CHAPTER 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.
(a) Answer: Here, we cannot show the data in class intervals. So, we cannot use histogram.
(b) Answer: Here, we can show the data in class intervals. So, we can use histogram.
(c) Answer: Here, we cannot show the data in class intervals. So, we cannot use histogram.
(d) Answer: Here, we can show the data in class intervals. So, we can use histogram.
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:
3. The weekly wages (in ₹) 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:
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 ₹850 and more?
(iii) How many workers earn less than ₹850?
Solution:
(i) 830-840 is the group having maximum numbers of workers.
(ii) Worker’s earning ₹850 and more = 1+ 3+ 1+1+ 4= 10
(iii) Workers earning ₹850 and less = 3+ 2+ 1+9+5=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?
Answer:
(i) The maximum number of students watched T.V. for 4 – 5 hours.
(ii) 34 students watched T.V. for less than 4 hours.
(iii) 14 students spent more than 5 hours in watching T.V.
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) Let, total number of people surveyed be x.
A/Q,
10% of x = 20
⸫Total number of people surveyed = 200
(ii) Maximum people like light music.
(iii) Here, total CD’s = 1000
⸫Classical = 10% of 1000 =
⸫Semi classical = 20% of 1000 =
⸫Light = 40% of 1000 =
⸫Folk = 30% of 1000 =
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) Winter
(ii) Total votes = 360
Central angle of Summer =
Central angle of Rainy =
Central angle of Winter =
(iii)
3. Draw a pie chart showing the following information. The table shows the colours preferred by a group of people.
Solution:
Total people = 36
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:
Total marks = 540
(i) The student scored 105 marks in Hindi.
(ii) Marks obtained in Mathematics = 135
Marks obtained in Hindi = 105
Difference = 135 – 105 = 30
Thus, 30 more marks were obtained by the student in Mathematics than in Hindi.
(iii) The sum of marks in Social Science and Mathematics = 65° + 90° = 155°
The sum of marks in Science and Hindi = 80° + 70° = 150°
⸫The sum of the marks 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.
Solution:
Total students = 72
Exercise 5.3
1. List the outcomes you can see in these experiments.
(a) Spinning a wheel
Answer: Outcomes = A, B, C, D
(b) Tossing two coins together
Answer: Outcomes = HH, HT, TH, TT
2. When a die is thrown, list the outcomes of an event of getting
(i) (a) a prime number (b) not a prime number.
Answer: (a) Outcomes = 2, 3, 5
(b) Outcomes = 1, 4, 6
(ii) (a) a number greater than 5 (b) a number not greater than 5.
Answer: (a) Outcomes = 6
(b) Outcomes = 1, 2, 3, 4, 5
3. Find the.
(a) Probability of the pointer stopping on D in (Question 1-(a))?
Answer:
Total number of outcomes = 5
Number of outcome of the pointer stopping on D = 1
⸫Probability of the pointer stopping on D =
(b) Probability of getting an ace from a well shuffled deck of 52 playing cards?
Answer:
Total number of outcomes = 52
Number of outcome of getting an ace = 4
⸫Probability of getting an ace =
(c) Probability of getting a red apple. (See figure below)
Answer:
Total number of outcomes = 7
Number of outcome of getting a red apple = 4
⸫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?
Answer:
Total number of outcomes = 10
(i) Number of outcome of getting a number 6 = 1
⸫Probability of getting a number 6 =
(ii) Number of outcomes of getting a number less than 6 = 5
⸫Probability of getting a number less than 6 =
(iii) Number of outcomes of getting a number greater than 6 = 4
⸫Probability of getting a number greater than 6 =
(iv) Number of outcomes of getting a 1-digit number = 9
⸫Probability of getting 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:
Total number of outcomes = 3 + 1 + 1 = 5
Number of outcomes of getting a green sector = 3
⸫Probability of getting getting a green sector =
Number of outcomes of getting a non blue sector = 3 + 1 = 4
⸫Probability of getting getting a non blue sector =
6. Find the probabilities of the events given in Question 2.
Solution:
Total number of outcomes = 6
Number of outcomes of getting a prime number = 3
⸫Probability of getting a prime number =
Number of outcomes of getting a non prime number = 3
⸫Probability of getting a prime non prime number =
Number of outcomes of getting a number greater than 5 = 1
⸫Probability of getting a number greater than 5 =
Number of outcomes of getting a number not greater than 5 = 5
⸫Probability of getting a number not greater than 5 =
