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: