Download Supp_2E13_sol

2 125
kg
40
 53.125 kg
Mean weight 
W orksheet 13B
(page 13.3)
1. Arrange the data in ascending order:
W orksheet 13A
(page 13.1)
0, 5, 5, 7, 8, 9, 10, 14
1  3  5  6  8  10
1. Mean 
6
33

6
 5.5
The median is the mean of the 4th and the 5th
data.
78
 Median 
2
 7 .5
18  42  72  108  120
5
360
$
5
 $72
120
2
 60
2. Half of the total frequency 
2. Mean price  $
 The median is 34 min.
3. Total number of students  4  8  5  3  6  13
$8  $12  $15  $ x
 $15
3.
4
x  35  60
 39
The median is the 20th datum.
 The median is 3.
x  25
4. (a) Total weight  (4  50  6  40) kg
 (200  240 ) kg
 440 kg
4. (a)
21  20  18  16  25  28  24  20  x  x
 22
10
2 x  172  220
2 x  48
x  24
440
kg
10
 44 kg
(b) Mean weight 
5.
Weight
(kg)
Class mark x
(kg)
(b) Arrange the data in ascending order:
16, 18, 20, 20, 21, 24, 24, 24, 25, 28
Frequency f
fx (kg)
40 - 44
42
8
336
45 - 49
47
6
282
50 - 54
52
11
572
55 - 59
57
5
285
60 - 64
62
4
248
65 - 69
67
6
402
40
2 125
Total
21  24
2
 22 .5
 Median 
88
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W orksheet 13C
(page 13.5)
1. The frequencies of both numbers 5 and 7 are 6,
which is the highest frequency.
 The modes are 5 and 7.
2. The percentage of Set D is the largest, which
means that the frequency of Set D is the highest.
 The mode is Set D.
3. In the pie chart, the angle at the centre occupied
by S5 is the largest, which means that the
frequency of S5 is the highest.
 The mode is S5.
6. Total amount payable  $122 .5  6
 $735
7. Total time taken  2.5  30 minutes
 75 minutes
2  5  x  2 x  3 x  1  12
6
6 x  18
6
6
6 x3
8. M ea n 
4. The frequency of the class interval 37 min - 39 min
is the highest.
 The modal class is 37 min - 39 min.
x3
9. Let x cm be the height of the 5th player.
B uild-up Exercise 13A
(page 13.7)
23 4588
6
5
1. (a) Mean 
x  180  182  184  190
 185
5
x  736  925
x  189
 The height of the 5th player is 189 cm.
(b) Mean
20  21  24  25  28  29  32  39  40  42

10
 30
10. Mean price  $
(c) Mean
10  15  20  50  120  150  200  315

8
 110
11. Mean time 
2. See p.96 for the answer.
3. Mean of the high jump records
172  170  163  176  165  183

cm
6
 171 .5 cm
95  3  102
4
 $96.75
54.16  5  55.2
s
6
 54.33 s (corr. to 2 d.p.)
12. Let x be the score got by Peggy in the 6th test.
45.5  5  x
50 
6
300  x  227 .5
x  72.5
 Peggy should get the score of 72.5 in the
6th test.
$294
4. Mean selling price 
7
 $42
12.5
kg
5. Mean weight 
100
 0.125 kg
 125 g
13. (a)
Datum x
Frequency f
fx
13
3
39
14
7
98
15
9
135
16
1
16
20
288
Total
89
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288
20
 14.4
18.
(b) Mean 
14. (a) Sum  10  2  15  3
65
5
 13
(b) Mean 
24.5  6  21  8
68
 22.5
15. Mean score 
Frequency f
8
12
12
x
2
Class mark x (kg)
32
37
42
47
52
fx (kg)
256
444
504
47x
104
19. Let x and y be the number of boys and girls in
S2A respectively.
Class
interval
Class
mark x
Frequency f
fx
26 - 30
28
3
84
31 - 35
33
9
297
36 - 40
38
15
570
41 - 45
43
8
344
46 - 50
48
5
240
40
1 535
Total
30 - 34 35 - 39 40 - 44 45 - 49 50 - 54
Mean weight  256  444  504  47 x  104 kg
8  12  12  x  2
1 308  47 x
39.75 kg 
kg
34  x
1 351 .5  39.75 x  1 308  47 x
47 x  39.75 x  1 351 .5  1 308
7.25 x  43.5

x6
 65
16. (a)
Weight (kg)
Mean of the number of push-ups 21  x  9  y

done by the whole class
30
21x  9 y
30
402  21x  9 y
13.4 
7 x  3 y  134 ................ (1)
 There are 30 students in the class.
 x  y  30
x  30  y ............................................ (2)
Substitute x  30  y into (1),
1 535
40
 38.375
(b) Mean 
7(30  y )  3 y  134
210  7 y  3 y  134
4 y  76
Time
Class mark x
(hour)
Frequency f
fx (hour)
16 - 20
18
15
270
21 - 25
23
25
575
26 - 30
28
30
840
31 - 35
33
20
660
36 - 40
38
10
380
100
2 725
17. (a) (hour)
Total
(b) Mean time spent in watching TV
2 725
hours

100
 27.25 hours
90
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y  19
Substitute y  19 into (2),
x  30  19
 11
 The number of boys in S2A is 11 and
the number of girls in S2A is 19.
20. Mean time

4  35.5  6  45.5  7  55.5  10  65.5  13  75.5
minutes
4  6  7  10  13
2 440
minutes
40
 61 minutes

21. Let x be the score got by Cindy in the 6th
dictation. If the mean score is over 80 in the
first six dictations,
65  72  72  80  90  x
 80
6
x  379  480
x  101
But the full score is 100, x cannot be greater
than 101.
 Cindy cannot get a mean score over 80 in
the first six dictations.
22. (a) See p.96 for the answer.
(b)  The mean price of mobile phones of
Sorry Edison is lower.
 Sorry Edison sets a lower selling price
in general.
B uild-up Exercise 13B
25. Arrange the weights of ten pumpkins (in kg) in
ascending order:
4.8, 5.4, 6.5, 6.8, 7.0, 7.2, 7.2, 7.5, 8.0, 8.4
Mean weight of these ten pumpkins
7 .0  7 .2
kg
2
 7.1 kg

26. [ Total number of students  49, and thus the
median pocket money is the pocket money of
the 25th student when the amounts of pocket
money are arranged in ascending order. ]
According to the table, when the amounts of
pocket money are arranged in ascending order,
the 1st and the 2nd students have got the pocket
money of $3 each,
the 3rd to the 7th students have got the pocket
money of $4 each,
the 8th to the 17th students have got the pocket
money of $5 each,
(page 13.10)
23. (a) Median  6
the 18th to the 29th students have got the pocket
money of $6 each.
 Median pocket money  $6
(b) Median  12
35  40
2
 37.5
(c) Median 
24. (a) Arrange the data in ascending order:
1, 2, 4, 5, 7, 8, 9
Median  5
(b) Arrange the data in ascending order:
10, 12, 13, 13, 16, 17, 18, 20, 21, 24
16  17
2
 16 .5
Median 
27. (a) Number of students in the class
 4  6  9  11  2
 32
(b) [ Total number of students  32, and thus the
median test score is the mean of the test
scores of the 16th and the 17th students
when the test scores are arranged in
ascending order. ]
From the figure,
68  68
marks
2
 68 marks
median test score 
(c) Arrange the data in ascending order:
4.1, 2.9, 1.8, 1.4, 0.8, 0.9, 2.3, 3.0, 8.2
Median  0.8
91
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28. [ Total number of students  100, and thus the
median I.Q. test results is the value corresponding
to the cumulative frequency 50. ]
I.Q. test results of 100 students
100
90
Cumulative frequency
80
70
60
32. (a) 4  8  13  y  8  3  50
50
y  36  50
40
y  14
30
(b) [ Total number of people  50, and thus the
median is the mean of the numbers of
movies watched by the 25th and the 26th
people when the numbers of movies watched
are arranged in ascending order. ]
20
10
0
40.5
60.5
80.5
100.5
50.5
70.5
90.5
Score
From the graph,
median I.Q. test result  64.5
Duration for holding breath among 50 students
29. (a)
According to the table, when the numbers of
movies watched are arranged in ascending
order,
the 1st to the 4th people have watched
0 movies each,
the 5th to the 12th people have watched
1 movie each,
the 13th
2 movies
the 26th
3 movies
50
Cumulative frequency
x x5
2
2x  5
20.5 
2
41  2 x  5
2 x  36
x  18
31. Median 
40
to the 25th people have watched
each,
to the 39th people have watched
each.
 Median number of movies watched
23

2
 2 .5
30
20
10
0
10
20
30
40
50
Duration for holding breath (s)
(b) From the graph of (a),
median duration for holding breath  18 s
30. Arrange the data in ascending order:
x  1, x  1, x  2, x  3, x  5
Median  x  2
92
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60
33. (a) Arrange the data (in glasses) in ascending
order:
103, 106, 106, 110, 113, 121
106  110
glasses
2
 108 glasses
Median 
(b) Arrange the data (in glasses) in ascending
order:
103, 106, 106, 110, 113, 121, 135
Median  110 glasses
34. (a) Arrange the quotations (in $) from ten
removal companies in ascending order:
800, 1 000, 1 100, 1 200, 1 200, 1 250,
1 300, 1 300, 1 400, 1 500
1 200  1 250
Median quotation  $
2
 $1 225
(b) Arrange the quotations (in $) from ten
removal companies in ascending order:
(b) [ Total number of chickens  30, and thus the
median weight is the mean of the weights
of the 15th and the 16th chickens when the
weights are arranged in ascending order. ]
From the figure,
median weight of chickens from farm B
2.5  2.6
kg
2
 2.55 kg

1 000, 1 100, 1 200, 1 200, 1 250,
1 300, 1 300, 1 400, 1 500, 1 800
1 250  1 300
Actual median quotation  $
2
 $1 275
54  82  125  163  x
5
x  424
$103  $
5
515  x  424
x  91
35. (a) (i) Mean  $
(ii) Arrange the amounts (in $) in ascending
order:
54, 82, 91, 125, 163
Median amount spent on these five
purchases  $91
(b) Arrange the amounts (in $) spent on these
six purchases in ascending order:
54, 82, 91, 102, 125, 163
Median amount spent on these six purchases
91  102
$
2
 $96.5
36. (a) [ Total number of chickens  30, and thus
the median weight is the mean of the
weights of the 15th and the 16th chickens
when the weights are arranged in ascending
order. ]
(c) (i) See p.96 for the answer.
(ii) [ Total number of chickens  60, and thus
the median weight is the mean of the
weights of the 30th and the 31st
chickens when the weights are arranged
in ascending order. ]
From the figure in (c)(i),
median weight of these 60 chickens from
farms A and B
3.0  3.0
kg
2
 3.0 kg

37.  The number of data is an odd number.
 The median 14 is one of the data.
 x  14 or x  2  14
If x  14 , then the five data are
10, 13, 14, 15, 16.
Median  14
If x  2  14 , i.e. x  12 , then the five data are
10, 12, 13, 14, 15.
Median  13  14
 x  2 cannot be 14.
 x  14
38. (a) From the graph,
From the figure,
median of the prices of flats in district A
median weight of chickens from farm A
3.4  3.4

kg
2
 3.4 kg
 3.5 thousand dollars/square foot
median of the prices of flats in district B
 6 thousand dollars/square foot
93
 2009 Chung Tai Educational Press. All rights reserved.
(b)  The median of the prices of flats in
district B is higher.
 District B has a higher flat price in
general.
42. [ The frequency of x is the highest. ]
Mode  x
43. [ The frequency of 1 child is the highest. ]
Mode of the number of children  1
B uild-up Exercise 13C
(page 13.14)
39. (a) [ The frequency of 10 is 4, which is the
highest frequency. ]
Mode  10
(b) [ The frequency of 9 is 3, which is the
highest frequency. ]
Mode  9
(c) [ The frequencies of both 21 and 26 are 2,
which is the highest frequency. ]
Modes  21 and 26
40. (a) Arrange the data in ascending order:
3, 3, 3, 4, 5, 6, 6, 8, 8
[ The frequency of 3 is 3, which is the
highest frequency. ]
Mode  3
(b) Arrange the data in ascending order:
44. The mode of the sales volume of fruit juice is
orange juice.
45. Angle at the centre occupied by folding
umbrellas
 360   106   50  42
 162 
 The angle at the centre occupied by folding
umbrellas is the largest.
 The mode of the types of umbrellas sold is
folding.
46. [ From the graph, the frequency of 4 is 3, which
is the highest frequency. ]
Mode of the sales volume  4
47. [ From the graph, the frequency of the class
interval 100 min - 109 min is the highest. ]
13, 13, 9, 8, 5, 5, 5, 0
The modal class of the duration of the movies is
[ The frequency of 5 is 3, which is the
highest frequency. ]
100 min - 109 min.
Mode  5
(c) Arrange the data in ascending order:
1.6, 1.7, 1.7, 1.9, 2.0, 2.1, 2.3, 2.3
[ The frequencies of both 1.7 and 2.3 are 2,
which is the highest frequency. ]
Modes  1.7 and 2.3
41. (a) [ The frequency of the class interval 36 - 40
is the highest. ]
Modal class  36 - 40
(b) [ The frequencies of the class intervals 7 - 9
and 13 - 15 are the highest. ]
Modal classes  7 - 9 and 13 - 15
94
 2009 Chung Tai Educational Press. All rights reserved.
48. (a) [ Most drivers are 22 years old. ]
The mode of the ages is 22 years old.
(b) (i)
Age
Frequency
18 - 22
13
23 - 27
16
28 - 32
9
33 - 37
5
38 - 42
4
43 - 47
3
(ii) [ The frequency of the class interval
23 - 27 is the highest. ]
The modal class of ages is 23 - 27.
49. (a)
 Let d  6, e  8.
Floor area (m 2 )
Frequency
10 - 29
3
 Mode  6
30 - 49
2
 At least two numbers are 6.
50 - 69
20
 Let c  6 .
70 - 89
5
 Mean  8
(b) [ The frequency of the class interval
50 m 2 - 69 m 2 is the highest. ]
The modal class of floor area is
50 m 2 - 69 m 2 .
50. (a)  Total frequency  200
 30  42  40  x  34  y  19  200
x  y  165  200
y  35  x
 x and y are positive integers and
y  35  x .
 The largest value of y is 34,
i.e. y  42 .
 The modal class cannot be 36 - 40.
(b) Suggested answer:
If the modal class is 26 - 30, then
40  x  42
x2
When x  3,

abcd e f  g h
8
8
a  b  6  6  8  f  g  h  64
a  b  f  g  h  44
Let a  1, b  2, f  9, g  10 , h  22 .
 The 8 numbers could be
1, 2, 6, 6, 8, 9, 10, 22.
52. Suggested answer:
Consider the following data:
1, 2, 10, 11, 11
Mode  11
Median  10
1  2  10  11  11
5
7
Mean 
 11  10  7
 The 5 numbers could be 1, 2, 10, 11, 11.
y  35  3
 32
When x  10 ,
y  35  10
 25
 x  3, y  32 and x  10 , y  25 are
two sets of possible values of x and y.
51. Suggested answer:
Let the 8 numbers be
a, b, c, d, e, f, g, h in ascending order.
 Median  7
d e
7

2
d  e  14
95
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B uild-up Exercise 13A
4 000  6 000  6 500  7 500  7 500  9 500  10 500  20 000
8
 $8 937 .5
2. Mean of monthly salaries  $
22. (a) Mean price of mobile phones of Nobia
480  980  1 480  1 780  2 680  3 280  4 380  5 680
8
 $2 592 .5
$
Mean price of mobile phones for Sorry Edison
399  699  1 099  1 299  1 699  2 499  3 099  3 699  4 499  5 999
10
 $2 499
$
B uild-up Exercise 13B
36. (c) (i)
The weights of a total of 60 chickens from farms A and B
Stem (1 kg)
Leaf (0.1 kg)
1
2 2 3 4 4 5 6 7 8 9
2
0 1 1 1 1 2 2 3 3 4 5 5 6 6 8 9 9 9
3
4
0 0 0 1 1 1 1 2 4 4 4 4 4 5 5 6 6 7 7 8 8 8
0 1 2 2 2 3 5 6 7 7
96
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