1. (a) The following table shows the lengths of 100 pencils. Complete the table.
Length (cm)
Class mark (cm)
Frequency
5-7
6
8 - 10
23
11 - 13
28
14 - 16
17
17 - 19
15
20 - 22
11
(b) Draw a frequency polygon.
Lengths of 100 pencils
30
Frequency
25
20
15
10
5
0
Length (cm)
7.1
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2. The following frequency polygon shows the time spent by a group of families in cooking dinner.
Time spent by a group of families
in cooking dinner
35
Frequency
30
25
20
15
10
5
0
8
13
18
23
28
33
38
43
48
Time (min)
(a) Based on the above frequency polygon, complete the following table.
Time (min)
Class mark (min)
11 - 15
13
16 - 20
18
Frequency
(b) The class interval
are
has most of the families, and there
families.
(c) There are
families in the group.
(d) There are
families who have spent 30.5 min or more in cooking dinner.
7.2
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(e) Find the percentage of families who have spent less than 25.5 min in cooking dinner.
Number of families who have spent less than 25.5 min in cooking dinner


Required percentage

(
(
)
 100 %
)

3. The following frequency polygons show the waiting time of passengers for the bus routes 885 and
996.
Waiting time of passengers
for the bus routes 885 and 996
Route 996
Frequency
25
Route 885
20
15
10
5
0
2
7
12
17
22
27
32
37
42
Time (min)
(a) For the bus route 885, there are
passengers who have waited for less than 14.5 min.
(b) For the bus route 996, there are
passengers who have waited for 29.5 min or above.
7.3
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(c) In general, which bus route has a more frequent service? Explain briefly.
7.4
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1. (a) The following table shows the selling prices of 36 magazines. Complete the table.
Selling price ($)
Class boundaries ($)
Frequency
1 - 10
0.5 - 10.5
6
11 - 20
14
21 - 30
10
31 - 40
4
41 - 50
2
(b) Complete the following cumulative frequency table.
Selling price less than ($)
Cumulative frequency
0.5
10.5
(c) Draw a cumulative frequency polygon.
Cumulative frequency
Selling prices of 36 magazines
10
0
0.5
10.5
Selling price ($)
7.5
 2009 Chung Tai Educational Press. All rights reserved.
2. The following cumulative frequency curve shows the time taken by a group of students to run 100 m.
Cumulative frequency
40
Time taken by a group of students
to run 100 m
30
20
10
0
9.5
10.5
11.5
12.5
13.5
14.5
15.5
Time (s)
(a) There are
students in the group.
(b) There are
students who have taken less than 10.9 s to run 100 m.
(c) There are
students who have taken 13.1 s or above to run 100 m.
(d) If the fastest 6 students are qualified to join the athletic team, the longest time taken by these
qualified students to run 100 m is
.
(e) Find the percentage of students who have taken less than 12.5 s to run 100 m.
From the graph, the number of students who have taken less than 12.5 s to run 100 m

Required percentage

(
(
)
 100 %
)

7.6
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3. The cumulative frequency curves show the scores of S2 students in Science and History examinations.
Scores of S2 students in
Science and History examinations
100
Cumulative frequency
90
80
Science
History
70
60
50
40
30
20
10
0
35
45
55
65
75
85
Score
(a) There are
students in S2.
(b) The highest score of the students in the Science examination is
.
(c) If the pass mark is 50, find the number of students passing each examination.
From the graph, the number of students whose scores are less than 50 in the Science examination

The number of students passing the Science examination



From the graph, the number of students whose scores are less than 50 in the History examination

The number of students passing the History examination



7.7
 2009 Chung Tai Educational Press. All rights reserved.
(d) Find the percentage of students whose scores are 70 or above in each examination.
From the graph, the number of students whose scores are less th an 70 in the Science examination

Required percentage

)(
(
(
)
)
 100 %

From the graph, the number of students whose scores are less than 70 in the History examination

Required percentage

)(
(
(
)
)
 100 %

7.8
 2009 Chung Tai Educational Press. All rights reserved.
1. The following cumulative frequency polygon shows the daily wages of workers in a factory.
Daily wages of workers in a factory
120
Cumulative frequency
100
80
60
40
20
0
299.5
339.5
379.5
419.5
459.5
499.5
539.5
Daily wage ($)
(a) There are
workers in the factory.
7.9
 2009 Chung Tai Educational Press. All rights reserved.
(b) (i) Cumulative frequency corresponding to P30

 30 %

From the figure,
P30 
(ii) Cumulative frequency corresponding to P80

 80 %

From the figure,
P80 
(c) If workers with the highest 15% of the daily wages will receive bonuses, find the minimum daily
wage among these workers.
The highest 15% of the daily wages are between P(
Cumulative frequency corresponding to P(


)
and P100 .
)
%

From the figure,
P(
)

 The minimum daily wage among these workers is
7.10
 2009 Chung Tai Educational Press. All rights reserved.
.
2. The following cumulative frequency curve shows the weights of a group of students.
Weights of a group of students
Cumulative frequency
60
50
40
30
20
10
0
38.5
43.5
48.5
53.5
58.5
63.5
Weight (kg)
(a) There are
students in the group.
(b) (i) Cumulative frequency corresponding to the lower quartile


%

From the figure, the lower quartile

(ii) Cumulative frequency corresponding to the median


%

From the figure, the median

(iii) Cumulative frequency corresponding to the upper quartile


%

From the figure, the upper quartile

7.11
 2009 Chung Tai Educational Press. All rights reserved.
(c) Find the percentage of students whose weights are 56 kg or above. (Give your answer correct to
3 significant figures.)
From the graph, the number of students whose weights are less than 56 kg

Required percentage


)(
(
(
)
)
 100 %
(
7.12
 2009 Chung Tai Educational Press. All rights reserved.
)