In chapter 4: Data Handling and Presentation we will know about Collecting and Organising Data, Pictographs, Bar Graphs, Artistic and Aesthetic Considerations, horizontal bars and vertical bars.
NCERT CLASS 6TH MATHS CHAPTER 4 DATA HANDLING AND PRESENTATION
Any collection of facts, numbers, measures, observations, or other
descriptions of things that convey information about those things is
called data. Maintain and represent of record of this data in form of table and graph are called data handling and presentation.
- NCERT CLASS 6TH MATHS CHAPTER 1 PATTERNS IN MATHEMATICS
- NCERT CLASS 6TH MATHS CHAPTER 2 LINES AND ANGLES
- NCERT CLASS 6TH MATHS CHAPTER 3 NUMBER PLAY
- NCERT CLASS 6TH MATHS CHAPTER 5 PRIME TIME
- NCERT CLASS 6TH MATHS CHAPTER 6 PERIMETER AND AREA
- NCERT CLASS 6TH MATHS CHAPTER 7 FRACTION
- NCERT CLASS 6TH MATHS CHAPTER 8 PLATING WITH CONSTRUCTIONS
- NCERT CLASS 6TH MATHS CHAPTER 9 SYMMETRY
- NCERT CLASS 6TH MATHS CHAPTER 10 THE OTHER SIDE OF ZERO
Topic 4.1 Collecting and Organising Data
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:
 |
Figure it Out
Question 1
What would you do to find the most popular game among Naresh’s and Navya’s classmates?
Solution:
First we will arrange given data in a table like gane's name and number of students like that game.
GAME’S NAME | NUMBER OF STUDENTS LIKE |
Kabaddi | 6 |
Hockey | 8 |
Satoliya (Pittu) | 5 |
Cricket | 6 |
Badminton | 2 |
Football | 4 |
Question 2
What is the most popular game in their class?
Solution:
The most popular game in ther class is 'Hockey' because most number of students favourite game is hockey.
Question 3
Try to find out the most popular game among your classmates.
Solution:
Try to yourself.
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 andput 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) 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? (✖)
* Shri Nilesh is a teacher. He decided to bring sweets to the class to celebrate the new year. The sweets shop nearby has jalebi, 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 
.
Figure it Out
Question 1
Complete the table to help Shri Nilesh to purchase the correct numbers of sweets:
(a) How many students choose jalebi?
(b) Barfi was choosen by students?
(c) How many students choose gujiya?
(d) Rasgulla was choosen by students?
(e) How many students choose gulab jamun?
Solution:
(a) 6 students choose jalebi.
(b) Barfi was choosen by 3 students.
(c) 13 students choose gujiya.
(d) Rasgulla was choosen by 7 students
(e) 9 students choose gulab jamun.
Question 3
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:
Yes, the sweets in the above table sufficient to distribute each type of sweet to the correct student because number of sweets is equal to number of students.
* 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
Figure it Out
Question 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.
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:
After arranging the data in ascending order we find the largest and the smallest shoe size very easily, the same shoe size came together by which we count number of students same shoe size quickly.
Question 3
Are there other ways to arrange the data?
Solution:
yes we can arrange this data in the form of tally marks.
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:
Activity based question do by your self because every student will get different answer of this question.
To collect number of different types of trees and fill in the table.
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:
Topic 4.2 Pictographs
Pictograph is way to represent the information by help of pictures and symbols.Each symbol or picture can represent one unit or multiple units.
Figure it Out
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) On wednesday the minimum number of books were borrowed.
(b) 24 books was borrowed during the week.
(c) On Saturday he maximum number of books were borrowed because next day is sunday .
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.
Prepare a pictograph using the symbol ム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 symbols
(b)Poonam ben purchased the maximum number of kites.
(c) Jasmeet purchased more kite than Chaman.
(c) Yes, she is not correct because Rani purchased 300 kites and Poonam ben purchased 700 kites ( 700 is more than double of 300).
Topic 4.3 Bar Graphs
Figure it Out
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:
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 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).
Solution:
(a) 24 tickets
(b)
20 tickets
(c)
Length of of the bar of Vidisha = 6 units
Number of tickets sold for vidisha = 24 tickets
So, 6 unit = 24 tickets
Therefore 1 unit = 24 ÷ 6 = 4 ticket
Hence, the scale of this bar graph is 1 unit = 4 ticket.
(d)
(e)
(f)
The bars for Seoni is correct but the bar for Indore is not correct . Correct bar graph for the given data are as follow
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:
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.
(a)
Bike was used the most as means of transport.
(c)
I use table of solution (a) to collect this data in the form of tally marks.
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:
Record of rolling a dice
frequency distribution table
(a)
Number 1 appeared minimum number of times
(b)
Number 2, 4 and 5 appeared maximum number of time
(c)
Number 3 and 6 both appeared 5 times, Number 2, 4 and 5 all three appeared 6 times.
(Note : Activity based question different answer possible each time)
(Note : Activity based question different answer possible each time)
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?
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)
This table is giving the information about number of wickets taken by Jaspreet Bumrah in his last 30 matches.
(b)
The title of this table may be "Wickets taken by Jaspreet Bumrah".
(c)
(d)
In 3 matches he has taken 4 wickets.
(e)
No, by adding 0 to 7 he cannot get total number of wickets.
(f)
If we want to know total number of wicket first we will have to find product of column of wicket taken and number of matches then add all the obtained product.
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?
Solution:
(a)
Village D has the smallest number of tractors.
(b)
Village C has the most tractors.
(c)
Village C have 3 tractors more than Village B.
(d)
Yes, she is right .
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:
a. Which class has the least number of girl students?
b. What is the difference between the number of girls in Classs 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?
Solution:
(a)
Class 8 ha the least number of girls.
(b)
Number of girls in class 5 = 10
Number of girls in class 6 = 16
Difference = 16 - 10 = 6 girls
Hence 6 girls more in class 6 than class 5.
(c)
Number of girls in class 2 = 18
Number of new girls = 2
Total number of girls now = 18 + 2 = 20
Hence, we can represent 20 girls with 5 complete symbols.
(d)
There are 12 girls in classs 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:
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:
Useful key for this pictograph will 1 dog symbol = 6 dogs because the number of dogs in different villages are multiple of 6.
(b)
We will use 6 symbols to represent the dogs in Village B.
(c)
Total number of dogs in village B and D = 36 + 48 = 84 dogs
Total number of dogs in village A, C, E and F = 18 + 12 + 18 + 24 = 72 dogs
Total number of dogs in village A, C, E and F = 18 + 12 + 18 + 24 = 72 dogs
Yes, Kamini is right the number of dogs in Village B and Village D together are more than the number of dogs in the other 4 villages.
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:
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 —
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 70.
(b)
The total number of saplings planted during the whole week is 312(approx.).
(c)
The greatest number of saplings were planted on saturday, and the least number of saplings were planted on wednesday.
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:
Figure it Out
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?
Solution:
We will use vertical bars because height is measured upwards from the ground.
Question 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?
Solution:
We will use horizontal bars because length is measured parallel to the ground.
Table of the longest rivers on each continent:
0 Comments