe size 5.
(d) 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:
Arranging the data in ascending order made it easier to identify the smallest and largest shoe size and to count how many students wear each size.
Question 3.
Are there other ways to arrange the data?
Solution:
Yes, data can also be arranged in descending order, where the largest size comes first or it can be categorised based on frequency of each shoe size.
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.
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 V, ‘f, V, 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.
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 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?
Solution:
Required pictograph is given below.
(a) Since, Rani purchased 300 kites^it is clear from the pictograph, 3 symbols represent the kites that Rani purchased.
(b) The shopkeeper who purchased the maximum number of kites is the one with the most symbols in pictograph. It is clear from the pictograph that Poonam Ben purchased the maximum number of kites.
(c) On comparing the number of symbols for Jasmeet and Chaman, we get Jasmeet purchased more kites.
(d) From the pictograph, it is clear that Poonam Ben has 7 kites symbols and Rani has only 3 symbols, s
Hence, Rukhsana is correct as 700 kites is more than double of 300 kites.
(a) 3 symbols represent the kites that Rani purchased.
(b) Poonam Ben purchased the maximum number of kites.
(c) In the pictograph number of symbols for Jasmeet is more than the number of symbols for Chaman. Therefore, Jasmeet purchased more kites than Chaman.
(d) Yes, Rukhsana is correct.
Kites purchased by Poonam Ben = 700 Kites purchased by Rani = 300 Double of 300 is 600. Clearly, 700 is more than 600. Hence, Poonam Ben purchased more than double the number of kites that Rani purchased.
4.3 Bar Graphs Figure it Out (Page No. 85 – 86)
Question 1.
Let’s take the data collected by Lakhanpal earlier, regarding the number of students absent on one day in each class.
He presented the same data using a bar graph
Answer the following questions using the bar graph:
(i) In Class 2, _____ students were absent that day.
(ii) In which class were the maximum number of students absent? _____
(iii) Which class had full attendance that day?
Solution:
(i) In class 2, 5 students were absent that day, because the bar corresponding to class 2 reaches up to the 5th line on the vertical axis, indicating that 5 students were absent.
(ii) The maximum number of students were absent in class 8.
(iii) The bar for class 5 does not rise above the baseline (0), indicating that no students were absent, meaning the class had full attendance.
Hence, class 5 had full attendance that day.
4.3 Bar Graphs Figure it Out (Page No. 87 – 88)
Question 1.
Let us look at an example of vehicular traffic at a busy road crossing in Delhi, which was studied by the traffic police on a particular day. The number of vehicles passing through the crossing each hour from 6 am to 12:00 noon is shown in the bar graph. One unit of length stands for 100 vehicles.
We can see that the maximum traffic at the crossing is shown by the longest bar i.e. for the time interval 7-8 am. The bar graph shows that 1200 vehicles passed through the crossing at that time.
The second longest bar is for 8-9 am. During that time, 1000 vehicles passed through the crossing. Similarly, the minimum traffic is shown by the smallest bar i.e. the bar for the time interval 6-7 am. During that time, only about 150 vehicles passed ‘ through the crossing. The second smallest bar is that for the time interval 11 am -12 noon, when about 600 vehicles passed through the crossing.
The total number of cars passing through the crossing during the two-hour interval 8:00-10:00 am as shown by the bar graph is about 1000+800 = 1800 vehicles.
(i) How many total cars passed through the crossing between 6 am and noon?
(ii) 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?
(iii) Why do you think the traffic was the heaviest between 7 am and 8 am?
(iv) Why do you think the traffic was lesser and lesser each hour after 8 am all the way until noon?
Solution:
(i) From the graph, we add the number of vehicles from each time interval.
6 – 7 am 150 vehicles
7 – 8 am 1200 vehicles
8 – 9 am 1000 vehicles
9 – 10 am 800 vehicles
10 – 11 am 700 vehicles
11 – 12 am 600 vehicles
Adding these together.
150 + 1200+1000 + 800+700+ 600 = 4450 vehicles Hence, total 4450 cars passed through the crossing between 6 am and noon.
(ii) The low traffic during the 6-7 am hour could be because it is very early in the morning and fewer people are on the roads at that time. Most people may not have started their daily activities yet, which is why fewer vehicles are on the road.
(iii) The traffic was likely the heaviest between 7 am and 8 am because this is a common time for people to commute to work or school. Many people start their day around this time, leading to a higher number of vehicles on the road.
(iv) The traffic likely decreased each hour after 8 am because most people have already reached their destinations, such a work or school. As the morning progresses, fewer people are travelling, leading to less traffic on the roads.
4.3 Bar Graphs Figure it Out (Page No. 93)
Question 1.
Use the bar graph to answer the following questions.
(i) On which item does Imran’s family spend the most and the second«most?
(ii) Is the cost of electricity about one-half the cost of education?
(iii) Is the cost of education less than one-fourth the cost of food?
Solution:
(i) It is clear from the graph that Imran’s family spend the most on food and second most on house rent.
(ii) Yes. It is clear from the bar graph that the cost of electricity about one-half the cost of education because we see in graph the cost of electricity is ₹ 400 and the cost of education is ₹ 800 i.e. amount ₹ 400 is the one-half off 800.
(iii) Yes. In the graph, we see that the cost of education is ? 800 and the cost of food is ₹ 3400.
Hence, one-fourth of the cost of food = \(\frac{3400}{4}\) = ₹ 850
∴ ₹ 800 < ₹ 850
Hence, the cost of education is less than one-fourth the cost of food.
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.
Required bar graph is given below.
Question 2.
Pooja collected data on the number of tickets sold at the Bhopal railway station for a few different cities of Madhya Pradesh over a 2-hour period.
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.
(i) Write the number of tickets sold for Vidisha above the bar.
(ii) Write the number of tickets sold for Jabalpur above the bar.
(iii) The bar for Vidisha is 6 unit lengths and the bar for Jabalpur is 5 unit lengths. What is the scale for this graph?
(iv) Draw the correct bar for Sagar.
(v) Add the scale of the bar graph by placing the correct numbers on the vertical axis.
(vi) Are the bars for Seoni and Indore correct in this graph? If not, draw the correct bar(s).
Solution:
(i) The number of tickets sold for Vidisha is 24.
(ii) 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.
(iii) If the bar for Vidisha (which represents 24 tickets) is 6 units long, then each unit represents 4 tickets.
Similarly, for Jabalpur, 20 tickets divided by 5 units, also equals 4 tickets per unit.
Hence, the scale for this graph is 4 tickets per unit length.
(iv) The bar for Sagar should be draw with a height of 4 units because 16 tickets were sold for Sagar and the scale is 4 tickets per unit.
(v) The seals should be labeled on the vertical axis with each unit representing 4 tickets.
The numbers would’be marked as 4, 8, 12,16, 20, 24, 28 and so on.
(vi) Seoni sold 16 tickets, so the bar should be 4 units high which is correct and Indore sold 28 tickets, so the bar should be 7 units high. Therefore, given bar for Indore is not correct.
Correct bar for Indone is given below.
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:
(i) Prepare a frequency distribution table for the data.
(ii) Which means of transport was used the most?
(iii) If you were there to collect this data, how could you do it? Write the steps or process.
Solution:
(i) Frequency distribution table for the given data is given below.
(ii) The bike has the highest frequency in the table, indicating it was the most common means of , transport observed.
(iii) This process ensures accurate data collection and help in organising the information for further analysis.
To collect this data, you could follow the steps given below.
Step I Choose a specific time period to observe e.g. 9 AM to 10 AM.
Step II Stand at a location where you can clearly see the road.
Step III Record each vehicle you see passing by in a notebook, noting the type of transport’.
Step IV After the observation period, tally the counts for each type of transport to prepare your frequency distribution table.
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:
(i) The minimum number of times.
(ii) The maximum number of times.
(iii) Find numbers that appeared an equal number of times.
Solution:
Do yourself.
(i) The number that appeared the least amount of times (which you can determine after recording your result).
(ii) The number that appeared the most number of times.
(iii) Any numbers that have the same frequency in your tally marks table.
Question 5.
Faiz prepared a frequency distribution table of data on the number of wickets taken by Jaspreet Bumrah in his last 30 matches:
(i) What information is this table giving?
Solution:
The table shows the frequency of different numbers of wickets taken by faspreet Bumrah in his last 30 matches.
(ii) What may be the title of this table?
Solution:
‘Number of wickets taken by Jaspreet Bumrah in his last 30 matches’ may be the title of this table.
(iii) What caught your attention in this table?
Solution:
It is interesting to see which number of wickets he most commonly took.
The most striking part is that Bumrah took 3 wickets in 8 matche which is the highest frequency.
(iv) In how many matches has Bumrah taken 4 wickets?
Solution:
Bumrah took 4 wickets in 3 matches.
(v) 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 …, upto: Can Mayank get the total number of wickets taken in this way? Why?
Solution:
No, Mayank cannot get the total number of wickets just by adding the numbers 0,1, 2, 3, upto 7 because he needs to multiply each number by its corresponding frequency first, then add those results.
(vi) Haw would you correctly figure out the total number of wickets taken by Bumrah in his last 30 matches, using this table?
Solution:
To find the total number of wickets
Multiply the number of wickets by the number of matches for each row.
Then, add up all these products.
e.g. (0 × 2) + (1 × 4) + (2 × 6) + (3 × 8) + (4 × 3) + (5 × 5) + (6 × 1) + (7 × 1) = 90
This will give us the total number of wickets taken across all 30 matches.
Question 6.
The following pictograph shows the number of tractors in five different villages.
Observe the pictograph and answer the following questions:
(i) Which village has the smallest number of tractors?
Solution:
Village D has the smallest number of tractors because in pictograph village D has the fewest symbols.
(ii) Which village has the most tractors?
Solution:
The village which shows the highest number of symbols is village C. Hence, village C has the most tractors.
(iii) How many more tractors does Village C have than Village B?
Solution:
It is clear from pictograph that village C has three more tractors than village B.
(iv) Komal says, ‘Village D has half the number of tractors as Village E.’ Is she right?
Solution:
Yes, komal is correct.
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:
(i) Which class has the least number of girls students?
(ii) What is the difference between the number of girls in class 5 and 6?
(iii) If two more girls were admitted in class 2, how would the graph change?
(iv) How many girls are there in class 7?
Solution:
(i) The pictograph shows the least number of symbols for class 8.
Hence, class 8 has the least number of girls students.
(ii) In the given pictograph, by counting the symbol for class 5 and class 6, we have 6 more girls in class 6 than in class 5.
(iii) Here, adding 2 more girls would increase the count by 2 and requires a half additional symbol.
The pictograph would show half additional symbol for class 2, assuming each symbol represent 4 girls.
(iv) There are 12 girls in class 7.
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.
∴ \(\frac{36}{6}\) =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 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?
Solution:
Required bar graph is given below.
From the bar graph, it is clear that ‘Reading story book’ is the most preferred activity after playing.
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:
(i) The total number of saplings planted on Wednesday and Thursday is _______.
(ii) The total number of saplings planted during the whole week is _______.
(iii) The greatest number of saplings were planted on _______ and the least number of saplings were planted 0n _______.
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:
(i) The total number of saplings planted on Wednesday and Thursday is (30 + 40) = 70.
(ii) The total number of saplings planted during the whole week is
50 + 40 + 30 + 40 + 50 + 60 + 40 = 310
(iii) The greatest number of saplings were planted on Saturday and the least number of saplings were planted on Wednesday.
Do it yourself.
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 are a few mistakes in the graph. Can you find those mistakes and fix them?
Solution:
To correct the bar graph, follow the steps given below.
(i) Ensure that the bars are drawn with the correct heights corresponding to the number in the table.
- 2006 1400 (bar height should correspond to 1400)
- 2010 1700 (bar height should correspond to 1700)
- 2014 2200 (bar height should correspond to 2200)
- 2018 3000 (bar height should correspond to 3000)
- 2022 3700 (bar height should correspond to 3700)
(ii) Check that the scale on the X-axis, match the numbers provided.
(iii) Correct any inconsistencies in the graph, where the height of the bars does not match the number of tigers.