NCERT Solutions for Class 8 Maths Chapter 5 Data Handling

NCERT solutions 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

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

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

NCERT solutions for 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)









Total

Answer:

(i) The size of the class intervals =

Class Interval (Daily Income in Rs.)	Frequency (Number of workers)









Total

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)



	<img alt="125" height="14"

src="https://lh3.googleusercontent.com/slbrWPeOGm17_lo97intJiZTf4j58pfYCJSEDerYAzhGsGXGC0TmOG_UJyxchAcf6k8MZVpZaupe8enwlrWY4r0c3uxgn70nfdz6RiTZbhibDVIsfgHfWa_rw0rXyfwzZgzvYMA" style="margin-left: 0px; margin-top: 0px;" width="23" />

Total

Answer:

(ii) The class which has the highest frequency = and the highest frequency is

Class Interval (Daily Income in Rs.)	Frequency (Number of workers)









Total

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)









Total

Answer:

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

Class Interval (Daily Income in Rs.)	Frequency (Number of workers)









Total

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)









Total

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)









Total

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)









Total

Answer:

(v) The two classes which have the same frequency are and also the frequency is 55.

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

, and so on.

Answer:

The frequency distribution table for the data given is :

intervels	students







total =

NCERT solutions for 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?

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Answer:

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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?

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Answer:

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(ii) The group which contains maximum girls is <img alt="140-145." height="14"

src="https://lh3.googleusercontent.com/kBhEW0edakLUwuw4AgFjMzv3Pjlun4JcaJUgTws7XJissO2P5hsW3C1YSmW3HWFmVR4KltDVZKqQk-bYSmnOaEolXWkfB8NZBgz-DIwHekBYOOCWgLfKBnchdnlZ71zjCMqoYME" style="margin-left: 0px; margin-top: 0px;" width="79" />

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?

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Answer:

(iii) The girls having a height of $145 \; cms$ and more are

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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

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Answer:

$150\; cm$ and more — Group A =

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

Less than $140\; cm$ — Group C =

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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 companies.

Answer:

Histogram can be represented for the data which can be represented as manner of intervals.The number of cassettes produced by 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:

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	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 :

latest

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

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

Q4 (i) Draw a histogram for the frequency table made for the data in Question 3, and answer the following questions.

Which group has the maximum number of workers?

Answer:

(i) The group which has the maximum number of workers is

Q4 (ii) Draw a histogram for the frequency table made for the data in Question 3, and answer the following questions.

How many workers earn $Rs.\; 850$ and more?

Answer:

(ii) The workers earning $Rs.\; 850$ and more are 1 + 3 + 1 +1 + 4 = 10

Q4 (iii) Draw a histogram for the frequency table made for the data in Question 3,and answer the following questions.

How many workers earn less than $Rs.\; 850$ ?

Answer:

(iii) The workers earning less than $Rs.\; 850$ are .

3 + 2 + 1 + 9 + 5 = 20

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

For how many hours did the maximum number of students watch TV?

Answer:

(i) From the graph we observed that the maximum number of students (32) watch TV for 4-5 hours.

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 hours?

Answer:

(ii) 34 students watched TV for less than 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 hours in watching TV?

Answer:

(iii) 14 students spent more than 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

NCERT solutions 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.

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Answer:

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

Q1 (iii) 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.

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Answer:

(iii)

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The circle represents that $85\%$ students love and $15\%$ students hate Mathematics.

Q2 (i) Answer the following questions based on the pie chart given (Fig 5.6 ).

Which type of programmes are viewed the most?

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Answer:

(i) Entertainment programmes are viewed the most i.e. $50 \%$ .

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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?

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Answer:

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

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NCERT solutions for 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:

NCERT solutions 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)

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
South Indian
Chinese
Others
Total

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)





	<img alt="125" height="14"

Total

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 = $(100\times 20)\div 10$ = 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.

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(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:

1596116746260

(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)

Q3 Draw a pie chart showing the following information.

The table shows the colours preferred by a group of people.

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Answer:

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colours	number of people	in fraction	central angles
Blue	18	$\frac{18}{36}=\frac{1}{2}$	$\frac{1}{2}\times 360 \degree= 180\degree$
Green	9	$\frac{9}{36}=\frac{1}{4}$	$\frac{1}{4}\times 360 \degree= 90\degree$
Red	6	$\frac{6}{36}=\frac{1}{6}$	$\frac{1}{6}\times 360 \degree= 60\degree$
Yellow	3	$\frac{3}{36}=\frac{1}{12}$	$\frac{1}{12}\times 360 \degree= 30\degree$

Q4 The adjoining pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were , answer the following questions.

(i) In which subject did the student score 105 marks?

( Hint: for marks, the central angle $=360^{\circ}$ . So, for marks, what is the central angle?)

Answer:

subject	central angle	marks obtained
mathematics	$90\degree$	$(90\degree\times 540)\div 360 = 135$
science	$80\degree$	$(80\degree\times 540)\div 360 = 120$
social science	$65\degree$	$(65\degree\times 540)\div 360 = 97.5$
english	$55\degree$	$(55\degree\times 540)\div 360 = 82.5$
hindi	$70\degree$	$(70\degree\times 540)\div 360 = 105$

(i) In hindi subject the student score 105 marks.

Q4 (ii) The adjoining pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were , answer the following questions.

How many more marks were obtained by the student in Mathematics than in Hindi?

Answer:

subject	central angle	marks obtained
mathematics	$90\degree$	$(90\degree\times 540)\div 360 = 135$
science	$80\degree$	$(80\degree\times 540)\div 360 = 120$
social science	$65\degree$	$(65\degree\times 540)\div 360 = 97.5$
english	$55\degree$	$(55\degree\times 540)\div 360 = 82.5$
hindi	$70\degree$	$(70\degree\times 540)\div 360 = 105$

(ii)

Hence, 30 more marks were obtained by the student in Mathematics than in Hindi.

Examine whether the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.

( Hint : Just study the central angles).

Answer:

subject	central angle	marks obtained
mathematics	$90\degree$	$(90\degree\times 540)\div 360 = 135$
science	$80\degree$	$(80\degree\times 540)\div 360 = 120$
social science	$65\degree$	$(65\degree\times 540)\div 360 = 97.5$
english	$55\degree$	$(55\degree\times 540)\div 360 = 82.5$
hindi	$70\degree$	$(70\degree\times 540)\div 360 = 105$

(iii) the sum of the marks obtained in Social Science and Mathematics =

the sum of the marks obtained in Science and Hindi =

Yes, the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.

Q5 The number of students in a hostel, speaking different languages is given below. Display the data in a pie chart.

Answer:

The pie chart is as shown below:

NCERT solutions for class 8 maths chapter 5 Data Handling Practise: Getting A Result

Q1 If you try to start a scooter, what are the possible outcomes?

Answer:

1.If you try to start a scooter,then there are two possibilities.

(i) . The scooter will start.

(ii) . The scooter will not start.

Q2 When a die is thrown, what are the six possible outcomes?

Answer:

2. When a die is thrown, the six possible outcomes are :

(i) 1

(ii) 2

(iii)3

(iv)4

(v)5

(vi)6

Q3 When you spin the wheel shown, what are the possible outcomes? (Fig 5.9) List them.

(Outcome here means the sector at which the pointer stops).

Answer:

3. When we spin the wheel shown, the possible outcomes are:

(i) A

(ii) B

(iii) C

Q4 You have a bag with five identical balls of different colours and you are to pull out (draw) a ball without looking at it; list the outcomes you would get (Fig 5.10).

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Fig 5.10

Answer:

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Fig 5.10

The possible outcomes are:

(i) W

(ii) R

(iii) B

(iv) G

(v) Y

Q5 In throwing a die:

• Does the first player have a greater chance of getting a six?

• Would the player who played after him have a lesser chance of getting a six?

• Suppose the second player got a six. Does it mean that the third player would not have a chance of getting a six?

Answer:

In throwing a die:

• No, the first player also have same chance of getting a six.

• No, the player who played after him have same chance of getting a six.

• Suppose the second player got a six.It does not mean that the third player would not have a chance of getting a six. Third person also have same chance of getting six.

NCERT solutions for class 8 maths chapter 5 Data Handling Excercise: Linking Chances of Probablity

Suppose you spin the wheel

Q1 (i) List the number of outcomes of getting a green sector and not getting a green sector on this wheel (Fig 5.11).

Answer:

(i) the number of outcomes of getting a green sector = 5

the number of outcomes of not getting a green sector = 3

Suppose you spin the wheel

Q1 (ii) Find the probability of getting a green sector.

Answer:

(ii) the probability of getting a green sector = 5/8 = 0.625

Suppose you spin the wheel

Q1 (iii) Find the probability of not getting a green sector.

Answer:

(iii) the probability of not getting a green sector = $\frac{3}{8}$ =

NCERT solutions for class 8 maths chapter 5 Data Handling Excercise: 5.3

Q1 (a) List the outcomes you can see in these experiments. Spinning a wheel

Answer:

(a) the outcomes you can see in these experiments are:

(i) A

(ii) B

(iii) C

(iv) D

Q1 (b) List the outcomes you can see in these experiments Tossing two coins together

Answer:

(b)The outcomes you can see in the experiments Tossing two coins together are :

(i) Head

(ii) tail

Q2 When a die is thrown, list the outcomes of an event of getting

(i) (a) a prime number (b) not a prime number.

(ii) (a) a number greater than (b) a number not greater than .

Answer:

When a die is thrown, the outcomes of an event of getting

(i) (a) a prime number are 2,3,5.

(b) not a prime number are 1,4,6.

(ii) (a) a number greater than 5 is 6.

(b) a number not greater than 5 are1,2,3,4,5.

Q3 (a) Find the Probability of the pointer stopping on D in (Question 1-(a))?

Answer:

(a) Probability of the pointer stopping on D $=\frac{1}{5}=0.2$

Q3 (b) Find the Probability of getting an ace from a well shuffled deck of 52 playing cards?

Answer:

(b) Probability of getting an ace from a well shuffled deck of 52 playing cards

$=\frac{4}{52}=\frac{2}{26}=\frac{1}{13}=0.769$

Q3 (c) Find the Probability of getting a red apple. (See figure below)

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Answer:

$=\frac{4}{7}= 0.571$

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Q4 Numbers 1 to 10 are written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of .

(i) getting a number ?

(ii) getting a number less than ?

(iii) getting a number greater than ?

(iv) getting a 1-digit number?

Answer:

(i) the probability of getting a number

$=\frac{1}{10}=0.1$

(ii) the numbers less than 6 are: 1,2,3,4,5=5 numbers.

the probability of getting a number less than

$=\frac{5}{10}=0.5$

(iii) the numbers greater than 6 are: 7,8,9,10=4 numbers.

the probability of getting a number greater than

$=\frac{4}{10}=0.4$

(iv) 1 digit numbers = 1,2,3,4,5,6,7,8,9 = 9 numbers

the probability of getting a 1 digit number

$=\frac{9}{10}=0.9$

Q5 If you have a spinning wheel with green sectors, blue sector and red sector, what is the probability of getting a green sector? What is the probability of getting a non blue sector?