**Data Handling**

** Question 1.****A survey was made to find the type of music that a certain group of young people liked in a city. Following 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?

**Solution:****(i)** Let x be the number of young people surveyed.

∴ 10% of x = 20

⇒ x x = 20

⇒ x = 20 x 10 = 200

Thus, number of young people surveyed = 200**(ii)** Light music is liked by the maximum number of people.**(iii)** Number of CD’s in respect of

**Question 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 information.

**Solution:****(i)** The winter season got the maximum votes.**(ii)** The proportion of sectors (winter, summer and rainy seasons) are as**(iii)** Central angle for winter season

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

Find the proportion of each sector. For example. Blue is ; Green is and so on.

Use this to find the corresponding angles.

**Solution:**

Central angle for the blue colour

,

Central angle for the green colour

,

Central angle for the red colour

,

central angle for the yellow colour

,

Now, various components may be shown by the adjoining pie chart.

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

**(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.

**Solution:****(i)** For 540 marks, the central angle = 360°

∴ For 1 mark, the central angle =

∴ For 105 marks, the central angle =

Hence, from the given pie chart, the subject is Hindi.

**(ii)** Difference between the central angles made by the subject of Mathematics and Hindi = 90° – 70° = 20°.

For the central angle of 360°, marks obtained = 540

For the central angle of 1°, marks obtained

For the central angle of 20°, marks obtained

Hence, 30 more marks were obtained by the student in Mathematics than Hindi.

**(iii)** Sum of the central angles made by Social Science and Mathematics = 65°+ 90° = 155°.

And, the sum of the central angles made by Science and Hindi = 80°+ 70° = 150°.

Since 155° >150°, therefore, the sum of the marks obtained in Social Science and Mathematics is more 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.**

**Solution:**

Let us find the central angle of each sector. Here the total scale = 72. We thus have the following table :

Now, we make the pie chart as shown below :