Data Handling

Exercise 5.2

Question 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.

data handling pie chart 1

From this pie chart answer the following:

(i) If 20 people liked classical music, how many young people were surveyed?

Answer: When 10 people liked classical music, number of people surveyed is 100
So, When 1 person liked the classical music, number of people surveyed is `(100)/(10)`

When 20 people like the classical music, number of people surveyed

`=(100)/(10)xx20=200`

(ii) Which type of music is liked by the maximum number of people?

Answer: Light music is liked by maximum number of people.

(iii) If a cassette company were to make 1000 CD’s, how many of each type would they make?

Answer: Number of CD’s for different music
Semi Classical `= 1000 xx 20% = 200`
Classical `= 1000 xx 10% = 100`
Folk `= 1000 xx 30% = 300`
Light `= 1000 xx 40% = 400`


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
Summer90
Rainy120
Winter150

(i) Which season got the most votes?
(ii) Find the central angle of each sector.
(iii) Draw a pie chart to show this information.

Answer: (i) Winter got the most number of votes.
(ii) Central Angle can be calculated as follows:

`text(Season’s number of votes)/text(Total votes)xx360°`

Central angle for summer `=(90)/(360)xx360°=90°`

Central angle for rains `=(120)/(360)xx360°=120°`

Central angle for winter `=(150)/(360)xx360°=150°`

(iii) Pie Chart is as follows:

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

ColoursNo. of people
Blue18
Green9
Red6
Yellow3
Total36

Calculate respective proportion of each colour and use that proportion to find the central angle.

Answer: Following is the required pie chart:

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Proportion of Blue `=(18)/(36)=1/2`

So, central angle for Blue `=360°xx1/2=180°`

Proportion of red `=(6)/(36)=1/6`

So, central angle for red `=360°xx1/6=60°`

Proportion of yellow `=(3)/(36)=1/12`

So, central angle for yellow `=360°(1)/(12)=30°`

Proportion of green `=(9)/(36)=1/4`

So, central angle for green `=360°xx1/4=90°`

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 students were 540, answer the following questions. All values are shown in degrees.

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(i) In which subject did the student score 105 marks?

Central Angle `=(105)/(540)xx360°=70°`

In the pie chart 70° is the angle for Math, so the student scored 105 marks in math.

(ii) How many more marks were obtained by the student in Mathematics than in Hindi?

Answer: The difference in central angle between Math and Hindi = 90°-70°=20°

So, difference in scores in Hindi and Maths `=(20°)/(360°)xx540=30`

(iii) Examine whether the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.

Answer: Total of Angles of Social Science and Math = 80°+70°=150°
Total of Angles of Science and Hindi = 65°+90°=155°
It is clear that sum of marks obtained in Social Science and Math is less than that 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.

LanguageHindiEnglishMarathiTamilBengaliTotal
No. of students401297472

Answer:

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