NCERT Solutions for Class 8 Maths Chapter 5 Data Handling Ex 5.2 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 5 Data Handling Ex 5.2.

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 8 |

Subject |
Maths |

Chapter |
Chapter 5 |

Chapter Name |
Data Handling |

Exercise |
Ex 5.2 |

Number of Questions Solved |
5 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 8 Maths Chapter 5 Data Handling Ex 5.2

**Question 1.**

A survey was made to find the type of music that a certain group of young people liked in a city. The 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?

**Solution.**

**(i)** Suppose that x young people were surveyed. Then, the number of young people who liked classical music = 10% of x

\(\frac { 10 }{ 100 } \times x=\frac { x }{ 10 } \)

According to the question,

\(\frac { x }{ 10 } =20\)

⇒ x = 20 x 10

⇒ x = 200

Hence, 200 young people were surveyed.

**(ii)** Light music is liked by the maximum number of people.

**(iii)** Total number of CD’s = 1000 Number of CD’s of Semi Classical music = 20% of 1000

⇒ \(\frac { 20 }{ 100 } \times 1000=200\)

Number of CD’s of Classical music = 10% of 1000

⇒ \(\frac { 10 }{ 100 } \times 1000=100\)

Number of CD’s of Folk music = 30% of 1000

⇒ \(\frac { 30 }{ 100 } \times 1000=300\)

Number of CD’s of Light music = 40% of 1000

⇒ \(\frac { 40 }{ 100 } \times 1000=400\)

**Question 2.**

A group of 360 people was asked to vote for their favorite 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.

**Solution.**

**(i)** Winter season got the most votes.

**(ii)** Total votes = 90 + 120 + 150 = 360. Central angle of winter sector

\(= \frac { Number\quad of\quad people\quad who\quad vote\quad for\quad winter\quad season }{ Total\quad number\quad of\quad people } \times { 360 }^{ \circ }\)

= \(\frac { 150 }{ 360 } \times { 360 }^{ \circ }={ 150 }^{ \circ }\)

Central angle of summer sector

\(= \frac { Number\quad of\quad people\quad who\quad vote\quad for\quad summer\quad season }{ Total\quad number\quad of\quad people } \times { 360 }^{ \circ }\)

= \(\frac { 90 }{ 360 } \times { 360 }^{ \circ }={ 90 }^{ \circ }\)

Central angle of rainy sector

\(= \frac { Number\quad of\quad people\quad who\quad vote\quad for\quad rainy\quad season }{ Total\quad number\quad of\quad people } \times { 360 }^{ \circ }\)

= \(\frac { 120}{ 360 } \times { 360 }^{ \circ }={ 120 }^{ \circ }\)

**(iii)**

**Question 3.**

Draw a pie chart showing the following information. The table shows the colors preferred by a group of people.

Find the proportion of each sector. For example, Blue is \(\frac { 18 }{ 36 } =\frac { 1 }{ 2 } \) ; Green is \(\frac { 9 }{ 36 } =\frac { 1 }{ 4 } \) ; and so on. Use this to find the corresponding angles.

**Solution.**

**Question 4.**

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 540, answer the following questions.

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

**(Hint:** For 540 marks, the central angle = 360°. So, for 105 marks, what is the central angle ?)

**(ii)** How many more marks were obtained by the student in Mathematics than in Hindi?

**(iii)** 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).

**Solution.**

**(i)** Total marks = 540

∵ Central angle corresponding to 540 = 360°

∴ Central angle corresponding to 105

\(\frac { { 360 }^{ \circ } }{ 540 } \times \left( 105 \right) ={ 70 }^{ \circ }\)

Since the sector having central angle 70° is corresponding to Hindi, therefore, the student scored 105 marks in Hindi.

**(ii)** Central angle corresponding to the sector of Mathematics = 90°

∴ Marks obtained by the student in Mathematics

\(\frac { { 90 }^{ \circ } }{ { 360 }^{ \circ } } \times 540=135\).

Marks obtained by the student in Hindi = 105.

Hence, the student obtained 135 – 105 = 30 marks more in Mathematics than in Hindi.

**(iii)** Sum of the central angles for Social Science and Mathematics

= 65° + 90° = 155°

Sum of the central angles for Science and Hindi

= 80° + 70° = 150°

Since the marks obtained are proportional to the central angles corresponding to various subjects and 155° > 150°, therefore the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.

**Question 5.**

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

**Solution.**

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