Class 6 Maths Chapter 4 Data Handling and Presentation (NCERT Ganita Prakash)

Data Handling and Presentation (NCERT Ganita Prakash)

Introduction

In everyday life, we collect information about different things. For example:

• Favourite games of students

• Number of students in a class

• Daily temperature

• Number of vehicles on roads

All such information is called data.

Facts, numbers, measures, observations and other descriptions of things that convey information about those things is called data. Data can be organised in a tabular form using tally marks for easy analysis and interpretation.

 Frequencies are the counts of the occurrences of values, measures or observations

Pictographs represent data in the form of pictures, or objects or parts of objects. Each picture represents a frequency which can be 1 or more than 1 — this is called the scale and it must be specified. 

 Bar graphs have bars of uniform width; the length or height that indicates the total frequency of occurrence. The scale that is used to convert length or height to frequency again, must be specified.

Data helps us:

• Understand information easily

• Compare different quantities

• Draw conclusions from observations

According to NCERT:

Data is a collection of facts, numbers, observations, or measurements that provide information about something. 

In this chapter, we learn how to collect, organise, represent and interpret data using different methods.

Section 4.1  

Page No. 75 

Figure it Out  

Q.1. What would you do to find the most popular game among Naresh’s and Navya’s 

classmates? 

Ans. One of the ways could be to arrange and organize the given data in a table. Think of 

some other ways. 

Q.2. What is the most popular game in their class? 

Ans. Hockey (frequency – 8). 

Q.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?       

Ans. 

a.  

b. ⨉  

c.  

d. ⨉  

Section 4.1  

Page No. 77 

Figure it Out  

Q.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. 

Ans. 

• 7 

• 3 

• 10 

• 15 

Q.2. How did arranging the data in ascending order help to answer these questions? 

Ans. Ordered data is helpful because in this form, frequency of any data is easy to count and 

the given information can be used easily. 

Q.3. Are there other ways to arrange the data? 

Ans. Yes, the data can be arranged in a frequency table. 

Section 4.2 

Page No. 83  

Q. What could be the problems faced in preparing such a pictograph, if the total number 

of students present in a class is 33 or 27? 

Ans.       represents 10 students and   represent 5 students. But to represent 3 or 7 students 

accurately by dividing these symbols is not possible. 

Figure it Out  

Q.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? 

Ans. a. Thursday  

b. 24 

c. Saturday. One of the reasons could be that  Sunday being a holiday students can read 

the borrowed books on Sunday. 

                                

 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? Ans. a.   3 symbols  b. Poonam Ben  c. Jasmeet  d. Yes. Number. of kites purchased by Poonam Ben = 700 = 2 x 300 +100  Section 4.3 Page no. 86 Q1. In Class 2, ___________ students were absent that day. Ans. 5 Q2. In which class were the maximum number of students absent? ___________ Ans. Class 8 Q3. Which class had full attendance that day? ___________ Ans. Class 5
Page no. 88 Figure it Out Q.1. How many total cars passed through the crossing between 6 am and noon? Ans. 4450 cars Section 4.4 Page No. 93 Q. On which item does Imran’s family spend the most and the second most? Ans. Imran’s family spends the most on food and the second most on house rent.  Q.2. Is the cost of electricity about one-half the cost of education? Ans. Yes, Q.3. Is the cost of education less than one-fourth the cost of food? Ans. Yes. Cost of education = Rs. 800 and cost of food = Rs 3400 =4 x Rs 850 So, cost of education = less than one-fourth of cost of food. Figure it Out Q.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.

Q.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).  Ans. a. 24  b. 20  c. 1unit length = 4 tickets   d. Q.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.  Q.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?  Ans. a. This table is giving the information about different number of wickets taken by  Jaspreet Bumrah in different number of matches.   b. The title of this table may be: Wickets Taken by Jaspreet Bumrah in Last 30  Matches.(think of more!)  c. In this table, attention seeking point is that in 1 match 7 wickets were taken by  Jaspreet Bumrah only.(think of more!)  d. In 3 matches Bumrah has taken 4 wickets.   e. No, Mayank can’t get the total number of wickets taken in this way. For example, 3  wickets per match were taken in 8 matches, which means total 24 wickets were taken.  f. To know the total number of wickets, prepare a next column of total wickets .It will  have products of corresponding numbers  of the two given columns. Then the sum of  the numbers in the 3rd column, will be the total number of wickets. Total number of  wickets =90   Q.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?  Ans. a. Village D.   b. Village C.  c. 3.  d. Yes   Q.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?  Ans. a. Class 8.  b. 6.  c. If 2 more girls were admitted in class 2, the last half symbol will be converted into  full symbol.  d. 12.  Q.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.  Ans.

                                             

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