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Data Handling : Exercise 5.2 (Mathematics NCERT Class 8th)


Q.1 A survey was made to 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?Sol. (i) It can be seen from the pie chart that the number of people who like class music is 10%. Hence, this 10% represents 20 people.
Now, 100% represents = = 200 people
Hence, 200 young people were surveyed.
(ii) ) It can be seen from the pie chart that light music is liked by the maximum number of people which forms 40% of all the type of music.
(iii) For classical music type, number of CD’s is 10% of 1000 = = 100
For semi - classical music type, number of CD’s is 20% of 1000 = = 200
For folk music type, number of CD’s is 30% of 1000 = = 300
For light music type, number of CD’s is 40% of 1000 = = 400

Q.2 A group of 360 people were asked to vote for their favourite 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 informationSol. (i) Winter season got the most votes.
(ii) Here, the toal number of votes = 90 + 120 + 150 = 360
The table below shows the central angle of each sector:

Season

No. of votes

Fraction

Central angle

Summer 90  {{90} \over {360}}  {{90} \over {360}} \times 360^\circ = 90^\circ
Rainy 120  {{120} \over {360}}  {{120} \over {360}} \times 360^\circ = 120^\circ
Winter 150  {{150} \over {360}}  {{150} \over {360}} \times 360^\circ = 150^\circ

(iii) The pie chart for the given data is shown below:Q.3 Draw a pie chart showing the following information. The table shows the colours preferred by a group of people.Sol. The table below shows the central angle for each colour:

Colours

Number of students

Fraction

Central angle

Blue 18 {{18} \over {36}}

{{18} \over {36}} \times 360^\circ = 180^\circ

Green 9 {9 \over {36}}

{9 \over {36}} \times 360^\circ = 90^\circ

Red 6 {6 \over {36}}

{{18} \over {36}} \times 360^\circ = 180^\circ

Yellow 3 {3 \over {36}}

{{18} \over {36}} \times 360^\circ = 180^\circ

Q.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).Sol. (i) Here, total marks are 540 which represents 360ᵒ.
Therefore, central angle for 105 marks = {{105} \over {540}} \times 360^\circ = 70^\circ
It can be seen from the pie-chart that, Hindi is the subject having central angle as 70^\circ .
Hence, the students scored 105 marks in Hindi.
(ii) The marks obtained in Mathematics = {{90^\circ } \over {360^\circ }} \times 540 = 135
The marks obtained in Hindi = {{70^\circ } \over {360^\circ }} \times 540 = 105
Therefore, difference of marks = 135 – 105 = 30
Hence, 30 more marks were obtained by the student in Mathematics than in Hindi.
(iii) It can be seen from the pie chart,
Sum of central angles of Social Science and Mathematics = 90^\circ + 135^\circ = 155^\circ
Sum of central angles of Science and Hindi = 80^\circ + 70^\circ = 150^\circ
Here, the sum of the central angles of Social Science and Mathematics is more than that in Science and Hindi. Hence, the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.

Q.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

Sol. The table below represents the central angle for each subject:

Language

Number of students

Fraction

Central angle

Hindi 40 {{40} \over {72}}

{{40} \over {72}} \times 360^\circ = 200^\circ

English 12 {{12} \over {72}}

{{12} \over {72}} \times 360^\circ = 60^\circ

Marathi 9 {9 \over {72}}

{9 \over {72}} \times 360^\circ = 45^\circ

Tamil 7 {7 \over {72}}

{7 \over {72}} \times 360^\circ = 35^\circ

Bengali 4 {4 \over {72}}

{4 \over {72}} \times 360^\circ = 20^\circ

The pie chart of the above data is shown below:



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