毅進文憑數學單元五...

20 17 /18

2

2017

1

3

4

4

5

9

10

26

26

27

33

41

46

52

52

61

67

69

Excel 92

Excel 92

Excel 93

105

112

: 113

: 114

117

1

Herbert George Wells18661946

1

70

2,500

55910

2457.4%

http://yrc.hkfyg.org.hk/chi/p186.html

1993

49

8

500800

http://www.cuhk.edu.hk/proj/growthstd/chinese/gs_surve.htm
http://yrc.hkfyg.org.hk/chi/p186.htmlhttp://www.cuhk.edu.hk/proj/growthstd/chinese/gs_surve.htm

2

3030

30

559500800

559

500

800

162016741662

1604

SurveySampling

Statistical ForecastingEconometrics

ManagerialStatisticsSocial Statistics

2
http://www.hudong.com/wiki/%E4%BF%A1%E6%81%AF

3

Legal StatisticsDemographic Statistics

BiostatisticsStatistical Linguistics

Statistical PhysicsPsychometrics

EnvironometricsChemometrics

8

mean

standard deviation

4

1000

500

3

4

5

X

5-1

census

sample survey

population

element / individual

sample

6

sampling frame5-1

sample size

5-1

00001 G032xxx(9) 23456789 3 312

00002 H453xxx(0) 34567899 23 2309

30000 D564xxx(3) 21111111 25 2511

7

5-2

8

5-1

5-1

5-2

TVC

500

500

5-1

9

5-3

405

55

5-4

5-3

35

random sampling

non-random sampling

10

1.

random sampling without replacement

Nn

nN

simple random sampling

5-5

203

20

1/20

19

1/19

181/18

simple random sample

11

5-5

n

5-6

10000500

10000500

5-7

12

5-1

1. 10020

(a) 100

(b) 20

(c) 20

(d) 100

2. 2020

5

3.

(a)

(b)

(c)

(d)

4.

5.

6.

(a) 100

(b)

(c) 10

(d) DVD20DVD

5

13

7.

(a) 3020

1202140

20

(b) 104

(c) 20050

1203030

15

2.

systematic sampling

countably

infinite

systematic sample

5-8

5

15

16

5-3

5A

1 09001 F 16

2 09002 M 16

3 09003 F 17

4 09004 F 16

5 09005 M 16

6 09006 F 17

7 09007 M 17

8 09008 M 16

9 09009 F 16

10 09010 M 17

11 09011 M 18

12 09012 F 19

13 09013 M 20

14 09014 M 19

15 09015 M 18

151~15

sampling intervalk

153

5

Nk

n

k3

17

random

start

RAN# Ran#

0.561

(a) = = 0.561 3 = 1.683 2

22+32+232+332+43258

1114

1a n k

5-4

5A

1 09001 F 16

2 09002 M 16

3 09003 F 17

4 09004 F 16

5 09005 M 16

6 09006 F 17

7 09007 M 17

8 09008 M 16

9 09009 F 16

18

10 09010 M 17

11 09011 M 18

12 09012 F 19

13 09013 M 20

14 09014 M 19

15 09015 M 18

5-9

6-94

153.75

4

Nk

n

153

123

4

Nk

n

361215

3

30

19

3.

stratified random sampling

5-10

5

20000

8000

50000

200000

300

20

70 40

20 10 60

N = 200

n=40

strata

group6-8

N=200n=40

: 40 : 200 1:5n N

70

5

40

5

20

5

10

5

60

5

1484212

21

14 + 8 + 4 + 2 + 12 = 40 =

= 70 : 40 :

20 : 10 : 60 = 14 : 8 : 4 : 2 : 12

n

N

(70)

(40)

(20)

(10)

(60)

2

3

12

4

8

5

4

2

14

1

22

5-2

1. 500

20 30 220

30 40 150

40 50 40

50 90

500

100

2. 3

1500

1200

1800

4500

450

24

1.

2.

1.

2.

1.

2.

5-3

1. 1200

30

2. 1534250

3 100

100001~100

(a) 0.75410

(b) 20

26

Data Representation

Variable

Data

quantitative variable

interval variable

qualitative variable

categorical variable

continuous

variable

discrete

variable

nominal

variable

ordinal

variable

27

5-5

1.

a.

b.

2.

a.

0 = 1 =

b.

frequency

distribution

raw data

number of classes

class width / size

28

520

k

max min x x R

ck k

maxx =

minx =

R = max minx x range

cc

c05051050100

150

k = 10 maxx = 106 minx = 10

106 109.6

10

Rc

k

10

29

5-6

max minx xR

k k

(c)

()

89.7 90 100

1.45 1.5

47.3 48 50

9.2 10

5-11

50HK$

9450 8850 9350 9200 8750 9900 7550 8350 8350

8100 8800 7700 9100 8400 8050 7900 8400 7600

8600 8900 9300 8800 10100 9700 8800 7700 7700

8050 8200 8650 7750 9500 8100 7750 10150 7900

10600 9500 11400 15100 16450 15950 15650 12550 14250

11250 11800 10000 14000 13000

30

6 maxx = 16450 minx = 7550

16 450 7 5501483.3

6

R

k

c= 1500

5-7

11115

7500< 9000 11111111111111111111 1 26

9000

31

5-12

2008

5-8

1 %

< 5 71 1.9

5 14 416 11.1

15 24 380 10.1

25 34 541 14.4

35 44 553 14.7

45 54 652 17.4

55 64 438 11.7

65 702 18.7

3753 100.0

1

2%

6518.7%

25343544550

32

5-13

2010

5-9

2

15.1 6.1

19.7 6.9

16.8 7.7

3.6 4.2

55.2 24.9

19700

3600

33

1.

Histogram

5-8

34

5-2

2.

frequency polygon

5-3

35

density

curve

5-3

5-4

37

3.

(cumulative frequency polygon) 5-10

:

(X)

()

(Y)

0 < 5 0 5 71 5 71

5 14 5 14.5 416 14.5 71+416=487

15 24 14.5 24.5 380 24.5 487+380=867

25 34 24.5 34.5 541 34.5 867+541=1408

35 44 34.5 44.5 553 44.5 1408+553=1961

45 54 44.5 54.5 652 54.5 1961+652=2613

55 64 54.5 64.5 438 64.5 2613+438=3051

65 74 64.5 74.5 702 74.5 3051+702=3753

3753

Y X

38

5-4

1. 2. ()32

:.

48 61 78 93 98 94 137 141

87 103 85 97 108 77 60 75

107 99 80 59 147 149 118 116

122 32 115 64 79 73 80 89

(a) ,

30-49, 50-69, ;

(b) (a);

(c) 100

2. 1824

40

129.2 185.3 218.1 182.5 142.8 155.2 170.0 151.3 187.5 145.6

167.3 161.0 178.7 165.0 172.5 191.1 150.7 187.7 165.0 172.5

191.1 150.7 187.0 173.7 178.2 161.7 170.1 165.8 214.6 136.7

278.8 175.6 188.7 132.1 158.5 146.4 209.1 175.4 182.0 173.6

(a) 8

(b) 121

(c) (b)

(d) (c)

(e)

(f) 181200

(g) 175

41

bar chart

pie chart

line charttime chart

1.

42

5-14

5-11 2010

21.9

35.8

64.8

13.7

24.5

160.7

5-5

43

2.

360

100%

:

=

360

5-15

5-145-11

:

5-12

21.9 21.9

360 49.1160.7

21.9

100% 13.6160.7

35.8 35.8

360 80.2160.7

35.8

100% 22.3160.7

64.8 64.8

360 145.2160.7

64.8

100% 40.3160.7

13.7

13.7360 30.7

160.7

13.7100% 8.5

160.7

24.5

24.5360 54.9

160.7

24.5100% 15.2

160.7

160.7 360 100

44

5-12

3.

45

5-16

20012009

5-13

2001 92578 38034

2002 90297 37319

2003 86738 36570

2004 84509 33664

2005 85784 33687

2006 84087 37991

2007 80690 24576

2008 84565 25009

2009 88234 30773

2006

46

1.

(Scatter Diagram) MS Excel

YX

10

()

(X)

()

(Y)

2.2 15

2.5 16

2.8 22

3.3 17

3.8 24

4.0 18

4.5 25

5.0 19

5.6 33

6.0 30

47

2.

(Stem and Leaf Diagram)

: 42, 44, 56, 56, 58, 59, 63, 63, 63, 65, 67

: 421042

4 2 4

5 6 6 8 9

6 3 3 3 5 7

() 67-42= 25

= 59, = 63

3.

(Pictogram),

201530

48

5-5

1.

1 374.7

2 592.6

3 553.8

4 511.5

5 204.1

6 82.0

2.

1524 285.0 273.6

2539 18.7 23.1

40 35.1 35.0

(a)

(b) (a)

49

3.

2479210

2036

(a) ?

(b)

(c) 1000

?

4. AB

A 11 10 8 12 20 30 24 4 6 16 20 18 25 34

B 7 8 10 11 14 22 18 2 6 8 6 7 9 13

(a) AB

(b)

?

50

5. 29

53, 42, 51, 60, 70, 31, 42, 51, 62, 74, 36, 35, 49, 59, 49,

35, 33, 69, 53,47, 32, 32, 44, 45, 65, 30, 79, 53, 65

(a)

(b)

6.

:

() 10 28 12 11 26 23 20 15 17 18

() 24 28 28 21 25 45 38 54 42 34

(a)

(b) ?

52

averageaverage

meanaverage

arithmetic mean

mode

weighted mean

median

53

geometric mean

truncated meanharmonic mean

Summation Notation

5-17

10000021 ..... xxx

10000021

100000

1

..... xxxxi

i

i= 1 x11

100,000

x

3

1 2 3

1

i

i

x x x x

i

3

1 2 3

1

k

k

x x x x

k

321

3

1

3

1

xxxxxk

k

i

i

54

1. (Sample Arithmetic Mean)

n nxxx ,.....,, 21

.

n

i

in x

nn

xxxx

1

21 1 .....

5-18

5

18, 19, 17, 21, 30

= 1

18 19 17 21 30 215

21

smoothing effect

30

55

4

3

2

0

17 21

18 21

30 21 4 3 2 0

19 21

21 21

30211718

1921

Bill Gates

Central

Tendency

61

56

2. (Weighted Mean)

weight

5-19

4

5-14

90 1

78 2

85 5

79 2

1

90 78 85 79 834

x

(*) 83 (79)4

1(85)

4

1(78)

4

1(90)

4

1x

1

4(*)

5-14

57

n

ii

ii

n

nnw

w

xw

wwwxwxwxwx

1

n

1i

21

2211

....

.....

1 90 2 78 5 85 2 7982.9

1 2 5 2wx

x = 83 wx = 82.9 x wx

5-20

9

$11,500$50,000

$15350

2345 6789

$15350

$11500

= 9 11500 50 000

$15 35010

58

3.

positional average

n

(1

2

n )th

1

2

nX

1

2 2

2

n nX X

2

5-21

97, 9, 15, 2, 32, 25, 14, 8, 47

2, 7, 8, 9, 14, 15, 25, 32, 47

9 1

2

= 5

M = 14

5-22

5-21592, 7, 8, 9,

14, 15, 25, 32, 47, 59

1010

52

101 6

2

= 14 15

14.52

59

5-23

5-20

11500, 11500, 11500, 11500, 11500, 11500, 11500, 11500,

11500, 50000

1010

52

101 6

2

=11500 11500

2

= $11500

$50000

5-24

5 5.5 6 6.5 7 7.5 8

5 7 25 28 28 15 4

60

6.57

4.

5-25

(i) 1, 2, 2, 2, 3, 4, 5

(ii) 1, 2, 2, 2, 3, 4, 5, 5, 5

(iii) 1, 2, 3, 4, 5

(i) 22

(ii) 2525

(iii)

5-25

,

61

(i)

62

010 1f 010.49 1f

1120 2f 10.520.49 2f

2130 3f 20.530.49 3f . . .

.

.

. . . .

.

.

.

0.01

(ii)

21

2421

63

1.

5-26

20

5-16

= X

0 < 2000 3

2000 < 4000 4

4000 < 6000 8

6000 < 8000 3

8000 < 18000 2

20 = n

nxn

xn

xn

x1

....11

21

ix

i i

w

i

f xx

f

if =i

ix =i

64

[a, b)

if

2i

a bx

0 < 2000 3 0 2 000

2

1000

2000 < 4000 4 3000

4000 < 6000 8 5000

6000 < 8000 3 7000

8000 < 18000 2 13000

20

X =[31 000+43 000+85 000+]/20

X 5100

2.

th1

2

n

2 L

mc

nf

M L cf

L =

n =

L

f =

mcf

=

c =

65

5-16

th th

th1 20 1 10.52 2

n

5-1710.5 15843

4000 < 600040006000

5-17

0< 2000 3

2000< 4000 4

4000< 6000 8

6000< 8000 3

8000< 18000 2

20

20 72 24 000 2 000 4 750

8

L

mc

nf

M L cf

0 2000 3 0 2000.5 3

2001 4000 4 2000.5 4000.5 4

4001 6000 8 4000.5 6000.5 8

L= 4000.540014,000.5 6,000.5

4,001 6,000

L 7L

f

mcf

66

3.

modal class

10

1 2

M L c

L =

1 =

2 =

c =

5-16

4000

67

5-27

5-18

A B

66 40

68 42

70 70

70 70

70 70

72 98

74 100

5-19

A B

70 70

70 70

70 70

68

5-19

5-7

5-185-7

A70

4

B30

69

dispersion

1.

(Range),

():

/

Range

Inter-quartile

range

Variance

Standard

deviation

() =

70

5-28

59, 60, 23, 80, 97, 45, 77, 20, 14, 87

= 97 14 = 83

():

5-29

80()

41 - 50 51 - 60 61 - 70 71 - 80 81 - 90

40.5 50.5 50.5 60.5 60.5 70.5 70.5 80.5 80.5 90.5

12 34 25 8 1

= 90.5 40.5 = 50

5-29

10

2.

3. (Inter-Quartile Range)

50%

nYYY ...,,, 21

() =

71

(quartile)

(Q1)

25%

(Q2)

50%

(Q3)

75%

InterQuartile Range, IQR

Quartile deviation

= (Q3) (Q1)

=

(Q3) (Q1))

72

1. th2

1)(n (Q2)

2.

3. th2

1)(n

(Q1)

(Q3)

5-30

20, 15, 40, 19, 2, 30, 16

2, 15, 16, 19, 20, 30, 40, n=7

(Q2) = 4 2

1)(7

th , Q2 = 19

3

() ()

2 15 16 19 20 30 40

Q1 = (3+1)/2 = 2

Q1 = 15

(Q2)

Q3 = (3+1)/2= 2,

(Q3) = 30

: Q1 = 15 Q2 = 19Q3 = 30,

5-31

44, 9, 9, -3, 1, -5, 6, 9, 2, 18

-5, -3, 1, 2, 6, 9, 9, 9, 18, 44, n=10

= 44 (-5) = 49

(Q2) = 5.5 2

1)(10

, Q2 = 7.5

2

9)(6

73

5

() ()

-5 -3 1 2 6 9 9 9 18 44

Q1 = (5+1)/2 = 3 ,

Q1 =1

7.5

(Q2)

Q3 = (5+1)/2= 3

(Q3) = 9

: Q1 = 1 Q2 = 7.5Q3 = 9,

Q3 - Q1 = 9 1 = 8

4 2

19

2

QQ 13

5-32

3 4 5 6 7 8 9 10

2 4 5 7 10 9 2 1

(n)2 + 4 +5 + 7 + 10 + 9 + 2 + 1 = 40

Q2 = 20.5 2

1)(40

2021,

Q2=7

Q1 _____ ______ Q1=_____

Q3 ______ ______Q3=______

=________ = _________

N

74

(Q1) 4

N (25%)

, (Q2)4

2N (50%)

(Q3)4

3N (75%)

5-33

5-29, 80()

41 - 50 51 - 60 61 - 70 71 - 80 81 - 90

12 34 25 8 1

(i)

(ii)

(i) 80

()

() 40.5 50.5 60.5 70.5 80. 90.5

0 12 46 71 79 80

(ii) Q1 N/4 =80/4=20Q3 3N/4=3(80/4)= 60

Q1=52 , Q3= 66

66 52=14

75

(Box and Whisker Diagram /Boxplot) ,

()

(Q1)(Q3)

(Q1) (Q3)(Q2)

5-34

()

(Q1) = 64, (Q3) = 72

(Q2) = 69, =72 64 = 8

= = 76 56 = 20

76

4.

ix x ix

ix x ix x

1 2, , , nx x x x

1

n

i

i

x x

1

n

i

i

x x

1

n

i

i

x x

1

0n

i

i

x x

2

1

n

i

i

x x

77

2

1

1n

i

i

x xn

x x ix x

2

1

1n

i

i

x xn

2

5.

(SD) = 2

1

1n

i

i

x xn

2

2s s

22

1

1

1

n

i

i

s x xn

2

1

1

1

n

i

i

s x xn

nn-1

78

(i)

2

1

1

1

n

i

i

s x xn

n=

(ii) N

2

1

1N

i

i

x xN

N=

79

5-35

59, 60, 23, 80, 97, 45, 77, 20, 14, 87

Casio fx-3650P Casio fx-50FH

1. SD MODEMODE1

SD MODEMODE4

SD

2. SHIFTMODE1

EXE SHIFT91

EXE

3.

59M+60M+23M+80M+ 14M+87M+

4. (n)

Shift13EXE10

( )

Shift21EXE56.2

(n-1)

Shift23EXE29.727

(n)

Shift22EXE28.202

(:)

SD = 2

1

1

1

n

i

i

x xn

= 29.7

SD = 2

1

1n

i

i

x xn

= 28.2

80

(i)

2

1

1

1

n

i i

i

s f x xn

n =

1

n

i

i

f

(ii)

2

1

1N

i i

i

f x xN

N =

N

ii

f1

5-36

100IQ

IQ 45-

81

100SHIFT29M+

110SHIFT24M+

120SHIFT12M+

129.5SHIFT4M+

4. (n)

Shift13EXE100

(n-1)

Shift23EXE14.544

(:)

2

1

114.5

1

n

i i

i

s f x xn

6.

Coefficient of Variation

100

20

=

= %100

x

s
https://zh.wikipedia.org/wiki/%E6%A6%82%E7%8E%87%E5%88%86%E5%B8%83https://zh.wikipedia.org/wiki/%E6%AD%B8%E4%B8%80%E5%8C%96

82

5-37

12, 14, 28, 36, 39, 42

= 6

423936281412 = 28.5

=

16

5.28425.28395.2836

5.28285.28145.2812

222

222

= 12.90

= %1005.28

90.12 = 45.25%

5-38

273.2

1205.6

= %85.11%10027

2.3

= %67.4%100120

6.5

5-39

5-28

59, 60, 23, 80, 97, 45, 77, 20, 14, 87

(a)

(b) 60.5 32

?

83

(a) = 10

87 14 20 77 45 97 80 23 60 59

= 56.20

=

110

2.5687..2.56802.5623222

= 29.73

(b) = %1002.56

73.29 = 52.90%

(c) = %10050.60

32 = 52.89%

(d)

5-6

1. 5-5, 5:

53, 42, 51, 60, 70, 31, 42, 51, 62, 74, 36, 35, 49, 59, 49,

35, 33, 69, 53, 47, 32, 32, 44, 45, 65, 30, 79, 53, 65

(a)

(b)

2.

10

A 8.2 10.2 7.6 7.8 7.4 7.8 8.0 6.6 10.8 8.6

C 10.8 9.4 9.8 9.5 11.4 10.5 11.0 9.6 10.4 10.6

(a)

(b) (a),

84

3. 20232425

20

4. 1285312

558

5. A30

90 5

80 22

78 1

10 1

2 1

30

5 90 22 80 1 78 1 10 1 276.7

30

i i

i

w xx

w

78

2, 10, 78, 80,..,80, 90,., 90

(22) (5)

3

6.

85

7.

8..

A 87 86 19 70 80 72 55

B 75 39 80 64 85 65 50

C 71 82 50 52 67 82 59

5% 10% 5% 15% 5% 10% 50%

(a)

(b) ?

9.

78 81 91

90 70 69

400

(a)

(b)

(c)

433

86

10.

1:002:0015

148

0 < 5 8

5 < 10 11

10 < 15 37

15 < 20 34

20 < 25 30

25 < 30 28

148

(a)

(b)

(c) (a)(b)

11.

100200

0 2 1 3 39

3 5 4 2 21

6 8 7 6 19

911 10 18 21

1214 13 35 22

1517 16 21 18

1820 19 9 24

2123 22 6 36

- 100 200

87

11. (a)

(b)

(c) (a)(b)

12.

1 2 3

250

280

290

300

350

270

250

290

300

300

320

310

(a) 1x 2x 3x

(b)

123x

(c) 1 2 33

x x xx

123x x

(d) (c) 123x x

13. 5-36100IQ

IQ 45-

88

14. 100

()

10-11 10.5 6

12-13 12.5 13

14-15 14.5 29

16-17 16.5 34

18-19 18.5 11

20-21 20.5 4

22-23 22.5 2

24-25 24.5 1

(a)

(b)

(c)

15. 15

():

23, 40, 23, 30, 22, 22, 29, 21, 28, 21, 28, 24, 20, 24, 18

(a)

(b)

(c)

16. , 20

0100

0 3 0 6 8 1 7

1 2 1 7 6

2 1 4

3 2 6 3 4

6 6 5 9 7

89

(a)

(b)

(c)

17.

40

46 48 48 50 52 53 55 55 56 56

57 57 58 58 59 60 60 61 61 61

61 62 62 62 63 63 63 64 64 65

65 66 67 67 68 68 68 69 70 74

(a)

(b)

(c) 5

46-5152-57

(d)

(e)

(f)

(g) (a) (c)(e)??

92

Excel

80

Microsoft Excel

Excel

1. Excel

Excel

Excel

Microsoft Excel 2013

93

Excel

C1 = A1 + B1

C1A1B1

C1

= A1 + B1

C1A1B1

Excel=

Excel

2.1

Excel

+ =

- >

* <

/ >=

%

94

2.

Excel

(Menu Bar)fx

1

Excel

Excel 2010

:

AVERAGE() AVERAGE(number 1, number2,..)

MEDIAN() MEDIAN(number 1, number2,..)

MODE() MODE.SNGL(number 1, number2,..)

MODE.MULT(number 1, number2,..)

SUM() SUM(number 1, number2,..)

STDEV.S() STDEV.S(number 1, number2,..)

VLOOKUP() VLOOKUP(lookup_value,table,..)

1

2

3

95

Excel

number1, number2,

number1, number2

ExcelA1C4A1C4

12

5-3

1 09001 F 16 61 30

2 09002 M 16 43 79

3 09003 F 17 77 57

4 09004 F 16 36 87

5 09005 M 16 40 58

6 09006 F 17 58 59

7 09007 M 17 45 73

8 09008 M 16 68 86

H1I1

96

2.1 SUM

SUM

(a)

H2=SUM(F2G2),

H2H9

(b)

1. H2fx (N)SUM

2. F2 G2

3. H2H9

97

SUMExcel

ExcelSUM

Enter

2.2 (AVERAGE)

AVERAGESUM

(a)

I2 fx (N)AVERAGE

F2 G2

I2I9

98

AVERAGE

40%60%

(b)

H2=F2*0.4+G2*0.6,

I2 I9

I2I9

(a)

1

2

99

2.3 (MEDIAN)

MEDIAN

MEDIAN1, 2, ...

MEDIAN1, 2, 3, 4, 53MEDIAN1, 2, 3, 4, 5, 6

3.534

K2=MEDIAN(I2:I9),

(61.8+64.6)/2= 63.2

2.4 (STDEV.S)

EXCEL 2010STDEVS

STDEV.S

STDEV.S1, 2, ...

(-3, 4, 5)STDEV.S(-3, 4, 54.35889..

K5=STDEV.S(I2:I9),

100

n-1 = 10.91208..

2.5 (Mode)

MODE

MODE.SGNL1, 2, ..., MODE.MULI1, 2, ...

MODE.SGNL1, 2, 2, 32

MODE.MULI1, 1, 2, 2, 31, 2

MODE.SGNLMODE.MULI

K8=MODE.SGNL (E2:E9),

16

MODE.SGNL

101

2.6 LOOKUP

VLOOKUP

LOOKUP

VLOOKUP(lookup_value,table_array,col_index_num,range_lookup)

lookup_value

table_array

col_index_num

range_lookup

range_lookupTrue

lookup_value

Falselookup_value

True

6b12b13

B12VLOOKUP

lookup_value 6 (6)

table_array A2:I9 ()

col_index_num 2 (2)

range_lookup

102

6.

6, B13VLOOKUP

(6,A2:I9,9) VLOOKUP(6,A2:I9,9)

6

58.6.

: VLOOKUP()

103

5-7

1. 5-3

1 9001 F 16 61 30 65

2 9002 M 16 43 79 59

3 9003 F 17 77 57 33

4 9004 F 16 36 87 69

5 9005 M 16 40 58 38

6 9006 F 17 58 59 35

7 9007 M 17 45 73 73

8 9008 M 16 68 86 85

9 9009 F 16 62 25 47

10 9010 M 17 30 62 24

11 9011 M 18 73 36 59

12 9012 F 19 53 66 84

13 9013 M 20 69 21 63

14 9014 M 19 62 41 47

15 9015 M 18 52 86 89

1. I1 ,

I2 I16

2. J1 1

, J2 J16

3. K1 2 2:3:5

, K2 K16

4. D18, D19, D20, D21, D22

E18 H23

5. D23

F24 H24

6. =VLOOKUP(8,A2:K16,11)

7. VLOOKUP()

105

?

106

(1)

X

80%X

(2)

107

(3)

(4)

5, 9, 37, 69, 70, 71, 72, 75, 78, 84

1

5 9 37 69 70 71 72 75 78 84 5710

x

59

(70 + 71)/2 = 70.5

108

1x

2x

2 1x x

Bill Gates 1x

1 2x x

(5)

5-40

ABC

BA

BA2

y

120/80=1.5

109

5-41

MokiaSamsang

20052009

Samsang

Mokia400800Samsang250

550Mokia

y

y

(6)

110

5-42

8

(7)

2040020600

r= +0.9 -0.9

r = +0.9

IQGPA

0.9IQGPA

r

xy

111

1. http://www.td.gov.hk/filemanager/tc/content_2015/08fig1.13c.pdf

2. http://www.statistics.gov.hk/publication/stat_report/labour/

B10500012010QQ01B0100.pdf

1. http://en.wikipedia.org/wiki/H._G._Wells

2. http://en.wikipedia.org/wiki/File:Graunt2.gif

3. http://www.hkqf.gov.hk/ind/tc/images/common/censtd_logo.png

4. http://hkupop.hku.hk/

5. http://en.wikipedia.org/wiki/File:Carl_Friedrich_Gauss.jpg

6. http://en.wikipedia.org/wiki/Pierre-Simon_Laplace

7. http://en.wikipedia.org/wiki/William_Sealy_Gosset
http://www.statistics.gov.hk/publication/stat_report/labour/B10500012010QQ01B0100.pdfhttp://www.statistics.gov.hk/publication/stat_report/labour/B10500012010QQ01B0100.pdf

112

(M)

=

=

=

=

=

( )

=

=

=

=

(s)

:

:

() ()

()

= 13 QQ

= 2

QQ 13

= %100x

s

113

: ()

114

normal distribution

Karl F.Gauss17771855

5

115

6-8

6-86-8

116

population

parameter

2

sample statistic

x

1 1

1 1

n N

i i

i i

x x xn N

2s 2

2 2

2 2

1 1

1 1

1

n N

i i

i i

s x x x xn N

117

5-1

1. (a) (b) (c) (d)

2. 20 5 100

3. (a)

4. (i)

(ii)

(iii)

5.

6. (a)

(b)

(c)

(d)

7. (a)

(b)

(c)

118

5-2

1. 20

119

5-4

1. (a)

() ()

30 - 49 29.5 49.5 2

50 - 69 49.5 69.5 4

70 - 89 69.5 89.5 10

90 - 109 89.5 109.5 8

110 - 129 109.5 129.5 4

130 - 149 129.5 149.5 4

32

(b)

()

29.5 0

49.5 2

69.5 6

89.5 16

109.5 24

129.5 28

149.5 32

(c) 20 100

0

5

10

15

20

25

30

35

0 15 30 45 60 75 90 105 120 135 150 165

()

120

2. (a) 20

(b)

121140 120.5 140.5 3

141160 140.5 160.5 8

161180 160.5 180.5 16

181200 180.5 200.5 9

201220 200.5 220.5 3

221240 220.5 240.5 0

241260 240.5 260.5 0

261280 260.5 280.5 1

- 40

(c) (d)

(e) (i) 161180

(16

100% 40%40

16)

(ii) 922.5%181200

(iii) 12602.5%

121

(f) 181200 = 22.5%

(g)

()

()

120.5 0

140.5 3

160.5 11

180.5 27

200.5 36

220.5 39

240.5 39

260.5 39

280.5 40

23 175

122

5-5

1.

60

2082000

50

2. (a)

123

(b) 1524

84% 82%

2539

6% 7%

40

10% 11%

3. (a) 144

(b) 4 620

4. (a)

(b) A

ABA

B

5. (a)

(10) (1)

3 0 1 2 2 3 5 5 6

4 2 2 4 5 7 9 9

5 1 1 2 3 3 9

6 0 2 5 5 9

7 0 4 9

(b) 49

124

6. (a)

(b)

5-6

1. (a)

n= 29

49.86

, 15, = 49

= 53

(b) 197.3374

14.0477

2. (a) A

= 8.3

6.6, 7.4, 7.6, 7.8, 7.8, 8.0, 8.2, 8.6, 10.2, 10.8

n = 10 () = 7.9

= 7.8

C = 10.3

9.4, 9.5, 9.6, 9.8, 10.4, 10.5, 10.6, 10.8, 11.0, 11.4

n = 10 () = (10.4 + 10.5) 2 = 10.45

125

(b) A C

C

A

C

3. = 24

= 24 () = 25 ()

4. 8 = 50

5. 2

10

90%

6.

7.

84 99

82 96

75 75

63 74

58 74

75

126

8.. (a) A = 63.1

B = 57.0

C = 63.1

b) AC

9. (a) = 100

= 120

= 180

(b)

(c)

10. (a) M74.5th

17.65

(b)

17.60x

7.08s

(c) 15 x M

11.

(a)

M50.5th, 13.8 ()

M100.5th, 12 ()

127

(b)

(c)

13.27 11.44

13.8 12

4.45 7.65

1 2s s

12. (a) 123

1 294x , 2 277.5x , 3 310x

(b)

123 292.5x

(c) 293.83x

123x x

1 2 3 1 2 31 1 1 1

3 3 3 3x x x x x x x (*)

(*)

128

(d) x

1 2 3

123

5 4 3

12 12 12

15 294 4 277.5 3 310

12

292.5

x x x x

x

13. (a) ( = 101.18), = 14.5 = 14.33%

(b) ( = 103.2), = 16.74 = 16.22%

14. (a) M = 50.5th

= 15.62

(b) 34, 16-17

= 15.86

(c)

)(x =15.62 , )(s = 2.67

(CV)= 17.09%

15. (a) ()

1 8

2 0 1 1 2 2 3 3 4 4 8 8 9

3 0

4 0

(b) : = 21, 22, 23, 24, 28

: = 22

, Q2 = 23Q1= 21Q3 = 28 = 7

129

15 (c)

16. (a)

0, 1, 3, 6, 7, 8, 11, 12, 16, 17, 21,

24, 32, 33, 34, 36, 65, 66, 67, 69

(b) :

= 69

Q2 = 19 Q1 = 7.5 Q3 = 35 = 27.5

(c)

17.

(a) = 60.5, = 61 = 6.56 (2d)

(b) = 56.5

() = 61

= 65

= 8.5

130

(c)

, xi , fi

46 51 45.5 51.5 48.5 4

52 57 51.5 57.5 54.5 8

58 63 57.5 63.5 60.5 15

64 69 63.5 69.5 66.5 11

70 75 69.5 75.5 72.5 2

(d) = 60.35 = 60.7= 6.298 ~ 6.30

(e)

(f) 61

(g)

0

2

4

6

8

10

12

14

16

45.5 51.5 51.5 57.5 57.5 63.5 63.5 69.5 69.5 75.5

131

5-7

1 - 3

1 2

156 52.0 53.7

181 60.3 61.8

167 55.7 49

192 64.0 67.8

136 45.3 44.4

152 50.7 46.8

191 63.7 67.4

239 79.7 81.9

134 44.7 43.4

116 38.7 36.6

168 56.0 54.9

203 67.7 72.4

153 51.0 51.6

150 50.0 48.2

227 75.7 80.7

5-7

4

258 829 866 870

17.2 55.3 57.7 58.0

1.3 14.1 22.6 20.2

17 58 59 59

16 62 86 59

5

25.51 39.20 34.91

6. 81.9

7. =VLOOKUP(9 , A1:K16 ,2)

20 17 /18

1

2

3

4

9

9

11

Error! Bookmark not defined.18

23

23

32

33

37

47

48

49

52

57

57

60

65

69

74

74

83

88

92

96

97

1

Albert Einstein18791955

1

1000

100020

100020

10004%1000

20456

4%1000202191

3

()

%

100%

%

, 22

7 2

(i) ...0.31818181 22

7

(ii) 100%0.31818181 = 31.82%

100%-

( + )

( )

6-1

460

391

%100460

460391

%100460

69

= 15% ()

4

1

= =

% %

100%

100%

% %

= ( 1 + % ), = ( 1 % )

6-2

1,440

38

36 38 1440 = 72 ()

%1001440

72

= 5%

6-3

238015%

= 2380 ( 1 15%)

= 2380 0.85

= 2800

5

2

=

100%

%

= %

= ( 1 % )

6-4

$450 $180

= ( 450 + 180 ) 70%

= 630 0.7

= $441

3

(Inflation)(Deflation)

=

100% ()

= (1 + )n n =

6

6-5

800900

?

=

100%

= %100800

800900

= %100800

100

= 12.5% ( _________________)

6-6

1,0002,0003,0004,000:

(a)

(b)

(a)

%1002000

20003000

= 50% ()

(b) x %

1,000(1 + x %)3 = 4,000

(1 + x %)3 = 4

1 + x % = 1.5874

x % = 58.74%

59% ()

59%

7

6-1

1. $95000 $38000

2. $80005%

$14000

3. $18040%

4. 10%6

5. 10 12

6. 2014 2009 2017 2009

2014 2017

1

7. 20% 15%

5%

8. 8% 8,000

9. 11,767,000 20

8% 20

9

interest

Simple Interest

Compound Interest

(P)(I)

(A)

A = P + I

I = P r t

1

A P I

P P rt

P rt

rt

10

6-7

70001.5%

7000 1.5% 1 = 105

6-8

8%2800

5

1

2 800(1 8% 5)

2 800(1 0.4)

3920

A P rt

2 800 8% 5

1120

2 800 1120

3 920

6-9

4.5%2760.75

1

2 760.75 (1 4.5% 0.5)

(1.0225)

2 700

A P rt

P

P

P

11

6-10

70000

26250.25

70 000 0.25 2 625

0.15

15%

r

r

6-2

1. 500010%

3500

2.

15008%

3. 15000

20400

4. 2500033750

5. 48000 12%

0.75

13

(Compound Interest)

1A P r

2

1 1

1 1

1

A P r r

P r r

P r

2

1A P r Pr

2At

1t

A P r

1.

= (1+)

14

2.

= [1 + ]

2

= 2

r

t2

2

12

tr

A P

2n

1

ntr

A P n

nt =

n

6-1

(n)

1 -

2 = 2

4 = 4

12 =12

52 = 52

365 = 365

15

A

A = P + I

1

1 1

nt

nt

I A P

r P P

n

rP

n

6-11

6-88% 2800

5

P = 2 800, r = 8%, n = 2, t = 5

2 5

1

82 800 1

2

4144 68

ntr

A P n

%

.

16

6-8

6-12

6-770001.5%

P = 7000, r = 1.5%, n = 4, t = 1

4 1

1

1 57 000 1 1

4

105 59

ntr

I P Pn

. %

.

4(1)1.5% 7 000(1 )4

7105.59

7105.59 7 000

105.59

17

6-13

6-1070000

70966.92

112

4

3

3

3 3

1

70 966 92 70 000 112

1 0138 112

1 0138 112

1 0046 112

0 055

5 5

ntr

A P n

r.

r.

r.

r.

r .

. %

6-13nt

nt = 3

nt

nt

6-14

50004%

34%1 5 000(1 ) 5151.51

4

ntr

A P n

18

6-15

123005%

1500

(1) logt

(2) log logma m a

12300 + 1500 = 13800

2

2

2

1

513800 12 300 1

2

51.12195 1

2

5log1.12195 log 1

2

5%2 log(1 )

2

log1.121952

5%log(1 )

2

2 4.66

2.33

nt

t

t

t

rA P

n

%

%

%

t

t

t

t

5%

4.8%

19

P

1

1

1 1

n

n

rI P P

n

r P

n

Effective Interest Rate,

ER

1

100%

1 1 100%

n

n

rP P

nER

P

r

n

ERP

tERPA )1(

(1 5%) 1 5%ER

524.8%

(1 ) 1 4.91%52

ER

20

6-3

1. 240003%

(a)

(b)

2. 20008%

3. 6000085694.77

4. 9

5. 2%

2020.08

6. 300003%

(a)

(b)

(c)

(d)

7. 2%

3%7%

10000020

8. (a) 1000 8%

4

(b)

21

9.

2.3%

2.2%

10. 10000024%

23

1

1

1520

20

()152020

6 %

83453.01

6-16

(a) 9700

(i) 10000

(ii) 13000

(iii) 21000

24

7%

()

(i) 12(1)

10 0009 325.83

7%(1 )

12

(ii) 12(3)

13 00010 544.03

7%(1 )

12

(iii) 12(6)

2100013814.83

7%(1 )

12

(iii)

(b) 5%

r

(i)

1

10 000 9 700 1

3.09

r

r %

(ii)

3

13 000 9 700 1

10.25

r

r %

(iii)

6

21000 9 700 1

13.74

r

r %

(iii) (ii)(iii)

planned savings

25

6-17

800

2.6%

6

2.6%800 1 810.46

12

5

2.6%800 1 808.70

12

4

2.6%800 1 806.96

12

3

2.6%800 1 805.21

12

2

2.6%800 1 803.47

12

2.6%

800 1 801.7312

810.46 808.70 806.96 805.21 803.47 801.73 4 836.53

6 5 4 3 22.6% 2.6% 2.6% 2.6% 2.6% 2.6%

800 1 1 1 1 1 112 12 12 12 12 12

4 836.53

:

(, , 2, , 1)

: (1)

1 , a=

2.6%1

12

, r=

2.6%1

12

, n=6

26

6-4

1.

(i) 5000 + 10000

(ii) 17000

(iii) 22000

6.7%

2.

(i) 100000

(ii) 6000060000

10%

3.

1 0003%

28

insurance

29

19Otto

von Bismarck18151898

annuity insurance

perpetuity

A PV

r

n

PVArn

6-18

5000

7%

n = 12

5 000 857142.86

7% /12PV

30

6-19

5000008%

500 000

8%

12

3 333.33

A

A

6-5

1.

100008.5%

2. 20000

8.5%

3.

23005%

32

lot

dividend

6-20

(a) 0.8

200

200 0.8 200 = 160

(b) 90

4

40.8 200 4 = 640

7 7.11 90

640 ()

(c)

33

7 630790

10630640

(d) 91

0.8

100% 0.88%91

retail bond

coupon rate

6-21

100000

4%5%

100 000 4% 2 8 000

100 000 5% 2 10 000

100 000 10 000 8 000 118 000

34

6-6

1. 1.051.2

(a) 62

(b) 5300

(c) 59

2. 611

1.9

2.11000

(a) 10

(b)

3. 500002%

3%4%

(a)

(b)

37

100000

2000000100001000

6-2

2000000 10000

100000 1000

return

on investment, ROI

= 100%

38

6-3

2000000 10000

100000 1000

100 000

100% 5%2 000 000

1000100% 10%

10 000

arithmetic rate of return

geometric rate of returninternal rate of return

1. arithmetic rate of return

n nrrrr ,.....,,, 321

= % 100....321

n

rrrr n

6-22

4

6-4

2007 2008 2009 2010

123 145 156 159

39

2007

2008145 123

100% 17.89%123

2009156 145

100% 7.59%145

2010159 156

100% 1.92%156

17.89% 7.59% 1.92%

9.13%3

2.

n

n1 2 3, , , , nr r r r 1, , ny y

= (1 + 1)(1 + 2)(1 + 3) (1 + )

-1

= +1

1

1

6-23

6-22

3 (1 17.89%)(1 7.59%)(1 1.92%) 1

3 (1.1789)(1.0759)(1.0192) 1

3 1.2927 1

1.0893 1

0.0893

8.93%

40

3159

1123

3 1.2927 1

1.0893 1

0.0893

8.93%

6-24

6-226-230.88%

100000118000

r

4

118 000 100 000 1

4.22

r

r %

4.22% 0.88%

41

3.

5%3%5%

Net Present Value, NPV

6-5

() () $

0 15000

1 6000

2 6000

5 7000

3%

6-6

$

0 15000 0

15 00015 000

1 3%

1 6000

6 0005825.24

1 3%

2 6000 2

6 0005 655.58

1 3%

5 7000 5

7 0006 038.26

1 3%

42

5825.24 5 655.58 6 038.26 15 000 2 519.08NPV

6-25

5%7%10%

() () $

0 15000

1 6000

2 6000

5 7000

5%

2 5

6 000 6 000 7 00015 000

1 5% 1 5% 1 5%

1641.15

7%

2 5

6 000 6 000 7 00015 000

1 7% 1 7% 1 7%

839.01

43

10%

2 5

6 000 6 000 7 00015 000

1 10% 1 10% 1 10%

240.33

7%10%

7%10%

7%10%

9%

6-7

1.

2014 2015 2016 2017 2018

() 1.36 2.50 3.48 3.79 4.11

(a)

(b)

2. 5.6%

6%

3.

2014 2015 2016 2017 2018

() 10.41 10.90 11.39 11.88

6%

44

4. 3

5. LC1000023000

6.

() ()

0 6000

2 3000

4 2000

6 2000

3%5%7%

7. 6

0 10000

1 5000

2 3000

4 2000

6 2000

3%5%7%

6

45

8.

0 17000

4 10000

6 14000

3%5%7%

47

(a) 5000

(b) 7000

(c) 10000

(a)

(c)

time value

5000

500070005000

10000

5000

present

value, PVdiscounted value

48

1

ntr

A P n

PVfuture value, FV

1

1

-nt

nt

FV rPV FV

nr

n

6%

(a) 5 000PV

(b) 7 000

6 603.77(1 6%)

PV

(c) 2

10 0008899.96

(1 6%)PV

(c)

6603.776%

7000 (b)

70006603.77

10000 (c)8899.96

(a) 5000

(b) 6603.77 7000

(c) 8899.96 10000

49

6-26

2540000

6.5%2540000

2(3)

2 540 0002 096 492.70

6.5%(1 )

2

trade-in

installment

pre-payment scheme

6-27

C

T

6-7

$98 $398

$5180 $0

12 $0 $2340

3%

50

1 2 113% 3% 3%

5180 98 1 1 1 112 12 12

6 340.00

12

2 340 12 195

203195398

1 2 113% 3% 3%

2 340 203 1 1 1 112 12 12

4 742.86

6-28

3D8988

1.

2. 12

4%

: (, , 2, , 1)

:(1)

1 , a=1, r=(1 +

3%

12)1, n=12

51

8 988 95% 8 538.6

8 988 12 749

1 2 114% 4% 4%

749 1 1 1 112 12 12

8825.57

6-29

360 40 100

900 100

1530 170

2700 300

*

50010040360

333.333100)(900

(1530 170) 6 283.33

(2700 300) 15 200

52

depreciation

4988

498835003200

straight-line

depreciation

accelerated depreciation

53

6-30

T5588

T650

T

T

5 588 650 4 2 988

6-31

6-8

0 1 2 3

2340000 1990000 1640000 1290000

0 1 2 3

2340000 1990000 1640000 1290000

350000 350000 350000

1 2 3

350 000100%

2 340 000

14.96%

350 000

100%1990 000

17.59%

350 000

100%1640 000

21.34%

54

6-32

7-24T5588

20%3

3 35 588 (1 20%) 2 861.06

6-33

7-26

5 588 20% 1117.6

(5588 1117.6) 20% 894.08

(5588 1117.6 894.08) 20% 715.26

6-8

1. -4588

(a) -450

(b) -15%

2. 56883344

(a)

(b)

55

3. 218000199000

(a)

(b)

(c) (a)

(d) (b)

4. 13800

(i)

(ii) 1212

(iii) 662400

2%

57

loan

monthly

interest rate interest rate

per annum

12

6-34

500002%

(a)

(b)

(a)

50 000 (1 2%) 51000

(b)

650 000 (1 2%) 56 308.12

58

minimum repayment

5%

10%outstanding loan

6-35

7-283%1500

1500

50 000 1500 48 500

48 500 (1 2%) 49 470

1500

MS Excel

($) ($)

1 1500.00 49470.00

2 1500.00 48929.40

3 1500.00 48377.99

4 1500.00 47815.55

5 1500.00 47241.86

6 1500.00 46656.70

7 1500.00 46059.83

49 1500.00 6571.49

50 1500.00 5172.92

51 1500.00 3746.38

52 1500.00 2291.30

53 1500.00 807.13

54 807.13 0.00

54

1500 53 807.13 80 307.13

59

5%30%

6-36

1155000021

31

(i) 32

4630%50 000 (1 ) 51925.80365

(ii)

18330%51925.80 (1 ) 60 350.24365

(iii) 50000

2295%50 000 (1 ) 51593.24365

60

mortgage loan

prime rate, PHIBOR, H

3%P 3%

6-9

2.50% $177.47 $94.27 $66.68 $52.99 $44.86 $39.51

2.75% $178.58 $95.41 $67.86 $54.22 $46.13 $40.82

3.00% $179.69 $96.56 $69.06 $55.46 $47.42 $42.16

3.25% $180.80 $97.72 $70.27 $56.72 $48.73 $43.52

3.50% $181.92 $98.89 $71.49 $58.00 $50.06 $44.90

3.75% $183.04 $100.06 $72.72 $59.29 $51.41 $46.31

4.00% $184.17 $101.25 $73.97 $60.60 $52.78 $47.74

4.25% $185.30 $102.44 $75.23 $61.92 $54.17 $49.19

4.50% $186.43 $103.64 $76.50 $63.26 $55.58 $50.67

4.75% $187.57 $104.85 $77.78 $64.62 $57.01 $52.16

5.00% $188.71 $106.07 $79.08 $66.00 $58.46 $53.68

5.25% $189.86 $107.29 $80.39 $67.38 $59.92 $55.22

5.50% $191.01 $108.53 $81.71 $68.79 $61.41 $56.78

5.75% $192.17 $109.77 $83.04 $70.21 $62.91 $58.36

6.00% $193.33 $111.02 $84.39 $71.64 $64.43 $59.96

6.25% $194.49 $112.28 $85.74 $73.09 $65.97 $61.57

6.50% $195.66 $113.55 $87.11 $74.56 $67.52 $63.21

6.75% $196.83 $114.82 $88.49 $76.04 $69.09 $64.86

7.00% $198.01 $116.11 $89.88 $77.53 $70.68 $66.53

61

6-37

11000008340

3%

3%

1100 000 2 75012

1100 000 2 750 8 340 1094 410

3%

1094 410 2 736.0312

1094 410 2 736.03 8 340 1088806.03

6-38

1797670

2.5%

(a)

(b)

(a) 1797 670

2 5681000.7

2 568100 (1 70%) 770 430

(b) 6-939.51

1797 67039.51 7102.59

10 000

62

6-39

5600000

12916.4

5600000 50%= 2800000

R

2 800 00012 916.4

10 000

46.13

R

R

6-92.75%

6-40

4780000

3.5%

(a)

(b)

(a)

4780000 50% = 2390000

25

2 390 00050.06 11964.34

10 000

(b)

4780000 20% = 956000

63

20

956 00058 5544.80

10 000

11964.34 + 5544.80= 17509.14

6-9

1. 30000

4%3%

() ()

30000 1200

2. 1560000

3. 4280000

17280.07

4.

2.75%6458.2

65

Prime rate

3%

(HIBOR)

11

20

1 12 20

14

Money Market

Offered Rate

20

+(H+)

-(P-)

P-Plan
https://zh.wikipedia.org/wiki/%E6%8C%89%E6%8F%ADhttps://zh.wikipedia.org/wiki/%E9%8A%80%E8%A1%8C%E5%90%8C%E6%A5%AD%E6%8B%86%E6%81%AFhttps://zh.wikipedia.org/wiki/%E7%BE%8E%E5%9C%8Bhttps://zh.wikipedia.org/wiki/%E8%81%AF%E9%82%A6%E5%9F%BA%E9%87%91%E5%88%A9%E7%8E%87https://zh.wikipedia.org/wiki/%E8%B2%A8%E5%B9%A3%E5%B8%82%E5%A0%B4

66

H-Plan (HiBOR Plan)

()

H

P+1

6-41

2088000

P 2% H + 1.5%

(a) P5%H1%

(b) P7%H4%

(a) 2 088 000 70% 1461600

P 2% = 3%H + 1.5% = 2.5%2.5%

6-952.99

146160052.99 7 745.02

10 000

(b) P 2% = 5%H + 1.5% = 5.5%5%

6-966

146160066 9 646.56

10 000

67

6-10

1. 8680000

P 1.5%

P5.25%

2. 3440000

P 2%

P 1%5%

(a)

(b)

3. 5000000

H + 1%

P 2% (H)

1.75% (P) 5%

(a)

(b)

(c)

69

Stress Test

(HKSCC)

+/-22%

+/-100%

A +/-10%

70

09

(Debt Servicing RatioDSR)DSR(

)

DSR

50%50%

3 (3) DSR60%

60%

25

43.6%30

41.5%

41.5%

2012915DSR

40%DSR50%25

36.3%30

34.5%

DSR

71

6-42

3700000

250001500000

15

280000

3%

3700000 75% = 2775000

925000+150000+280000 = 1355000 < 1500000

277500047.4210000 = 13159.05

13159.05 > 250000.5 = 12500

DSR50%

6-43

5600000

25 2.5%

45000

56000000 70% = 3920000

392000044.8610000 = 17585.12

72

(1)

(17585.12+0)(450000)0.5= 22500

(2) 3% (2.5+3) = 5.5%

25 392000061.4110000 = 24072.72

22257.76 450000.6 = 270000

60%

22257.6 > 4500041.5% = 1867541.5%

6-11

1. 4200000

3.5%

188045800

2.

3. 6-4238000

2.5%

74

http://www.ird.gov.hk/

41331

2017/18

salaries tax

allowances

deductionsnet chargeable income

6-106-12

= + +

=

=

= +

2000121

2013

1165007100

20146 25 000 30 000
http://www.ird.gov.hk/

75

200012

5%

2013117100

5%1500

18000

7100 5%

7100 30 000 5% 5%

30 000 1500 $1500

6-10

2017/18

$

132 000

264 000

100 000

100 000

37 500

60 46 000

5560 23 000

76

60 46 000

5560 23 000

132 000

75 000

6-11

2017/18

$

100 000

92 000

100 000

18 000

6-12

2017/18

$ $

45 000 2% 900

45 000 7% 3150

90 000 4050

45 000 12% 5400

135 000 9450

17%

15%

77

15%standard rate

15%15%

provisional salaries tax

6-44

32 000 15444

(a)

(b)

(c)

()

(a) = 32 000 13 = 416 000

(b) = 264 000

= 100 000

= 264 000 + 100 000 = 364 000

(c)

=

= 416 000 364 000 15444 18 000

= 18 556

78

6-45

25 00064

()

= 25 000 12 = 300 000

= 300 000 132 000 46 000 46 000

25 000 5% 12

= 61 000

45 000 = 45 000 2% = 900

16 000 = 16 000 7% = 1120

= (900 + 1120) 2 = 4040

6-46

35 00019

5761

()

= 35 000 12 = 420 000

= 420 000 132 000 37 500

23 000 2 46 000 2 18 000

= 94 500

90 000 = 45 000 2% + 45 000 7% = 4050

4500 = 4500 12% = 540

= (4500 + 540) 2 = 9180

79

6-47

27 000 63 000

25 000

63

11 000

()

= 27 000 12 + 63 000 + 25 000 12

= 687 000

= 687 000 264 000 100 000 2 (46 000 2) 2

(25 000 5% 12 + 27 000 5% 11 + 1500)

= 7650

7650 = 7650 2% = 153

= 153 2 11 000 = 10 694

10 694

6-48

70

()

= 132 000 + 46 000 + 18 000

= 196 000

x

= 9450 + (x 196 000 135 000) 0.17

9450 > 135 000

0.15(x 18 000)

9450 + (x 196 000 135 000) 0.17 0.15(x 18 000)

80

9450 + 0.17x 56 270 0.15x 2700

0.02 x 44 120

x 2 206 000

2 206 000

6-49

2 000 000

()

= (2 000 000 18 000) 0.15 2 = 594 600

http://www.gov.hk/tc/residents/taxes/etax/services/tax_computation.htm

6-12

1. 15 000

(a)

(b)

(c)

(d) ()

2. 34 000

60 5 600

(a)

(b)

(c)

(d) ()

81

3. (a) 62

(b) 740 000

32 000

()

(c) 700012 000

32 000

()

4. 20

()

5. 34 000

28 000

500

()

6. 625717

()

7. 140 000 600

()

8. 45 000 30 500

70

11 007

()

9. 210 000 150 000

61 050

()

83

rates

1845

1888

http://www.rvd.gov.hk/

ratable value

20142015

5%2013101

government rent

1997627

1997630

2047630

3%1985527

199771

2

84

5%

5%

10%

= 5% 4

= 3% 4

= 8% 4

6-50

84 000

84 000 8% 4 = 1680

6-51

7-424

]

1680 (1 + 5%) = 1764

6-52

7000

94 300

94 300 8% 4 3 = 628.67

4 3

7000 628.67 = 6371.33

85

6-53

756

4350

(a)

(b)

(a) x

x 8% 4 = 4350

x = 217 500

217500

(b) 217 500 12 756 = 23.97

6-13

1. 156 500

2. 4900

60 000

3. 2100

(a)

(b)

4. 90 000

86

5. 452

1600

(a)

(b)

(c)

6. 2 000 000

3.25% 72 000

(a)

(b)

88

profits

tax

2014/15

16.5%15%

15%

6-13

2008/09 16.5%

15%

=

=

6-54

1 403 000 500 000

= 1 403 000 500 000 = 903 000

= 903 000 16.5% = 148 995

89

6-55

420 000 240 000

= 420 000 240 000 = 180 000

= 180 000(1 15%) = 153 000

6-56

245253.9

= 245 253.9 (1 15%) = 288 534

= 288 534 245 253.9 = 43 280.1

6-57

11 000 22 500

25 000 2000 4000

365

= 4000 365 = 1 460 000

= (11 000 + 22500 1.05 + 25 000 + 2000) 12

= 739 500

(1 460 000 739 500) 15% = 108 075

property tax

15%

=

80% 15%

90

6-58

5700

5 700 12 80% 15% 8 208

6-59

7800

4300

(7 800 12 4 300) 80% 15% 2 21432

6-14

1. 10 000

24 000 7000 6000

76 200

2. 20%

3. 134 000 74 000

4. 366 000

5. 20%

780 000

91

6. 9000

33 000 5400 1500

2000

7. 8200

1. http://en.wikipedia.org/wiki/File:Albert_Einstein_(Nobel).png

2. http://www.rvd.gov.hk/

92

2015-2016

13.9%2016-2017

10%3

.

(a) : ()

1.5%8.5% 6-13

(b) :2014 ()(2 )

100 4.25%

(i) (ii)

6-13 ()

$2,000,000 1.5%

$2,000,000 $2,176,470 $30,000 $2,000,000

20%

$2,176,470 $3,000,000 3%

$3,000,000 $3,290,330 $90,000 $3,000,000

20%

$3,290,330 $4,000,000 4.5%

$4,000,000 $4,428,580 $180,000 $4,000,000

20%

$4,428,580 $6,000,000 6%

$6,000,000 $6,720,000 $360,000 $6,000,000

20%

$6,720,000 $20,000,000 7.5%

$20,000,000 $21,739,130 $1,500,000 $20,000,000

20%

$21,739,130 8.5%

$1$1

93

2. : 1 0.25%

3. : 0.1%

20101120()

2010112024 (

2010112020121027) 36(

2012 10 27 )

(SSD)

() ,

:

6-14 ()

20101120

20121027

20121027

6 15% 20%

612

10% 15%

1224

5% 10%

2436

- 10%

6-15 ()

6-15 ()

200 $100

200300 1.5%

300400 2.25%

400600 3%

6002,000 3.75%

2000 4.25%

http://www.ird.gov.hk/chi/faq/ssdexample.htm

94

6-60

5700

5700120.25% =171

6-61

20141 4267890

(a)

(b) 201512 4988000

(a) 180000 + (4267890 4000000)0.2

= 233578

(b) 49880000.06 + 49880000.1

= 528728

6-15

. 190002

2. 20154 20 888 000

2016119 994 000 (a)

(b)

(c)

96

(PV)

=

(1 +

) = (1 +

)

()

2017/2018

$132,000

264,000

()

100,000

() 100,000

() 37,500

// ()

60 46,000

55 60 23,000

// ()

60 46,000

55 60 23,000

132,000

75,000

()

100,000

92,000

100,000

18,000

2017/2018

($) ($)

45,000 2% 900

45,000 7% 3,150

90,000 4,050

45,000 12% 5,400

135,000 9,450

120,000 8,400

17%

15%

97

6-1

1. = 40%

2. = 6000

= 120000

3. = 180 (1 + 40%) = 180 1.4 = 252

4. 4.5

5. = 20%

6. 20.6%

7. 10%

8. 11 755

9. 20 5 450 398

6-2

1. 7t

2. 9 375P

3. 24r %

4. 10r %

5. 52 320

98

6-3

1. (a) 25 868 66A .

(b) 1868 66I .

2. 480

540.47

60.47

3. 24r %

4. 7 73r . %

5. 2 000.00

6. (a) 910 18I .

(b) 912.48I

(c) 913.37I

(d) 913.60I

7. 107 412.25A

8. (a) 1372.79A

(b) 1320A

9. 2.31%

2.22%

10. 153 760A

6-4

1. (i)13446.24

99

(ii)13 950.38

(iii)14 814.84

(iii)

2. (i)100 000

(ii)114 545.45

(i)

3. 6 052.72

6-5

1. 235 294.12

2. 1 700

3. 1 91.67

6-6

1. (a) 3.63%

(b) 3375

(c) 30

1605

2. (a) 315

10 315

(b) 540

3. (a) 5 4 500

(b) 9%

100

6-7

1. (a) 35.09%

(b) 31.85%

2. 7.21%6%

3. 13.13

4. 5.98%

5. 23.15%

6. 3% 279.73

5% 141.08

7% 521.21

3%5%

7. 3%1134.10

5% 620.83

7%151.69

7%

8. 3% 3 586.54

5%1617.25

7% 140.92

5%7%

101

6-8

1. (a) 2 338

(b) 2 035.72

2. (a) 781.33

(b) 16.23%

3. (a) 19 000

(b) 8.72%

(c) 104 000

(d) 126 098.60

4. (i) 13110

(ii) 13 674.41

(iii) 14 340.23

6-9

1.

() ()

30 000 1 200

29 664 1186.56

29 331.76 1173.27

29 003.24 1160.13

28 678.40 1147.14

28 357.20 1134.29

102

2. 468 000

1092 000

3. 2.5%

4. 1701586.13

6-10

1. 36 024.60

2. (a) 2511418.74

(b) 15 588.02

3. (a) 3014 287

(b) 19 795.39

(c) 2 295 837

6-11

1. 15 = 21 018.06

2. 202 940 000 58 10 000 = 17 052

3. 2 775 000 44.86 10 000 = 12 448.65

6-12

1. (a) 180 000

103

(b) 169 500

(c) 10 500

(d)

210

420

2. (a) 408 000

(b) 339 600

(c) 68 400

(d) 5076

3. (a) 656 000

(b) 2780

(c) 823 294.12

4. 3 255 750

271 312.5

5. 436 000

364 000

21 050

50 950

2133

6. 25 625

7. 139 000

104

1000

560

8. 906 000

692 000

214 000

34 753

9. 734 550

6-13

1. 1956.25

1173.75

2. 5 300

3. (a) 168 000

(b) 168

4. 6 900

5. (a) 80 000

(b) 14.75

(c) 1848

6. (a) 6 822.2

(b) 7 302.2

6-14

1. 50 400

105

2. 253 030 303.03

3. 67.70%

4. 402 600

5. 30 826.35

6. 34 346.33

7. 23 616

6-15

1.

2. (a) 5677600

(b) 4498650

(c) 9282250 (44.44% )
DYJ-Maths-M5-student-20170804DYJ-Maths-M6-student-20170804

毅進文憑 數學 單元五...

Documents

毅進文憑數學單元五...