Name: ____________________ Class: __________( ) Date: __________

Junior Secondary Foundation Topics Supplement

7. Statistics and Probability

Exercise 7A Conventional Questions  Exam Tips

1. The pie chart below shows the distribution of the numbers of books
owned by Lily. It is given that she has 6 novels.

Distribution of the numbers of books owned by Lily

Novels

Cookbooks 30° Travel

105° books
75°

Reference
Sports books books

(a) Find the total number of books owned by Lily. 1. (a) Note that the percentage of the
novels is not 30%.
(b) Find the number of reference books owned by Lily.

2. The frequency distribution table and the cumulative frequency

distribution table below show the distribution of the weights of a batch
of apples, where a, b, c, d, p and q are positive integers.

Weight less than Cumulative

Weight (g) Frequency
(g) frequency
201–220 5 220.5 5
221–240 a 240.5 13
241–260 14 260.5 p
261–280 b 280.5 36
281–300 c 300.5 q
301–320 d 320.5 60

(a) Find the values of a and b.

Explain (b) Jack claims that 25% of the apples in the batch have weights lying 2. (b) Find the total number of apples
in the batch from the cumulative
in the class interval 261 g−280 g. Do you agree? Explain your frequency distribution table.

answer.

© Oxford University Press 2012 W07-1

 Name: ____________________ Class: __________( ) Date: __________
3. The following table shows the distribution of the numbers of times that
the employees in a company were late for work in a month.

Number of times 0 1 2 3 4 5
Frequency 11 8 5 3 4 1

Find
(a) the mean,
(b) the mode,
(c) the median
of the distribution.

4. 6 is a 2-digit number, where  is an integer from 0 to 9 inclusive.

Find the probability that the 2-digit number is divisible by 4.

5. A box contains four cards numbered 1, 5, 8 and p respectively, where p

is an integer. It is given that the median of the four numbers is 3.5.
(a) Find the value of p.
(b) A bag contains three balls numbered 3, 4 and 7 respectively. If one 5. (b) First, list all the possible
outcomes. Then, determine
card and one ball are randomly drawn from the box and the bag whether each outcome is a
multiple of 3. Remember to
respectively, find the probability that the sum of the numbers simplify the final answer.

drawn is a multiple of 3.

6. The pie chart below shows the distribution of the numbers of members
in some societies. The number of members in society C is 50% more
than that in society A and 25% less than that in society B.
Distribution of the numbers of members in some societies

A
B 66°
y°
D
x°
C

(a) Find the values of x and y.

Explain (b) Which society has the least number of members? Explain your 6. (b) First, find the angle of the sector
representing society D. Then,
answer. compare it with the angles of
the sectors representing the
remaining societies.

© Oxford University Press 2012 W07-2

 Name: ____________________ Class: __________( ) Date: __________
7. The following table shows the distribution of the numbers of times that
a group of teenagers have meals in a restaurant in a month.
Number of times 1 4 7 10
Number of teenagers 6 8 k 8
It is given that k is a positive integer.
(a) Suppose that the mean of the distribution is 6.
(i) Find the value of k. 7. (a)(i) Do not use the sum of 1, 4, 7
and 10 as the total number of
(ii) A teenager is randomly selected from the group of teenagers. teenagers in the group.

Find the probability that the number of times that the selected
teenager has meals in the restaurant in that month is not less
than 4.
Explain (b) If the median of the distribution is 4, how many possible values of
k are there? Explain your answer.

8. The bar chart below shows the distribution of the colours of a batch of
buttons.
Distribution of the colours of a batch of buttons
36
Number of buttons

30

12

Red Yellow Green Blue

If a button is randomly selected from the batch of buttons, then the
probability that a yellow button is selected is 3 .
16
(a) Find the number of yellow buttons.
(b) Suppose that the above distribution is represented by a pie chart.
(i) Find the angle of the sector representing the blue buttons.
Explain (ii) k blue buttons are now taken away, where k is a positive 8. (b)(ii) Assume that the angle of the
sector representing the blue
integer. Does there exist a value of k such that the angle of the buttons will be halved. Then,
try to find the value of k
sector representing the blue buttons will be halved? Explain according to the question.

your answer.

© Oxford University Press 2012 W07-3

 Name: ____________________ Class: __________( ) Date: __________
9. The stem-and-leaf diagram below shows the distribution of the times
(in min) spent by 20 participants to finish a task in a game show.

Stem (tens) Leaf (units)

1 4 5 6 7 8 9
2 0 1 2 3 5 5 5 5
3 0 2 3 5 7 8

(a) Find the mean, the median and the mode of the above distribution. 9. (a) Remember to write down the
units of the answers. Do not
(b) Two more participants finish the task. Their times spent are overlook the numbers in the
stem.
combined with the above data to form a set of 22 data.
(i) According to the times spent by the 22 participants, find the
least possible median and the greatest possible median.
Explain (ii) Is the mode of the times spent by the 22 participants the same
as the mode obtained in (a)? Explain your answer.
Explain (iii) If the mean of the times spent by the 22 participants is the 9. (b)(iii) Let a min and b min be the
times spent by the two
same as the mean obtained in (a), is it possible that the more participants.

median of the times spent by the 22 participants is the same as

the median obtained in (a)? Explain your answer.

10. The total value of all the coins in the wallet of Ricky is $50. The bar
chart in Fig. I shows the distribution of the numbers of coins in the
wallet. The pie chart in Fig. II shows the distribution of the total value
of each kind of coins in the wallet.
Distribution of the numbers of Distribution of the total
coins in the wallet value of each kind of coins
Number of coins

12 $1

$2 $5
20%
0
$1 $2 $5
Fig. I Fig. II

(a) Find the percentage of the total value of $2 coins in the wallet.
(b) Find the number of $5 coins in the wallet.
Explain (c) Ricky randomly selects a coin from the wallet. He claims that the
probability of selecting a $1 coin is smaller than the probability of
selecting a coin which is not a $1 coin. Do you agree? Explain your
answer.

© Oxford University Press 2012 W07-4

Name: ____________________ Class: __________( ) Date: __________

Junior Secondary Foundation Topics Supplement

7. Statistics and Probability

Exercise 7B MC Questions 3. When the selling price of a vase increases,

1. The pie chart below shows the expenditure of the number of vases sold decreases. Which of
Vincent in a month. the following scatter diagrams may represent
Expenditure of Vincent in a month the relation between the selling price of a
vase and the number of vases sold?
A.

Number of vases sold

Food
108°
Rent
144°
18° 54°
Transportation

Others O
Clothing Selling price ($)

The percentage of the expenditure on

transportation was B. Number of vases sold

A. 10%. C. 15%.
B. 12.5%. D. 36%.

2. The pie chart below shows the distribution of

the numbers of traffic accidents occurring in a O
Selling price ($)
city in a year.
Distribution of the numbers of traffic
C.
Number of vases sold

accidents occurring in a year

Area A
35% Area B
10%

Area C
O
Area E Selling price ($)
Area D
15%
D.
Number of vases sold

If the total number of traffic accidents

occurring in areas C and E was 232, then the
number of traffic accidents occurring in area A
was
A. 135. C. 387.
O Selling price ($)
B. 203. D. 580.

© Oxford University Press 2012 W07-5

Name: ____________________ Class: __________( ) Date: __________
4. The stem-and-leaf diagram below shows the 5. The bar chart below shows the annual
distribution of the waiting times (in min) for a expenditures (in million dollars) of companies
group of patients to consult a doctor in a clinic. P and Q in the year 2011.

Annual expenditure
Stem (10 min) Leaf (1 min) 6

(million dollars)
1 7 8
2 0 2 6 7
3
3 2 4 5 5 8 8
4 1 1 2 3 4 6 6 7 7 8 9 1
2 3 4 4 5 6 7 8 8 9 P Q
5
Which of the following statements about the
6 0 2 4 5 7
annual expenditures of the two companies in
Which of the following frequency curves the year 2011 is true?
may represent the distribution of their A. The annual expenditure of company P is
waiting times? 100% less than that of company Q.
A. B. The annual expenditure of company Q is
Frequency

50% more than that of company P.

C. The annual expenditure of company Q is
twice that of company P.
D. The annual expenditure of company Q is
Waiting time (min)
three times that of company P.

B.
Frequency

6. The pie charts below show the distributions of

the numbers of stamps owned by Roy and Amy.
Distribution of the Distribution of the numbers
numbers of stamps of stamps owned by Amy
owned by Roy
$1 $1
Waiting time (min)
40° 40°
$2 50° Others Others 100°
C. $2
Frequency

Which of the following must be true?

I. The total number of stamps owned by
Waiting time (min) Roy is less than that owned by Amy.
II. The number of $2 stamps owned by Roy
D. is 50% of that owned by Amy.
Frequency

III. The percentage of the number of $1

stamps owned by Roy is the same as the
percentage of the number of $1 stamps
owned by Amy.
Waiting time (min) A. III only C. I and III only
B. I and II only D. II and III only

© Oxford University Press 2012 W07-6

Name: ____________________ Class: __________( ) Date: __________
7. The cumulative frequency polygon below 10. Let a and b be positive integers. If the mean of
shows the distribution of the heights (in cm) of 6, 10, 4, 2, a and b is 5, and there is only one
40 students. mode, then the mode is
Distribution of the heights of 40 students A. 2. C. 5.
B. 4. D. 6.
40
Cumulative frequency

30 11. Consider the following data:

27 27 26 21 25 27 30 m n
20
If the mean and the median of the above data
10 are 25 and 26 respectively, which of the
following must be true?
0
140 150 160 170 180 I. m + n = 42
Height (cm) II. m ≤ 26
Find the median of the distribution. III. The only mode of the data is 27.
A. 158 cm A. I only
B. 159 cm B. I and II only
C. 160 cm C. II and III only
D. 161 cm D. I, II and III

8. The mean weight of a pile of 23 oranges is 12. The scores of two students in three papers of
291 g. The mean weight of another pile of an examination and the weight of each paper
37 oranges is 285 g. If the two piles of are listed in the following table.
oranges are combined into one, find the
Score of Score of
mean weight of the combined pile of Paper Weight
student A student B
oranges.
1 40% 52 64
A. 287.3 g
2 30% 63 52
B. 288 g
3 30% 50 49
C. 288.7 g
D. 289 g If the weighted mean score of a student is not
less than 55, the student can get a certificate.
9. The heights of five plants are (x + 1) cm, Which of the following is/are true?
(x + 4) cm, (x – 2) cm, (x + 8) cm and I. The weighted mean score of student A is
(x – 1) cm. If the median of the heights of the 55.
plants is 9 cm, then the mean of the heights of II. The weighted mean score of student B is
the plants is greater than the weighted mean score of
A. 9 cm. student A.
B. 10 cm. III. Both students A and B can get certificates.
C. 11 cm. A. II only
D. 12 cm. B. I and II only
C. I and III only
D. II and III only

© Oxford University Press 2012 W07-7

Name: ____________________ Class: __________( ) Date: __________
13. There are k boys and 24 girls in a group of 16. 7 is a 3-digit number, where both  and 
students. If a student is randomly selected from are integers from 0 to 9 inclusive. Find the
the group of students, then the probability probability that the 3-digit number is divisible
that a boy is selected is 1 . Find the value of k. by 7.
3
A. 3
A. 8 20
B. 12 B. 5
33
C. 48
C. 7
D. 72 50
D. 16
99
14. Two fair dice are thrown. Find the probability
that the sum of the two numbers thrown is
17. There are two $10 notes and one $20 note in
greater than 8.
the wallet of Vivian. If Vivian randomly selects
A. 2 two notes from her wallet, find the probability
3
B. 3 that she will get enough money to buy a toy of
4 price $25.
C. 5
12 A. 1
2
D. 5 1
18 B.
3
C. 2
15. The stem-and-leaf diagram below shows the 3
distribution of the numbers of pop songs stored D. 3
4
in the mobile phones of a group of students,
where k is an integer.
18. A bag contains five balls numbered 1, 3, 5, 6
Stem (tens) Leaf (units) and 7 respectively. If two balls are randomly
1 3 4 8 drawn from the bag at the same time, find the
2 0 2 3 5 probability that the product of the two numbers
3 2 k 7 8 8 9 drawn is a multiple of 3.
4 4 7 8 A. 2
5
The median of the distribution is 32. If a B. 3
student is randomly selected from the group of 10

students, then the probability that the number C. 7

10
of pop songs stored in the mobile phone of the D. 16
25
selected student is not greater than 33 is
A. 1.
2
B. 3.
8
C. 7 .
16
D. 9 .
16

© Oxford University Press 2012 W07-8

Name: ____________________ Class: __________( ) Date: __________
19. The bar chart below shows the distribution of 21. The histogram below shows the distribution of
the blood groups of employees in a company. the weights (in kg) of a group of students.
If an employee is randomly selected from the Distribution of the weights of a group of students
employees of the company, then the

Number of students
probability that the blood group of the selected
12
employee is O is 3 . Find the value of p.
14
8
Distribution of the blood groups of
the employees in a company
4
p
Number of employees

0
42 46 50 54 58
Weight (kg)
7
6 If a student is randomly selected from the
group of students, find the probability that the
2
selected student comes from the modal class.
A B O AB
A. 7
A. 13 44

B. 14 B. 9
44
C. 15 C. 5
22
D. 16
D. 1
4
20. The pie chart below shows the distribution of
the books on a shelf.
Distribution of the books on a shelf

Novels

78°
Textbooks

Magazines
Comic
books

If a book is randomly selected from the shelf,

find the probability that the selected book is a
novel or a comic book.
A. 2
5
B. 7
15
C. 8
15
D. 13
15

© Oxford University Press 2012 W07-9