5 . Data Handling

Chapter 5 : Data Handling

5. Data Handling

Exercise 5.1

1. For which of these would you use a histogram to show the data?
(a) The number of letters for different areas in a postman’s bag.
(b) The height of competitors in an athletics meet.
(c) The number of cassettes produced by 5 companies.
(d) The number of passengers boarding trains from 7:00 a.m. to 7:00 p.m. at a station. Give reasons for each.

Solution: (a) The number of letters for different areas in a postman’s bag . In this case , the data can not be divided into class interval .
(b) The height of competitors in an athletics meet . In this case , the data can be divided into class interval .
(c) The number of cassettes produced by 5 companies. In this case , the data can not be divided into class interval .
(d) The number of passengers boarding trains from 7:00 a.m. to 7:00 p.m. at a station. In this case , the data can be divided into class interval .

2. The shoppers who come to a departmental store are marked as: man (M), woman (W), boy (B) or girl (G). The following list gives the shoppers who came during the first hour in the morning:
W W W G B W W M G G M M W W W W G B M W B G G M W W M M W W W M W B W G M W W W W G W M M W W M W G W M G W M M B G G W
Make a frequency distribution table using tally marks. Draw a bar graph to illustrate it.

Solution : We construct the frequency distribution table :

We make a bar graph :

3. The weekly wages (in Rs ) of 30 workers in a factory are.
830, 835, 890, 810, 835, 836, 869, 845, 898, 890, 820, 860, 832, 833, 855, 845, 804, 808, 812, 840, 885, 835, 835, 836, 878, 840, 868, 890, 806, 840
Using tally marks make a frequency table with intervals as 800–810, 810–820 and so on.

Solution: We construct the frequency distribution table :

4. Draw a histogram for the frequency table made for the data in Question 3, and answer the following questions.
(i) Which group has the maximum number of workers?
(ii) How many workers earn Rs 850 and more?
(iii) How many workers earn less than Rs 850 ?

Solution: We make a histogram

(i) The maximum number of workers has class interval 830 - 840 .

(ii) The number of the workers earns Rs 850 and more is 10 .

(iii) The number of the workers earn less than Rs 850 is 20 .

5. The number of hours for which students of a particular class watched television during holidays is shown through the given graph. Answer the following.
(i) For how many hours did the maximum number of students watch TV?
(ii) How many students watched TV for less than 4 hours?

iii) How many students spent more than 5 hours in watching TV?

Solution: (i) The maximum number of students watch TV between 4 to 5 hours .

(ii) There are 34 students watched TV for less than 4 hours .

(iii) There are 14 students spent more than 5 hours in watching TV .

Exercise 5.2

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?

Solution: (i) The number of young people

(ii) The light music is liked by the maximum number of people (i.e., 40%).
(iii) The number of classical music like by young people

The number of folk music like by young people

The number of light music like by young people

The number of semi classical music like by young people

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

(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) Winter .

(ii) The central angle of each sector :

Season	No. of votes	Central angle
Summer	90
Rainy	120
Winter	150

(iii) We make the pie chart :

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

Colours	Number of people
Blue Green Red Yellow	18 9 6 3
Total	36

Solution: We find central angle each sector .

Colours	No. of people	Central angle
Blue	18
Green	9
Red	6
Yellow	3
Total	36	= 360°

Now , we make the pie chart:

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).

Solution: (i) The student score 105 marks

Therefore, the student score 105 marks in Hindi .

(ii) The number of the student score in mathematics

Therefore, the number of marks was obtained by the students in Mathematics than Hindi = 135 – 105 = 30 .

(iii) The sum of the mark obtained in Social Science and Mathematics = 65°+90° = 155°

And the sum of the mark obtained in Science and Hindi = 80° + 70° = 150°

Yes . Thus, the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.

5. The number of students in a hostel, speaking different languages is given below. Display the data in a pie chart.

Language	No. of students
Hindi	40
English	12
Marathi	9
Tamil	7
Bengali	4
Total	72

Solution: We find the central angle of each sector .

Language	No. of students	Central angle
Hindi	40
English	12
Marathi	9
Tamil	7
Bengali	4
Total	72

Now, we make the pie chart :

Exercise 5.3

1. List the outcomes you can see in these experiments.
(a) Spinning a wheel (b) Tossing two coins together

Solution: The sample space of the spinning a wheel

(a) The number of outcome

(b) The sample space of two coins

The number of outcome

2. When a die is thrown, list the outcomes of an event of getting
(i) (a) a prime number (b) not a prime number.
(ii) (a) a number greater than 5 (b) a number not greater than 5.

Solution: The sample space

(i) (a) the outcome of an event .

(b) The number of outcome

(ii) (a) The number of outcome .

(b) The number of outcome

3. Find the.
(a) Probability of the pointer stopping on D in (Question 1-(a))?
(b) Probability of getting an ace from a well shuffled deck of 52 playing cards?
(c) Probability of getting a red apple. (See figure below)

Solution: (a) The total number of outcome = 5

The probability of the pointer stopping on D

(b) The total number of outcome

The number of an ace = 4

The probability of getting an ace

The number of a red apple = 4

The probability of getting a red apple

4. Numbers 1 to 10 are written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of .
(i) getting a number 6?
(ii) getting a number less than 6?
(iii) getting a number greater than 6?
(iv) getting a 1-digit number?

Solution: The total number of slips = 10

(i) The number of outcome

The probability getting a number 6
(ii) The number of outcome

The probability getting a number less than 6
(iii) The number of outcome

The probability getting a number greater than 6
(iv) The number of outcome

The probability getting a 1-digit number

5. If you have a spinning wheel with 3 green sectors, 1 blue sector and 1 red sector, what is the probability of getting a green sector? What is the probability of getting a non blue sector?

Solution: The total number of a spinning wheel

(i) The number of a green sector

The probability of getting a green sector

(ii) The number of a non blue sector

The probability of getting a non blue sector

6. Find the probabilities of the events given in Question 2.

Solution: The sample space

The total number of outcome = 6

(i) (a) The number of a prime number

The probability of getting a prime number

(b) The number of ‘‘ not a prime number ”

The probability of getting not a prime number

(ii) (a) The number of a number greater than 5

The probability of getting a prime number

(b) The number of a number not greater than

The probability of getting a prime number