Question 1
For which of these would you use a histogram to show the data?(a) The number of letters for different areas in a postmanâ€™s bag.
(b) The height of competitors in an athletics meet.
(c) The number of cassettes produced by 5 companies.
Solution:
Histogram can be used for (b) and (d) as the given data can be divided into class intervals. In (a) and (c) the data cannot be divided into class intervals.
Question 2
The shoppers who come to a departmental store are marked as: man (M), womanW 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:
Question 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 800â€“810, 810â€“820 and so on.
Solution:
Question 4
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
Draw a histogram for the above data 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:
(i) 830  840
(ii) 10 workers earn Rs 850 and more.
(iii) 20 workers earn less than Rs 850
Question 5
The number of hours for which students of a particular class watched television during holidays is shown through the given graph.(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?
(i) 4  5 hours
(ii) 34 students
(iii) 14 students
Question 6
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 CDâ€™s, how many of each type would they make?
(i) 200 people
(ii) Light music
(iii) A cassette company would make 100 CD's of Classical music, 200 CD's of Semi classical music, 400 CD's of Light music and 300 CD's of Folk music
Question 7
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 season
(ii) The central angle of the Winter season sector is 150Â°, Rainy season sector is 120Â° and Summer season sector is 90Â°
(iii)Total number of votes = 360 the corresponding angles of summer,rainy and winter seasons are 90Â° , 120Â° and 150Â° respectively
Question 8
Draw a pie chart showing the following information. The table shows the colors preferred by a group of people.Solution:
Total number of people in a group = 36
Therefore corresponding central angles are calculated as below:
Â
Colours 
No. of People 
In Fractions 
Central Angle 
Blue 
18 


Green 
9 


Red 
6 


Yellow 
3 


Question 9
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 = 360Â°.
So, for 105 marks, what is the central angle?)
(ii) How many more marks were obtained by the student in Mathematics than in Hindi?
(Hint: Just study the central angles).
Solution:
Total marks scored = 540
(i) Mark scored in the subject = 105
Â Â Â Â Â Â The central angle for 105 marks =
Â Â Â Â Â Â From the pie chart we see that the central angle for Hindi is 70Â° .
Â Â Â Â Â Â Â âˆ´The student has scored 105 marks in Hindi.
(ii) The central angle for Mathematics = 90Â°
Â Â Â Â Â Â Â Â âˆ´The marks obtained by the student in Mathematics =
Â Â Â Â Â Â Â Â Â Â âˆ´The difference in the marks obtained in Mathematics and Hindi = 135  105 = 30
Â Â Â Â Â Â Â Â Â Â âˆ´The student has scored 30 marks more in Mathematics than in Hindi.
(iii) Sum of the central angles for Social Science and Mathematics = 90Â° + 65Â° = 155Â°
Â Â Â Â Â Â Â Â Sum of the central angles for Science and Hindi = 80Â° + 70Â° = 150Â°
Â Â Â Â Â Â Â Â Â âˆ´The sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi
Question 10
The number of students in a hostel, speaking different languages is given below. Display the data in a pie chart.Solution:
Total number of students in a hostel = 72
The central angle for drawing the pie chart is calculated as follows:
Language 
Number of Students 
In Fractions 
Central Angle 
Hindi 
40 


English 
12 


Marathi 
9 


Tamil 
7 


Bengali 
4 


Question 11
List the outcomes you can see in these experiments.(b) Tossing two coins together
Solution:
(a) The outcomes of the spinning wheel are A, B, C, D
(b) The outcomes of tossing two coins together are HT, HH, TH, TT.
Question 12
(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:
(i)
(a) The outcomes of getting a prime number are 2, 3, 5
(b) The outcomes of getting not a prime number are 1, 4, 6
(ii)
(a) The outcomes of getting a number greater than 5 is 6
(b) The outcomes of getting a number not greater than 5 are 1, 2, 3, 4, ,5
Question 13
Find the
(a) Probability of the pointer stopping on D in the spinner given below.
(b) Probability of getting an ace from a well shuffled deck of 52 playing cards.
(c) Probability of getting a red apple from the basket shown below.
(a) Total number of outcomes = 5
Â Â Â Â Â Â Â Â Â Â Getting a D consists of 1 outcome.
Â Â Â Â Â Â Â Â Â Â âˆ´Probability of getting a D =
(b) Total number of outcomes = 52
Â Â Â Â Â Â Â Â Â Getting an ace consists of 4 outcome.
Â Â Â Â Â Â Â Â Â âˆ´Probability of getting an ace =
(c) Total number of outcomes = 7
Â Â Â Â Â Â Â Â Â Getting a red apple consists of 4 outcome.
Â Â Â Â Â Â Â Â Â âˆ´Probability of getting a red apple =
Question 14
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 .(ii) getting a number less than 6?
(iii) getting a number greater than 6?
(iv) getting a 1digit number?
Solution:
(i) Total number of outcomes = 10
Â Â Â Â Â Â Â Â Â Â Â Â Â Â The number of outcomes for getting the number 6 = 1Â Â
Â Â Â Â Â Â Â Â Â Â Â Â Â \ Probability of getting the number 6 =
(ii) The number of outcomes for getting a number less than 6 = 5
Â Â Â Â Â Â Â Â Â Â Â Â âˆ´Probability of getting a number less than 6 =
(iii) The number of outcomes for getting a number greater than 6 = 4
Â Â Â Â Â Â Â Â Â Â Â âˆ´Probability of getting a number greater than 6 =
(iv) The number of outcomes for getting a 1digit number = 9
Â Â Â Â Â Â Â Â Â Â Â âˆ´Probability of getting a 1digit number =
Â
Question 15
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
The number of outcomes for getting a green sector = 3
âˆ´Probability of getting a green sector =
The number of outcomes for getting a non blue sector = 4
âˆ´Probability of getting a non blue sector =
Question 16
When a die is thrown, find the probability 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:
Total number of outcomes = 6
(i) (a) The number of outcomes for getting a prime number = 3
âˆ´Probability of getting a prime number =
(b) The number of outcomes for getting not a prime number = 3
âˆ´Probability of getting not a prime number =
(ii) (a) The number of outcomes for getting a number greater than 5 = 1
âˆ´ Probability of getting a number greater than 5 =
(b) The number of outcomes for getting a number not greater than 5 = 5
âˆ´Probability of getting a number not greater than 5 =