Gujarat BoardĀ GSEB Textbook Solutions Class 8 Maths Chapter 5 Data Handling Ex 5.2 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 8 Maths Chapter 5 Data Handling Ex 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:

- If 20 people liked classical music, how many young people were surveyed?
- Which type of music is liked by the maximum number of people?
- If a cassette company wants to make 1000 CD’s how many of each type would they make?

Solution:

1. Let the required number of young people = x

ā“ 10% 0f x = 20

or \(\frac{10}{100}\) Ć x = 20 or x = \(\frac{20Ć100}{10}\) = 200

2. Maximum number of people like the light music.

3. Total number of CDās = 1000

ā“ Number of CDās for semi classical

= 20% of 1000

= \(\frac{20}{100}\) Ć 1000 = 200

Number of CDās for classical

= 10% of 1000 = \(\frac{10}{100}\) Ć 1000 = 100

Number of CDās for folks

= \(\frac{30}{100}\) Ć 1000 = 300

Number of CDās for light music

= 40% of 1000 = \(\frac{40}{100}\) Ć 1000 = 400

Question 2.

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

- Which season got the most votes?
- Find the central angle of each sector?
- Draw a pie chart to show this information?

Solution:

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

2. Total votes = 90 + 120 + 150 = 360

ā“ Central angle of the sector corresponing to:

Summer season = \(\frac{90}{360}\) Ć 360Ā° = 90Ā°

Rainy season = \(\frac{120}{360}\) Ć 360Ā° = 120Ā°

Winter season = \(\frac{150}{360}\) Ć 360Ā° = 150Ā°

3.

Question 3.

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

Solution:

Central angle of the sector corresponding to:

(a) The blue colour = \(\frac{18}{36}\) Ć 360Ā°

= 18 Ć 10 = 180Ā°

(b) The green colour = \(\frac{9}{36}\) Ć 360Ā°

= 90Ā°

(c) The red colour = \(\frac{6}{36}\) Ć 360Ā° = 60Ā°

(d) The yellow colour = \(\frac{3}{36}\) Ć 360Ā° = 30Ā°

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?

- In which subject did the student score 105 marks?

Hint: For 540 marks, the central angle = 360Ā°. So, for 105 marks, what is the central angle? - How many 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?

Solution:

1. Total marks = 540

ā“ Central angle corresponding to 540 marks = 360Ā°

Central angle corresponding to 105 marks

= \(\frac{360}{540}\) Ć 105Ā° = 70Ā°

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

Thus, the student obtained 105 marks in Hindi.

2. āµ The central angle corresponding to the sector of Mathematics = 90Ā°

ā“ Marks obtained in Mathematics

= \(\frac{90}{360}\) Ć 540Ā° = 135

Thus, marks more in Mathematics than in Hindi

= 135 – 105 = 30

3. Since, the sum of the central angles for Social Science and Mathematics

= 65Ā° + 90Ā° = 155Ā°

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

= 80Ā° + 70Ā° = 150Ā°

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

ā“ Marks obtained 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?

Solution:

Central angle of the sector representing:

(a) Hindi language = \(\frac{40}{72}\) Ć 360Ā° = 40 Ć 5Ā° = 200Ā°

(b) English language = \(\frac{12}{72}\) Ć 360Ā° = 60Ā°

(c) Marathi language = \(\frac{9}{72}\) Ć 360Ā° = 45Ā°

(d) Tamil language = \(\frac{7}{72}\) Ć 360Ā° = 35Ā°

(e) Bengali language = \(\frac{4}{72}\) Ć 360Ā° = 4 Ć 5 = 20Ā°

Thus, the required pie chart is given below: