Gujarat Board 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

∴ 10% 0f x = 20

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

2. Maximum number of people like the light music.

3. Total number of CD’s = 1000

∴ Number of CD’s for semi classical

= 20% of 1000

= \(\frac{20}{100}\) × 1000 = 200

Number of CD’s for classical

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

Number of CD’s for folks

= \(\frac{30}{100}\) × 1000 = 300

Number of CD’s for light music

= 40% of 1000 = \(\frac{40}{100}\) × 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

∴ Central angle of the sector corresponing to:

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

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

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

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 = \(\frac{18}{36}\) × 360°

= 18 × 10 = 180°

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

= 90°

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

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

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 = 360°. 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

∴ Central angle corresponding to 540 marks = 360°

Central angle corresponding to 105 marks

= \(\frac{360}{540}\) × 105° = 70°

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

Thus, the student obtained 105 marks in Hindi.

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

∴ Marks obtained in Mathematics

= \(\frac{90}{360}\) × 540° = 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

= 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 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 = \(\frac{40}{72}\) × 360° = 40 × 5° = 200°

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

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

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

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

Thus, the required pie chart is given below: