NCERT Solutions for Class 8 Maths Chapter 5 Data Handling

 

NCERT solutions for class 8 maths chapter 5 Data Handling - In our daily life, we come across various types of data through the newspaper, television, social media which are related to many things like sports, economy, GDP, etc. Also, you must have seen these data are represented in the graphs, charts, and in the tabular form. Why we need data? What is the purpose of representing these data into a chart or in graph form? In CBSE NCERT solutions for class 8 maths chapter 5 data handling, you will get answers to all these questions. Basically, data is the collection of information and observations which can be used to make some important decisions. In this chapter, you will learn to represent data in organized form so that its interpretation and analysis become easier. You will get to know about types of graphs and charts to represent data and some are listed below.  

  • Tabular Chart- The most simple form of data presentation is Tabular chart where data is always represented in matrix form which is most easy to the readable form of data representation.

                 

  • Pie Chart - Pie Chart is the chart where the data represented either in percentage or in the angle made in the middle by that particular sector of the circle.

             

  • Bar Graph - It is the most preferred method of data representation where data always present in bars and multiple bars makes a bar graph.

               

  • Line Graph - Line Graph is the extended and updated version of Bar Graph where the top of every bar is connected to the next bar’s top and the adjoining of these tops makes a line graph.

               

There are many questions in the solutions of NCERT for class 8 maths chapter 5 data handling where you will get to know about the use of different types of graphs for different types of data based on the need. There are 3 exercises with 16 questions in this chapter. You will get detailed explanations of these questions in the CBSE NCERT solutions for class 8 maths chapter 5 data handling. Check NCERT solutions from class 6 to 12 to perform well in the exam.

Solutions of NCERT for class 8 maths chapter 5 Data Handling Topic: Looking For Infortmation

Q1 Draw an appropriate graph to represent the given information.

Month           July      August September   October  November December

Number of 

Watches sold

  1000      1500    1500     2000     2500    1500

Answer:

The above given graph represents the data given in the table.

Month           July      August September   October  November December

Number of 

Watches sold

  1000      1500    1500     2000     2500    1500

Q2 Draw an appropriate graph to represent the given information.

Children Who prefer

School  A 

School  B School C
     Walking        40       55       15
    Cycling        45       25        35

Answer:

Above graph represents the data shown in the table.

Children Who prefer

School  A 

School  B School C
     Walking        40       55       15
    Cycling        45       25        35

Q3 Draw an appropriate graph to represent the given information

Percentage wins in ODI by 8 top cricket teams

Team

From Champions

Trophy to World Cup-06

Last 10  ODI in 07

South Africa 

         75\; ^{o}/_{o}       78\; ^{o}/_{o}

Australia 

         61\; ^{o}/_{o}       40\; ^{o}/_{o}

Sri Lanka 

         54\; ^{o}/_{o}       38\; ^{o}/_{o}

New Zealand 

        47\; ^{o}/_{o}       50\; ^{o}/_{o}

England 

         46\; ^{o}/_{o}       50\; ^{o}/_{o}

Pakistan 

         45\; ^{o}/_{o}       44\; ^{o}/_{o}

West Indis

        44\; ^{o}/_{o}      30\; ^{o}/_{o}

India 

       43\; ^{o}/_{o}      56\; ^{o}/_{o}

Answer:

The above graph represents the data given in table.

Team

From Champions

Trophy to World Cup-06

Last 10  ODI in 07

South Africa 

         75\; ^{o}/_{o}       78\; ^{o}/_{o}

Australia 

         61\; ^{o}/_{o}       40\; ^{o}/_{o}

Sri Lanka 

         54\; ^{o}/_{o}       38\; ^{o}/_{o}

New Zealand 

        47\; ^{o}/_{o}       50\; ^{o}/_{o}

England 

         46\; ^{o}/_{o}       50\; ^{o}/_{o}

Pakistan 

         45\; ^{o}/_{o}       44\; ^{o}/_{o}

West Indis

        44\; ^{o}/_{o}      30\; ^{o}/_{o}

India 

       43\; ^{o}/_{o}      56\; ^{o}/_{o}

 

NCERT solutions for class 8 maths chapter 5 Data Handling Topic: Organising Data

Q1 A group of students were asked to say which animal they would like most to have as a pet. The results are given below:

dog, cat, cat, fish, cat, rabbit, dog, cat, rabbit, dog, cat, dog, dog, dog, cat, cow, fish, rabbit, dog, cat, dog, cat, cat, dog, rabbit, cat, fish, dog. Make a frequency distribution table for the same.

Answer:

The above data can be represented as shown below:

 

Animals

Tally marks

Number of animals

Cat

   \bcancel{\mahsf{\mid \mid \mid \mid }} \bcancel{\mahsf{\mid \mid \mid \mid }}

    10

Dog

\bcancel{\mahsf{\mid \mid \mid \mid }} \bcancel{\mahsf{\mid \mid \mid \mid }}

    10

Fish

     \mid \mid \mid

     3

Cow

     \mid

     1

Rabbit

     \mid \mid \mid \mid

     4

Solutions for NCERT class 8 maths chapter 5 Data Handling Topic: Grouping Data

Q1 Study the following frequency distribution table and answer the questions given below.

What is the size of the class intervals?

Frequency Distribution of Daily Income of 550 workers of a factory

                                            Table 5.3

       Class Interval

   (Daily Income in Rs.) 

        Frequency

  (Number of workers)

           100-125  

         45

          125-150

         25

         150-175

         55

        175-200

         125

        200-225

         140

       225-250

         55

       250-275

        35

     275-300

        50

      300-325

        20

      Total

         550

Answer:

(i) The size of the class intervals = 125-100=25

       Class Interval

   (Daily Income in Rs.) 

        Frequency

  (Number of workers)

           100-125  

         45

          125-150

         25

         150-175

         55

        175-200

         125

        200-225

         140

       225-250

         55

       250-275

        35

     275-300

        50

      300-325

        20

      Total

         550

 

Q1 (ii) Study the following frequency distribution table and answer the questions given below.

Which class has the highest frequency?

Frequency Distribution of Daily Income of 550 workers of a factory                            

                                Table 5.3

       Class Interval

   (Daily Income in Rs.) 

        Frequency

  (Number of workers)

           100-125  

         45

          125-150

         25

         150-175

         55

        175-200

         125

        200-225

         140

       225-250

         55

       250-275

        35

     275-300

        50

      300-325

        20

      Total

         550
 

Answer:

(ii) The class which has the highest frequency = 200 - 225 and the highest frequency is 140 

 

       Class Interval

   (Daily Income in Rs.) 

        Frequency

  (Number of workers)

           100-125  

         45

          125-150

         25

         150-175

         55

        175-200

         125

        200-225

         140

       225-250

         55

       250-275

        35

     275-300

        50

      300-325

        20

      Total

         550

 

Q1 (iii) Study the following frequency distribution table and answer the questions given below.

Which class has the lowest frequency?

Frequency Distribution of Daily Income of 550 workers of a factory                            

                                Table 5.3

       Class Interval

   (Daily Income in Rs.) 

        Frequency

  (Number of workers)

           100-125  

         45

          125-150

         25

         150-175

         55

        175-200

         125

        200-225

         140

       225-250

         55

       250-275

        35

     275-300

        50

      300-325

        20

      Total

         550
 

Answer:

(iii) The class which has the lowest frequency = 300-325 and lowest frequency is 20.

 

       Class Interval

   (Daily Income in Rs.) 

        Frequency

  (Number of workers)

           100-125  

         45

          125-150

         25

         150-175

         55

        175-200

         125

        200-225

         140

       225-250

         55

       250-275

        35

     275-300

        50

      300-325

        20

      Total

         550

 

Q1 (iv) Study the following frequency distribution table and answer the questions given below. What is the upper limit of the class interval 250-275?

Frequency Distribution of Daily Income of 550 workers of a factory                            

                                Table 5.3

       Class Interval

   (Daily Income in Rs.) 

        Frequency

  (Number of workers)

           100-125  

         45

          125-150

         25

         150-175

         55

        175-200

         125

        200-225

         140

       225-250

         55

       250-275

        35

     275-300

        50

      300-325

        20

      Total

         550
 

Answer:

(iv) The upper limit of the class interval 250-275 is 275 and frequency is 35.

 

       Class Interval

   (Daily Income in Rs.) 

        Frequency

  (Number of workers)

           100-125  

         45

          125-150

         25

         150-175

         55

        175-200

         125

        200-225

         140

       225-250

         55

       250-275

        35

     275-300

        50

      300-325

        20

      Total

         550

 

Q1 (v) Study the following frequency distribution table and answer the questions given below.

Which two classes have the same frequency?

Frequency Distribution of Daily Income of 550 workers of a factory                            

                                Table 5.3

       Class Interval

   (Daily Income in Rs.) 

        Frequency

  (Number of workers)

           100-125  

         45

          125-150

         25

         150-175

         55

        175-200

         125

        200-225

         140

       225-250

         55

       250-275

        35

     275-300

        50

      300-325

        20

      Total

         550

Answer:

(v) The two classes which have the same frequency are 150-175 and  225-250 also the frequency is 55.

Q2 Construct a frequency distribution table for the data on weights (in kg) of  20 students of a class using intervals

30-35,, 35-40,  and so on.

40,38,33,48,60,53,31,46,34,36,49,41,55,49,65,42,44,47,38,39

Answer:

The frequency distribution table for the data given is :

intervels students
30-35 3
35-40 5

40-45

3
45-50 5
50-55 2
55-60 1
60-65 1
  total = 20

 

Solutions for NCERT class 8 maths chapter 5 Data Handling Excercise: Bars With A Difference

Q1 (i) Observe the histogram (Fig 5.3) and answer the questions given below.

What information is being given by the histogram?

Answer:

The above histogram represents the number of girls as y-axis and heights in cm as x-axis.

Q1 (ii) Observe the histogram (Fig 5.3) and answer the questions given below.

Which group contains maximum girls?

Answer:

 

(ii) The group which contains maximum girls is 140-145.

Q1 (iii) Observe the histogram (Fig 5.3) and answer the questions given below. How many girls have a height of 145 \; cms and more?

Answer:

(iii) The girls having a height of 145 \; cms and more are 4+2+1=7

 

Q1 (iv) Observe the histogram (Fig 5.3) and answer the questions given below.

If we divide the girls into the following three categories, how many would there be in each?

150\; cm and more                     —  Group A

140\; cm to less than 150\; cm   — Group B

Less than 140\; cm                     — Group C

Answer:

150\; cm and more                          — Group A = 2+1=3

140\; cm to less than 150\; cm        — Group B = 7+4=11

Less than 140\; cm                           — Group C = 1+2+3=6

NCERT solutions for class 8 maths chapter 5 Data Handling Excercise: 5.1

Q1 (a) For which of these would you use a histogram to show the data?

The number of letters for different areas in a postman’s bag.

Give reasons for each.

Answer:

(a) The number of letters for different areas in a postman’s bag.

Histogram can be represented for the data which can be represented as manner of intervals.The number of letters for different areas in a postman’s bag cannot be represented in form of interval so this cannot be represented using histogram.

Q1 (b) For which of these would you use a histogram to show the data?

The height of competitors in an athletics meet.

Answer:

(b) The height of competitors in an athletics meet.

Histogram can be represented for the data which can be represented as manner of intervals.The height of competitors in an athletics meet can be represented in form of interval so this can be represented using histogram.

Q1 (c) For which of these would you use a histogram to show the data?

The number of cassettes produced by 5 companies.

Answer:

(c) The number of cassettes produced by 5 companies.

Histogram can be represented for the data which can be represented as manner of intervals.The number of cassettes produced by 5 companies cannot be represented in form of interval so this cannot be represented using histogram.

Q1 (d) For which of these would you use a histogram to show the data?

The number of passengers boarding trains from 7:00\; a.m. to 7:00\; p.m. at a station.

Answer:

(d) The number of passengers boarding trains from 7:00\; a.m. to 7:00\; p.m. at a station.

Histogram can be represented for the data which can be represented as manner of intervals.The number of passengers boarding trains from 7:00\; a.m. to 7:00\; p.m. at a station can be represented in form of interval so this can be represented using histogram.

Q2 The shoppers who come to a departmental store are marked as: man (M), woman (W), boy (B) or girl (G). The following list gives the shoppers who came during the first hour in the morning:

WWWGBWWMGGMMWWWWGBMWBGGMWWMMWWWMWBWGMWWWWGWMMWWMWGWMGWMMBGGW

Make a frequency distribution table using tally marks. Draw a bar graph to illustrate it.

Answer:

The frequency distribution table using tally marks is as shown :

Shopper Tally marks      Number of shoppers
     W \bcancel{\mahsf{\mid \mid \mid \mid }} \bcancel{\mahsf{\mid \mid \mid \mid }}\bcancel{\mahsf{\mid \mid \mid \mid }}\bcancel{\mahsf{\mid \mid \mid \mid }}\bcancel{\mahsf{\mid \mid \mid \mid }}\, \mid \mid \mid           28
     M \bcancel{\mahsf{\mid \mid \mid \mid }} \bcancel{\mahsf{\mid \mid \mid \mid }}\bcancel{\mahsf{\mid \mid \mid \mid }}           15
     B \bcancel{\mahsf{\mid \mid \mid \mid }}            5
     G \bcancel{\mahsf{\mid \mid \mid \mid }} \bcancel{\mahsf{\mid \mid \mid \mid }}\, \mid \mid           12
              60

 

The graph is as shown : 

 

Q3 The weekly wages (in Rs.) of 30 workers in a factory are.

830,835,890,810,835,836,869,845,898,890,820,860,832,833,855,845,804,808,812,840,885,835,836,878,840,868,890,806,840 

Using tally marks make a frequency table with intervals as 800–810, 810–820 and so on.

Answer:

Using tally marks a frequency table with intervals as 800–810, 810–820 and so on is as shown:

Intervals Tally MARKS Frequency
800-810               \mid \mid \mid 3
810-820                \mid \mid 2
820-830                  \mid 1
830-840          \bcancel{\mahsf{\mid \mid \mid \mid }} \mid \mid \mid \mid 9
840-850                 \bcancel{\mahsf{\mid \mid \mid \mid }} 5
850-860                   \mid 1
860-870                  \mid \mid \mid 3
870-880                   \mid 1
880-890                   \mid 1
890-900                 \mid \mid \mid \mid 4
     

Q5 (ii) The number of hours for which students of a particular class watched television during holidays is shown through the given graph. Answer the following.

How many students watched TV for less than 4 hours?

Answer:

(ii) 34 students watched TV for less than 4 hours.

The number of students who watched TV for less than 4 hours = sum of  the students who watched TV for (3–4hours) + (2–3hours) + (1–2hours.)

So, the total number of students = 4 + 8 + 22 = 34

Q5 (iii) The number of hours for which students of a particular class watched television during holidays is shown through the given graph. Answer the following.

How many students spent more than 5 hours in watching TV?

Answer:

(iii) 14 students spent more than 5 hours in watching TV.

The number of students who watched TV for >5 hours =  number of students who watched TV for (5 – 6 hours) + (6 – 7 hours).

So the no. of students = 8 + 6 = 14

Solutions of NCERT for class 8 maths chapter 5 Data Handling Topic: Circle Graph or Pie Chart

Q1 (i) Each of the following pie charts (Fig 5.5) gives you a different piece of information about your class. Find the fraction of the circle representing each of this information.

Answer:

50 \% of the fraction of the circle represent girls and other 50 \%  represent boys of class.

Q1 (ii) Each of the following pie charts (Fig 5.5) gives you a different piece of information about your class. Find the fraction of the circle representing each of these information.

Answer:

The circle represents that 20\% students use cycle for transportation,40\% walk and 40\% use bus or car for transportation.

Q2 (ii) Answer the following questions based on the pie chart given (Fig 5.6 ). Which two types of programmes have number of viewers equal to those watching sports channels?

Answer:

Informative and News together have a number of viewers equal to those watching sports channels.

 

Solutions for NCERT class 8 maths chapter 5 Data Handling Excercise: Drawing Pie Chart

Q1 Draw a pie chart of the data given below.

The time spent by a child during a day.

         Sleep —8\; Hours

        School — 6\; Hours

Homework —4\; Hours

             Play —4\; Hours

         Others — 2\; Hours

 

                     

Answer:

Pie chart of the data is given below:

 

Solutions of NCERT for class 8 maths chapter 5 Data Handling Excercise: Drawing Pie Chart

Q1 Which form of graph would be appropriate to display the following data.

Production of food grains of a state.

     Year   2001   2002   2003   2004   2005

  2006

   Production

(in lakh tons)

   60    50    70     55     80    85

Answer:

 

Data can be represented as shown below as bar graph. 

 

 

Q2 Which form of graph would be appropriate to display the following data.

Choice of food for a group of people.

   Favourite food

   Number of people

    North Indian 

      30

    South Indian 

      40

    Chinese

      25

    Others

      25

   Total

    120

 

Answer:

The given data can be represented as shown below as pie chart.

 

Q3 Which form of graph would be appropriate to display the following data.

The daily income of a group of factory workers

Daily Income

(in Rupees)

Number of workers

(In a factory)

    75-100

        45

   100-125

        35

   125-150

        55

   150-175

        30

   175-200

        50

   200-225

      125

   225-250

       140

Total

       480

Answer:

The data can be represented as shown below as bar graph.

 

NCERT solutions for class 8 maths chapter 5 Data Handling Excercise: 5.2

Q1 A survey was made to find the type of music that a certain group of young people liked in a city. Adjoining pie chart shows the findings of this survey. From this pie chart answer the following:

(i) If 20 people liked classical music, how many young people were surveyed?

(ii) Which type of music is liked by the maximum number of people?

(iii) If a cassette company were to make 1000 CD’s, how many of each type would they make?

 

Answer:

(i)If 20 people liked classical music

Total number of people = (100\times 20)\div 10 = 200 people.

(ii)  Maximum number of people light music i.e.40 \%.

(iii) If a cassette company were to make 1000 CD’s, then

     Light music CD's = ( 40\times 1000) \div 100\:\:=400

     Folk music CD's = \left ( 30\times 1000 \right )\div 100\:\:=300

     Classical music CD's = \left ( 10\times 1000 \right )\div 100\:\:=100

     Semi classical music CD's = \left ( 20\times 1000 \right )\div 100\:\:=200

 

Q2 A group of 360 people were asked to vote for their favourite season from the three seasons rainy, winter and summer.

 

(i) Which season got the most votes?

 

(ii) Find the central angle of each sector.

(iii) Draw a pie chart to show this information.

Answer:

(i) Winter season got the most votes.

(ii)  Total Votes = 90+120+150 = 360

central angle of summer = (90\degree\times 360\degree)\div 360\degree  =  90\degree

      central angle of rainy =  (120\degree\times 360\degree)\div 360\degree =120\degree

      central angle of winter = (150\degree\times 360\degree)\div 360\degree = 150\degree

(iii)