The document NCERT Solutions(Part- 2)- Data Handling Class 8 Notes | EduRev is a part of the Class 8 Course Mathematics (Maths) Class 8.

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**Question 1.** Each of the following pie charts gives you a different piece of information about your class. Find the fraction of the circle representing each of these information.

**Solution: **

**(i) **Fraction of the circle representing the ‘girls’ 50% = 50/100 = 1/2

Fraction of the circle representing the ‘boys’ 50% = 50/100 = 1/2**(ii)** Fraction of the circle representing ‘walk’ 40% = 40/100 =2/5

Fraction of the circle representing ‘bus or car’ 40% = 40/100 = 2/5

Fraction of the circle representing ‘cycle’ 20% =20/100 =1/5**(iii) **Fraction of the circle representing those who love mathematics

Fraction of the circle representing those who hate mathematics = 15% = 15/100 = 3/20**Question 2. **Answer the following questions based on the pie chart given.**(i)** Which type of programmes are viewed the most?**(ii)** Which two types of programmes have number of viewers equal to those watching sports channels?

**Solution: **From the given pie chart, we have

Type of viewers | Percentage |

Sports viewers News viewers Information viewers Entertainment viewers | 25% 15% 10% 50% |

Obviously,

**(i)** The entertainment programmes are viewed the most.

**(ii) **The news and informative programmes have the equal number of viewers.**Question 3.** Draw a pie chart of the data given below.

The time spent by a child during a day.

Sleep—8 hours

School—6 hours

Home work—4 hours

Play—4 hours

Others—2 hours

**Solution:** First we find the central angle corresponding to the given activities.

Activity | Duration of the activity in a day out of 24 hours | Central angle corresponding to the activity |

Sleep | 8 hours | |

School | 6 hours | |

Home work | 4 hours | |

Play | 4 hour | |

Others | 2 hours |

Now, the required pie chart is given below:

**Exercise 5.2**

**Question 1.** A survey was made of 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?

**Solution: **

**(i) **Let the required number of young people = x

∴10% of x = 20

or

or

**(ii)** Maximum number of people like the light music.

**(iii)** Total number of CD’s = 1000

∴Number of CD’s for semi classical = 20% of 1000

Number of CD’s for classical = 10% of 1000

Number of CD’s for folks

Number of CD’s for light music = 40% of 1000

**Question 2. **A group of 360 people were asked to vote for their favourite season from the three seasons rainy, winter and summer.

Season | No. of votes |

Summer Rainy Winter | 90 120 150 |

**(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)** Number of votes are maximum (150) for the winter season.

**(ii)** Total votes = 90 + 120 + 150 = 360

∴Central angle of the sector corresponding to:

Summer season

Rainy season

Winter season

**Question 3.** Draw a pie chart showing the following information. The table shows the colours preferred by a group of people.

Colours | Number of people |

Blue Green Red Yellow | 18 9 6 3 |

Total | 36 |

Find the proportion of each sector. For example,

Blue is 18/36 = 1/2 ; Green is 9/36 =1/4 and so on.

Use this to find the corresponding angles.

**Solution: **Central angle of the sector corresponding to:

**(a)** The blue colour

**(b) **The green colour

**(c) **The red colour

**(d) **The yellow colour

Thus, the required pie chart is given below:

**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 student 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 marks = 360°

Central angle corresponding to 105 marks

Since the sector having central angle 70° is corresponding to Hindi.

Thus, the student obtained 105 marks in Hindi.

**(ii)** ∵ The central angle corresponding to the sector of Mathematics = 90°

∴Marks obtained in Mathematics

Thus, marks more in Mathematics than in Hindi = 135 – 105 = 30

**(iii) **Since, the sum of the central angles for Social Science and Mathematics

= 65° + 90° = 155°

Also, the sum of the central angles for Science and Hindi

= 80° + 70° = 150°

∵ Marks obtained are proportional to the central angles corresponding to various items and 155° > 150°.

∵Marks of in Science and Mathematics are more than the marks obtained 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.

Language | Hindi | English | Marathi | Tamil | Bengali | Total |

Number of students | 40 | 12 | 9 | 7 | 4 | 72 |

**Solution: **Central angle of the sector representing:

**(a) **Hindi language

**(b) **English language

**(c)** Marathi language

**(d) **Tamil language

**(e)** Bengali language

Thus, the required pie chart is given below:

**Chance and Probability**

Probability is the measure of the change of the happening of an event. The probability of an out come is represented by a number between 0 and 1.

**Note:** For an impossible event probability is 0 and for a certain event, the probability is 1.

**Equally Likely Outcomes**

When each of the outcomes of an experiment has the same chance of occurring, we say that it is equally likely outcome.

**Example:** A die is thrown. Number of the six outcomes are almost equal to each other, i.e. they are equally likely to occur.

**Outcomes as Events**

Each of the outcomes of an experiment or a collection of outcomes make an event.

**For example:**

(i) Throwing a die and getting each of the outcomes 1, 2, 3, 4, 5 or 6 is an event.

(ii) Tossing a coin and ‘getting a head’ or ‘getting a tail’ is an event.

**Finding Probability**

**Question:** (i) Let us toss a coin once. Then there are only two equally likely outcomes—Head or tail.

Since, Likely hood of getting a Head as an outcome out of the two outcomes.

∴ Probability of getting a Head = 1/2 =

Similarly,

Probability of getting a Tail = 1/2

**(ii)** A die is marked 1, 2 3, 4, 5 and 6 on its faces, such that one number is on one face. If we throw it once, the outcomes are 1, 2, 3, 4, 5 or 6.

∴ There are 6 equally likely outcomes.

So, probability of getting 4 as an outcome

Similarly, we get the probability of other numbers.

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