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.
What would you do to find the most popular game among Naresh’s and Navya’s classmates?
Answer:
Question 2.
What is the most popular game in their class?
Solution:
Hockey
Question 3.
Try to find out the most popular game among your classmates.
Solution:
Do it yourself. [To find the most popular game among your classmates, collect the data from each student about his/her favourite game. Game liked by maximum number of students is the most popular game in your class.]
(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.
Complete the table to help Shri Nilesh to 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?
Solution:
(a) How many students chose Jalebi? 6
(b) Barfi was chosen by 3 students.
(c) How many students chose gujiya? 13
(d) Rasgulla was chosen by 7 students.
(e) How many students chose Gulab Jamun? 9
(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.
Help her to figure out the following:
- 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.
Solution:
- The largest show 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?
Answer:
In mathematics, ascending order arranges the numbers in increasing 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
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 bund 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) In the table, there is no picture for Thursday. This means on Thursday the minimum number of books were borrowed.
(b) There are total 24 pictures in the table and 1 picture = 1 book. Therefore, total 24 books were borrowed during the week.
(c) In the table there are maximum number of pictures for Saturday. Therefore, maximum number of books were borrowed on Saturday.
The maximum number of books borrowed on Saturday might by because people have more free time to read or study over weekend.
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?
Answer:
(a) 3 symbols represent the kites that Rani purchased.
(b) Poonam Ben purchased the maximum number of kites.
(c) Jasmeet purchased more kites than Chaman.
(d) Yes, Poonam Ben purchased 700 kites and it is more than double of 300 (double of 300 is 600).
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 on the insects and critters she saw there. Here is the data she collected-
Help her prepare a bar graph representing this data.
Solution:
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.
(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 Sag5r.
(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 bafts).
Solution:
(a and b)
(c) For Vidisha, bar length is 6 units, number of tickets 24. Therefore, scale = 24 ÷ 6 = 4 tickets per unit.
For Jabalpur, bar length is 5 units, number of tickets 20. Therefore, scale = 20 ÷ 5 = 4 tickets per unit.
Hence, the scale for this graph is 1 unit = 4 tickets.
(d)
The bar for Seoni was correct but the bar for Indore was incorrect. Following is the correct graph.
(e – f)
Question 3.
China 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:
(i) The frequency distribution table for the data is as follows:
| Transport vehicle | Number of vehicles |
| Bike | 13 |
| Car | 6 |
| Bus | 4 |
| Auto | 8 |
| Bicycle | 8 |
| Bullock cart | 2 |
| Scooter | 9 |
(ii) Bike is used most with a frequency of 13.
(iii) Do it by yourself.
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.
Solution:
Do it 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?
Solution:
The table is giving information about number of wickets taken by Jaspreet Bumrah in his last 30 matches.
(b) What may be the title of this table?
Solution:
Title of the given table could be “Number of wickets taken by Jaspreet Bumrah”.
(c) What caught your attention in this table?
Solution:
Out of 30 matches, Jaspreet Bumrah has taken 5 wickets in a match 5 times i.e. in 5 matches.
(d) In how many matches has Bumrah taken 4 wickets?
Solution:
Jaspreet Bumrah has taken 4 wickets in 3 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?
Solution:
No, the way Mayank is finding total number of wickets taken by Bumrah in his last 30 matches is wrong. In the« first column, each entry represents the number of wickets taken in some matches that is mentioned in the next column. 1 wicket in 4 matches means, he has taken 1 wicket in each of the 4 matches. Means a total of 4 wickets in 4 matches. Therefore, the method of Mayank will not give the correct number of wickets.
(f) How 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, we need to multiply wickets taken by number of matches in each row of the table and then add the results.
Therefore, total number of wickets taken in last 30 matches can be found as
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 wickets.
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?
(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?
Answer:
(a) Village D
(b) Village C
(c) Number of tractors in Village C = 8
Number of tractors in Village B = 5
So, Village C has 8 – 5 = 3 tractors more than village B.
(d) Village E has 6 tractors and Village D has 3 tractors.
So, Komal is right that village D has half the number of tractors as village E.
Question 7.
The number of female 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?
(b) What is the difference between the number of girls in Class 5 and 6?
(c) If 2 more girls were admitted in Class 2, how would the graph change?
(d) How many girls are there in Class 7?
Answer:
(a) Class 8 has the least number of girl students.
(b) Number of girls in class 5 = 2 × 4 + \(\frac{1}{2}\) × 4 = 8 + 2 = 10
Number of girls in class 6 = 4 × 4 = 16
Difference between them = 16 – 10 = 6
(c) The graph changes like as follows:
(d) Number of girls in class 7 = 4 × 3 = 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 the 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 dogs in Village B and Village D together will be more than the number of dogs in the other 4 villages. Is she right? Give reasons for your response.
Solution:
(a) 1 * = 6 dogs will be a useful scale or key to draw this pictograph.
(b) 6 symbols.
(c) Yes, because Total no. of dogs in villages B and D = 6 + 8 = 14 dogs = 14 × 6 = 84 dogs
Total no. of dogs in remaining 4 villages = 3 + 2 + 3 + 4 = 12 dogs = 12 × 6 = 72 dogs
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:
Other than playing, reading story books is preferred mostly by students.
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 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:
(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 52 + 40 + 30 + 40 + 50 + 60 + 40 = 312.
(iii) The greatest number of saplings were planted on Saturday, and the least number of saplings were planted on Wednesday.
More saplings were likely planted on days like Friday and Saturday because more students and teachers were free or willing to help. On other days, especially earlier in the week like Wednesday, there might have been more schoolwork or activities, so fewer people could join in.
The weather might have also played a role. Better weather on some days could have made it easier to plant more saplings, while rain or bad weather on other days may have slowed things down.
How to Check If These Ideas Are True:
- Look at the school schedule to see if some days had more free time or fewer lessons, which might explain why tnore people helped on certain days.
- Ask the students and teachers who took part about their availability and any difficulties they faced during the week.
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:
(i) The number of tigers (approximately) is 1400 in 2006. But in the bar graph, if is shown less than 1000 (bar is drawn and finished before 1000)
(ii) In 2014, the number of tigers is 2200 as given in the frequency table. But in the bar graph, if is shown close to 3000 (bar is approaching 3000).
(iii) In 2018, the number of tigers is 3000 as given in the frequency table. But in the bar graph, if is in correct (bar is very close to 2000).
The correct bar graph is shown below:
