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Trường ĐHBK Tp.HCM Thng Kê - Chương 1 TS. Cao Hào Thi 1 CHƯƠNG 1 CHƯƠNG 1 DLIU DLIU 1 THNG KÊ THNG KÊ NI DUNG CHÍNH NI DUNG CHÍNH Thng kê và các ng dng trong kinh doanh và kinh tế Dli2 Dliu Ngun dliu Thng kê mô t Thng kê suy din THNG KÊ VÀ NG DNG TRONG THNG KÊ VÀ NG DNG TRONG KINH DOANH VÀ KINH TKINH DOANH VÀ KINH TThng kê là mt Nghthut Khoa hcv: Thu thp 3 Phân tích Trình bày Và gii thích DLIU www.daykemquynhon.ucoz.com

Bài giảng Thống kê Tác giả: TS. Cao Hào Thi, Trường Đại học Bách khoa, ĐHQG Tp.HCM, 2010

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Text of Bài giảng Thống kê Tác giả: TS. Cao Hào Thi, Trường Đại học Bách khoa, ĐHQG...

  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 1

    CHNG 1CHNG 1

    D LIU D LIU

    1

    vv

    THNG KTHNG K

    NI DUNG CHNHNI DUNG CHNH

    Thng k v cc ng dng trong kinh doanh v

    kinh t

    D li

    2

    D liu

    Ngun d liu

    Thng k m t

    Thng k suy din

    THNG K V NG DNG TRONG THNG K V NG DNG TRONG KINH DOANH V KINH TKINH DOANH V KINH T

    Thng k l mt Ngh thut v Khoa hc v:

    Thu thp

    3

    Phn tch

    Trnh by

    V gii thch D LIU

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 2

    THNG K V NG DNG TRONG THNG K V NG DNG TRONG KINH DOANH V KINH TKINH DOANH V KINH T

    ng dng trong kinh doanh v kinh t:

    Cc ng dng ca thng k rt hin nhin trong nhiu

    4

    lnh vc

    Thng k c s dng :

    Thng bo cho cng chng

    D bo cho vic lp k hoch v ra quyt nh

    THNG K V NG DNG TRONG THNG K V NG DNG TRONG KINH DOANH V KINH TKINH DOANH V KINH T

    ng dng trong kinh doanh v kinh t:

    Cc lnh vc kinh doanh v kinh t da trn cc k thut v thng tin thng k:

    5

    k thut v thng tin thng k:

    K ton

    Ti chnh

    Tip th

    Sn xut

    Kinh t

    THNG K V NG DNG TRONG THNG K V NG DNG TRONG KINH DOANH V KINH TKINH DOANH V KINH T

    Cc phn mm thng k so vi Excel

    Cc phn mm thng k thng l Hp en MINITABMINITAB: l mt phn mm thng k c ngun gc

    6

    c thit k ti i hc Penn State c bit dnh cho sinh vin.

    SAS: SAS: Statistical Analysis System H thng phn tch thng k

    SPSS: SPSS: Statistical Package for the Social Science Phn mm thng k cho khoa hc x hi

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 3

    THNG K V NG DNG TRONG THNG K V NG DNG TRONG KINH DOANH V KINH TKINH DOANH V KINH TCc phn mm thng k so vi Excel

    S dng Excel phn tch thng k bi v: Excel sn c cc vn phng

    Excel mnh gii quyt cc vn thng k thng

    7

    Excel mnh gii quyt cc vn thng k thng gp

    Ngi s dng c th hiu c ngha ca cc vn thng k

    Cc nh qun l v ra quyt nh thnh cng l nhng ngi c th hiu v s dng cc thng tin mt cch hiu qu nht

    D LIUD LIU

    D liu D liu l cc s kin v con s c thu thp, phn

    tch v tng kt trnh by v gii thch

    8

    Tp d liu l tt c cc d liu c thu thp cho mt nghin cu c th

    Thang o D liu nh tnh so vi nh lng D liu cho so vi chui thi gian

    D LIUD LIU

    Cc phn t, cc bin v cc quan st Phn t l tan b thc th da vo d liu c thu

    thp

    9

    Bin l cc c tnh c quan tm i vi cc phn t

    Quan st l tp cc i lng o lng c thu thp

    i vi mt phn t c th

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 4

    D LIUD LIU

    VariablesVariablesStockStock Annual Earn/Annual Earn/

    CompanyCompany Exchange Sales($M) Sh.($)Exchange Sales($M) Sh.($)

    DataramDataram AMEXAMEX 73.1073.10 0.860.86

    10

    ElementsElements Data SetData Set DatumDatum

    EnergySouthEnergySouth OTCOTC 74.0074.00 1.671.67KeystoneKeystone NYSENYSE 365.70365.70 0.86 0.86 LandCareLandCare NYSENYSE 111.40111.40 0.330.33PsychemedicsPsychemedics AMEXAMEX 17.6017.60 0.130.13

    Cu hi?Cu hi?

    Tham kho Bng 1.1:B D LIU CA 5 LAI CHNG KHAN:

    11

    C bao nhiu phn t trong b d liu ny ? C bao nhiu bin trong b d liu ny? C bao nhiu quan st trong b d liu ny? C bao nhiu s lng d liu trong b d liu

    ny?

    D LIUD LIU

    Thang o Xc nh lng thng tin c trong d liu v ch ra s tng kt d liu v phn tch thng k no l thch hp nht

    12

    Thang o ch danh

    Thang o th t

    Thang o khong

    Thang o t l

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 5

    D LIUD LIU Thang o ch danh

    S dng nhn hiu hoc tn nhn dng mt thuc tnh ca phn t bng s hoc khng bng s

    Thang o th tC c tnh ca thang o ch danh v c th dng sp hng hoc th t d liu bng s hoc khng bng sTh kh

    13

    Thang o khongC c tnh ca thang o th t v khong cch gia cc quan st c din t di dng cc n v o lng c nh lun lun bng s

    Thang o t lC c tnh ca thang o khong v t l ca 2 gi tr l c ngha lun lun bng s(Cha gi tr Zero C ngha l khng c g)

    D LIUD LIU

    D liu nh tnh so vi nh lng

    D liu nh tnh

    D liu nh tnh l cc nhn hiu hay tn c dng

    14

    D liu nh tnh l cc nhn hiu hay tn c dng

    nhn dng v c trng cho mi phn t

    BIn nh tnh l bin vi d liu nh tnh

    D liu nh tnh s dng thang o ch danh hoc thang

    o th t; c th o bng s hoc khng bng s

    D LIUD LIU

    D liu nh tnh so vi nh lng

    D liu nh lng

    15

    D liu nh lng l d liu cho bit s lng bao nhiu

    ca mt i lng no

    Bin nh lng l bin vi d liu nh lng

    D liu nh tnh s dng thang o khong hoc thang o

    t l; lun o bng s

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 6

    D LIUD LIU

    D liu nh tnh so vi nh lng

    S khc nhau gia d liu nh lng v nh

    16

    tnh Cc php tnh s hc thng thng ch c ngha i vi

    d liu nh lng

    Tuy nhin, khi d liu nh tnh c ghi nhn nh cc gi tr bng s th cc php tnh s hc s cho ra cc kt qu khng c ngha

    Cu hi ?Cu hi ?

    Hy pht biu xem cc bin sau y bin no l bin nh tnh, bin no l bin nh lung v hy ch ra thang o thch hp cho mi bin.

    T i

    17

    Tui Gii tnh Th hng trong lp Nhit Thu nhp

    D LIUD LIU

    D liu cho v d liu chui thi gian

    D liu cho l cc d liu c thu thp trong cng

    18

    p g g

    hay gn cng mt thi im

    D liu chui thi gian l cc d liu c thu thp

    trong cc thi im lin tip nhau

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 7

    NGUN D LIU NGUN D LIU

    Ngun d liu c th thu thp t:

    Cc ngun hin c:

    19

    Internet tr thnh mt ngun d liu quan trng

    Cc nghin cu thng k:

    Nghin cu th nghim

    Nghin cu quan st

    NGUN D LIUNGUN D LIU

    Cc sai s ca thu thp d liu Mt sai s trong thu thp d liu xy ra khi gi tr ca d

    liu thu thp c khng bng vi gi ng/thc c

    20

    c t mt qui trnh thu thp ng

    S dng d liu sai c th xu hn khng s dng bt k d liu no

    GIGO Garbage In Garbage Out Rc vo Rc Ra

    THNG K M TTHNG K M T

    Thng k m t: Thu thp, Tng kt v M t d liu

    Cc phng php c s dng tng kt d liu:

    Lp Bng

    21

    Lp Bng

    Th

    Bng s

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 8

    THNG K M TTHNG K M T

    Thng k m t:

    Cc tham s thng k

    22

    g

    Tn s

    Phn phi xc sut

    THNG K SUY DINTHNG K SUY DIN

    Tng th l tp tt c cc phn t cn quantm trong mt nghin cu c th

    Mu l mt tp con ca tng th

    23

    p g

    Thng k suy din: l qu trnh s dng dliu thu thp c t mu c lng hockim nh cc gi thuyt thng k v cc ctrng ca tng th

    THNG K SUY DINTHNG K SUY DIN

    Ly MuLy Mu

    24

    Tng thTng thNN

    MuMunn

    c Lngc LngKim nh gi thuytKim nh gi thuyt

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 9

    CHNG 2CHNG 2

    TRNH BY TRNH BY

    25

    BNG BNG v BIU BNG BNG v BIU

    NI DUNG CHNHNI DUNG CHNH

    Tng kt d liu nh tnh

    Tng kt d liu nh lng

    26

    Phn tch d liu khm ph: Trnh by dng

    cnh v l

    th phn tn im v bng cho

    TNG KT D LIU NH TNH TNG KT D LIU NH TNH

    Phn phi tn sPhn phi tn s l mt bng tng kt mt tp d

    liu trong trnh by tn s (hay s) ca cc gi tr

    27

    g y ( y ) g

    quan st c trong mi lp ca cc lp khng trng

    ln nhau

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 10

    TNG KT D LIU NH TNHTNG KT D LIU NH TNHD LIU T MT MU GM 50 LON NC GII KHT

    Coke Classic Sprite Pepsi-ColaDiet Coke Coke Classic Coke ClassicPepsi-Cola Diet Coke Coke ClassicDiet Coke Coke Classic Coke ClassicCoke Classic Diet Coke Pepsi-ColaCoke Classic Coke Classic Dr Pepper

    28

    Coke Classic Coke Classic Dr.PepperDr.Pepper Sprite Coke ClassicDiet Coke Pepsi-Cola Diet CokePepsi-Cola Coke Classic Pepsi-ColaPepsi-Cola Coke Classic Pepsi-ColaCoke Classic Coke Classic Pepsi-ColaDr.Pepper Pepsi-Cola Pepsi-ColaSprite Coke Classic Coke ClassicCoke Classic Sprite Dr.PepperDiet Coke Dr.Pepper Pepsi-ColaCoke Classic Pepsi-Cola SpriteCoke Classic Diet Coke

    TNG KT D LIU NH TNHTNG KT D LIU NH TNH

    PHN PHI TN SCA LON NC GII KHT

    Nc gii kht Tn s

    29

    Nc gii kht Tn sCoke Classic 19Diet Coke 8Dr.Pepper 5Pepsi-Cola 13Sprite 5Tng 50

    TNG KT D LIU NH TNHTNG KT D LIU NH TNH

    Phn phi tn s tng i v tn s phn trm Phn phi tn s tng i: Mt bng tng kt tp

    t d li t t h b t t i h

    30

    mt d liu trong trnh by tn s tng i ngha l, t s ca tng s cc gi tr quan st c trong mi lp ca cc lp khng trng ln nhau

    Tn s tng i ca 1 lp = Tn s ca 1 lp / n

    Tn s phn trm = Tn s tng i* 100

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 11

    TNG KT D LIU NH TNHTNG KT D LIU NH TNH

    Phn phi tn s tng i v tn s phn trm

    31

    Phn phi tn s tng i: Mt bng tng kt tp

    mt d liu trong trnh by phn trm ca tng s

    cc gi tr quan st c trong mi lp ca cc lp

    khng trng ln nhau

    TNG KT D LIU NH TNHTNG KT D LIU NH TNH

    PHN PHI TN S TNG I v PHN TRMCA LON NC GII KHT

    Nc gii kht Tn s tng i Tn s phn trm

    32

    Nc gii kht Tn s tng i Tn s phn trmCoke Classic .38 38Diet Coke .16 16Dr.Pepper .10 10Peppsi-Cola .26 26Sprite .10 10

    Tng 1.00 100

    TNG KT D LIU NH TNHTNG KT D LIU NH TNHBiu hnh thanh v biu hnh trnBIU HNH THANH CA NC GII KHT

    1820

    33

    02468

    1012141618

    CokeClassic

    Diet Coke Dr. Pepper Pepsi- Cola Sprite

    Nc gii kht

    Tn

    s

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 12

    TNG KT D LIU NH TNHTNG KT D LIU NH TNH

    Biu hnh thanh v biu hnh trn

    BIU HNH TRN CA NC GII KHT

    34

    Coke Classic

    38%

    Diet Coke16%

    Dr. Pepper10%

    Pepsi- Cola26%

    Sprite10%

    TNG KT D LIU NH LNGTNG KT D LIU NH LNG

    Phn phi tn sPhn phi tn s l mt bng tng kt mt tp d

    liu trong trnh by tn s (hay s) ca cc gi tr

    35

    g y ( y ) g

    quan st c trong mi lp ca cc lp khng trng

    ln nhau

    TNG KT D LIU NH LNGTNG KT D LIU NH LNG

    Phn phi tn s Xy dng mt phn phi tn s

    Thu thp d liu mu

    36

    Xc nh s lp khng trng lp

    Xc nh chiu rng ca mi lp

    Xc nh cc gii hn ca mi lp

    m s cc gi tr d liu c trong mi lp

    Tng kt cc tn s ca lp vo trong mt bng phn phi tn s

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 13

    TNG KT D LIU NH LNGTNG KT D LIU NH LNGPhn phi tn s S lp (K): 5 K 20 Chiu rng lp

    Chiu rng lp = (Gi tr ln nht Gi tr nh nht) / K

    37

    Cc gii hn ca lpCc gii hn ca lp l s ln nht v nh nht thuc v lp

    Gii hn di ca lp = S nh nht

    Gii hn trn ca lp = S ln nht

    S khc bit gia gii hn di ca cc lp lin nhau s cho ta chiu rng ca lp

    TNG KT D LIU NH LNGTNG KT D LIU NH LNG

    Phn phi tn s Cc bin gii ca lp

    Cc bin ca lp l cc ng phn chia gia cc

    38

    Cc bin ca lp l cc ng phn chia gia cc

    lp

    im gia ca lp

    im gia ca lp l gi tr nm gia cc gii

    hn di v gii hn trn ca lp

    TNG KT D LIU NH LNGTNG KT D LIU NH LNG

    CC THI GIAN KIM TON CUI NM(Tnh theo s ngy)

    39

    12 14 19 1815 15 18 1720 27 22 2322 21 33 2814 18 16 13

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 14

    TNG KT D LIU NH LNGTNG KT D LIU NH LNG

    PHN PHI TN S I VI D LIU THI GIAN KIM TAN

    Thi gian kim tan Tn s

    40

    g(ngy)10-14 415-19 820-24 525-29 230-34 1Tng 20

    TNG KT D LIU NH LNGTNG KT D LIU NH LNG

    Phn phi tn s tng i v tn s phn trm

    41

    Tn s tng i ca 1 lp = Tn s ca 1 lp / n

    Tn s phn trm = Tn s tng i* 100

    TNG KT D LIU NH LNGTNG KT D LIU NH LNG

    PHN PHI TN S TNG I V TN S PHN TRM

    I VI D LIU THI GIAN KIM TAN

    Thi i T t i T h t

    42

    Thi gian Tn s tng i Tn s phn trm(ngy)10-14 .20 2015-19 .40 4020-24 .25 2525-29 .10 1030-34 .05 5Tng 1.00 100

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 15

    TNG KT D LIU NH LNGTNG KT D LIU NH LNG

    Biu im

    Trc honh trnh by min cc gi tr ca d liu.

    43

    Mi gi tr c biu th bng mt im nm trn trc

    01234

    10 15 20 25 30 35

    Thi gian kim tan tnh theo ngy

    TNG KT D LIU NH LNGTNG KT D LIU NH LNG

    Biu tn s

    Mt biu tn s c xy dng bng t cc

    44

    bin quan tm trn trc honh v tn s, tn s

    tng i, tn s phn trm trn trc tung

    Biu tn s m t dng ca tp d liu

    TNG KT D LIU NH LNGTNG KT D LIU NH LNG

    6789

    45

    0

    1

    2

    3

    4

    0 5 10 15 20 25 30 35

    012345

    5 10 15 20 25 30 35Thi gian kim tan tnh theo ngy

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 16

    TNG KT D LIU NH LNGTNG KT D LIU NH LNG

    Cc phn phi tch ly

    Phn phi tn s tch ly trnh by s cc quan

    46

    st c gi tr nh hn hoc bng gii hn trn

    ca lp ca mi lp

    TNG KT D LIU NH LNGTNG KT D LIU NH LNG

    CC PHN PHI TN S TCH LY, TN S TNG I TCH LY V TN S PHN TRM TCH LY

    I VI D LIU THI GIAN KIM TAN

    Thi gian (ngy) Tn s Tn s tng i Tn s %Tch ly Tch ly Tch ly

    47

    Tch ly Tch ly Tch ly

    Nh hn hoc bng 14 4 .20 20Nh hn hoc bng 19 12 .60 60Nh hn hoc bng 24 17 .85 85Nh hn hoc bng 29 19 .95 95Nh hn hoc bng 34 20 1.00 100

    TNG KT D LIU NH LNGTNG KT D LIU NH LNG

    OgiveOgive l th ca phn phi tch ly

    25

    48

    0

    5

    10

    15

    20

    5 10 15 20 25 30 35

    Thi gian kim tan tnh theo ngy

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 17

    PHN TCH D LIU KHM PH: PHN TCH D LIU KHM PH: TRNH BY DNG CNH V LTRNH BY DNG CNH V L

    Trnh by dng cnh v l: Mt k thut phn

    tch khm ph theo sp hng cc th t ca

    49

    tch khm ph theo sp hng cc th t ca

    d liu nh lng v cho thy su sc v dng

    ca phn phi cng mt lc

    PHN TCH D LIU KHM PH: PHN TCH D LIU KHM PH: TRNH BY DNG CNH V LTRNH BY DNG CNH V L

    S CU HI C TR LI NG K THI NNG KHIU

    112 72 69 97 10773 92 76 86 73

    50

    126 128 118 127 12482 104 132 134 8392 108 96 100 92115 76 91 102 8195 141 81 80 10684 119 113 98 7538 98 115 106 95100 85 94 106 119

    PHN TCH D LIU KHM PH: PHN TCH D LIU KHM PH: TRNH BY DNG CNH V LTRNH BY DNG CNH V L

    6 8 9

    7 2 3 3 5 6 6

    8 0 1 1 2 3 4 5 6

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

    51

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

    10 0 0 2 4 6 6 6 7 8

    11 2 3 5 5 8 9 9

    12 4 6 7 8

    13 2 4

    14 1

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 18

    TH PHN TN IM TH PHN TN IM v BNG CHOv BNG CHO

    Bng cho Bng cho l mt tng kt di dng bng ca d

    liu gm 2 bin. Cc gi tr ca mt bin c trnh

    52

    liu gm 2 bin. Cc gi tr ca mt bin c trnh

    by theo cc hng. Cc gi tr ca mt bin khc

    c trnh by theo cc ct

    Bng cho c s dng rng ri trong vic xem xt

    mi quan h gia hai bin

    TH PHN TN IM TH PHN TN IM v BNG CHOv BNG CHO

    BNG CHO V NH GI CHT LNG V GI CA CC BA N TI 300 NH HNG LOS-ANGELES

    Gi ba n

    53

    Gi ba nCht lng $10-19 $20-29 $30-39 $40-49 TngTt 42 40 2 0 84Rt tt 34 64 46 6 150Xut sc 2 14 28 22 66Tng 78 118 76 28 300

    TH PHN TN IM TH PHN TN IM v BNG CHOv BNG CHO

    PHN TRM TNH THEO HNG I VI MI LOI CHT LUNG

    Gi ba nCht lng $10 19 $20 29 $30 39 $40 49 Tng

    54

    Cht lng $10-19 $20-29 $30-39 $40-49 TngTt 50.0 47.6 2.4 0.0 100Rt tt 22.7 42.7 30.6 4.0 100Xut sc 3.0 21.2 42.4 33.4 100

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 19

    TH PHN TN IM TH PHN TN IM v BNG CHOv BNG CHO

    th phn tn im v ng xu hng

    Mt th phn tn im l mt trnh by di dng th i h h i bi Mt bi

    55

    th v mi quan h ca hai bin. Mt bin c trnh by trn trc honh v bin khc c trnh by trn trc tung

    Mt ng xu hng l mt ng cho thy mt cch gn ng mi quan h gia hai bin

    TH PHN TN IM TH PHN TN IM v BNG CHOv BNG CHO

    D LIU MU I VI CA HNG THIT B STEREO V M THANHTun S thng v Doanhs ($100s)

    x y1 2 50

    56

    1 2 502 5 573 1 414 3 545 4 546 1 387 5 638 3 489 4 5910 2 46

    TH PHN TN IM TH PHN TN IM v BNG CHOv BNG CHO

    th phn tn im th phn tn im i vi ca hn thit b Stereo v m thanh

    60

    65

    57

    35

    40

    45

    50

    55

    60

    0 1 2 3 4 5 6

    Sales ($100s)

    Number of commercials

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 20

    TH PHN TN IM TH PHN TN IM v BNG CHOv BNG CHO

    th phn tn im Cc loi quan h c miu t bng th phn tn im

    58

    Quan h ng bin Dng nh khng quan h Quan h nghch bin

    CC QUI TRNH BNG BIU V TH CC QUI TRNH BNG BIU V TH I VI TNG KT D LIU I VI TNG KT D LIU

    D LIU

    D liu nh tnh

    D liu nh lng

    59

    Phng php Bng

    Phng php th

    Phng php Bng

    Phng php th

    Phn phi tn s

    Phn phi tn s tng i

    Phn phi tn s phn trm

    Bng cho

    Biu hnh thanh

    Biu hnh trn

    Phn phi tn s

    Phn phi tn s tng i

    Phn phi tn s tch ly

    Phn phi tn s tng i tch ly

    Cnh v l - Bng cho

    Biu im

    Biu tn s

    Biu tn s tch ly (Ogive)

    th phn tn im

    CHNG 3CHNG 3

    CC I LNGCC I LNG

    60

    CC I LNGCC I LNG

    BNG SBNG S

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 21

    CC NI DUNG CHNHCC NI DUNG CHNH

    Gii thiu i lng v v tr i lng v s bin thin

    61

    i lng v dng phn phi, v tr tng i v nhn dng cc im c bit

    Phn tch d liu khm ph i lng v s lin h gia 2 bin Trung bnh c trng s v x l d liu nhm

    GII THIUGII THIU

    Mt i lng m t l mt con s n gin

    c tnh ton t d liu mu cung cp thng

    62

    tin v d liu tng th

    C hai loi i lng m t:

    i lng v v tr

    i lng v s bin thin

    GII THIUGII THIU

    Tham s ca tng th (population parameter) l mt gi tr bng s c dng nh mt i lng tng kt i vi mt d liu ca tng th

    63

    lng tng kt i vi mt d liu ca tng th

    Cc tr thng k ca mu (sample statistics) c dng nh mt i lng tng kt i vi mt mu

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 22

    CC I LNG V V TR CC I LNG V V TR (measure of location)(measure of location)

    Mt s cc i lng v v tr l: S trung bnh (Mean)

    S trung v (Median)

    64

    S trung v (Median)

    S yu v (Mode)

    S phn v (Percentiles)

    S t phn (Quartiles)

    CC I LNG V V TRCC I LNG V V TR

    S trung bnh S trung bnh c s dng ph bin nht o

    lng v tr

    65

    Trung bnh ca tng th:

    Trung bnh ca mu:

    Nx

    nx

    x

    CC I LNG V V TRCC I LNG V V TR

    S yu v (Md)

    S trung v l gi tr gia tp d liu c sp xp

    66

    theo th t

    n l s l, Md l gi tr gia tp d liu

    n l s chn, Md l trung bnh ca hai gi tr gia

    tp d liu

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 23

    CC I LNG V V TRCC I LNG V V TR

    S yu v (Mo)

    S yu v l gi tr d liu xut hin vi tn s

    67

    ln nht

    Bimodal c hai s yu v

    Multimodal > two hai s yu v

    CC I LNG V V TRCC I LNG V V TR

    S phn v

    S phn v pth l gi tr c t nht p % s hng ca

    68

    tp d liu c gi tr nh hn hoc bng gi tr ny,

    v c t nht (100-p) % s hng ca tp d liu c

    gi tr ln hn hoc bng gi tr ny

    Phn v 50th l s trung v

    CC I LNG V V TRCC I LNG V V TR

    S phn vXc nh phn v pth

    Bc 1: Sp xp tp d liu theo th t tng dn

    69

    Bc 1: Sp xp tp d liu theo th t tng dn

    Bc 2: tnh ch s i:

    Bc 3: Nu i khng l s nguyn lm trn ln trn. S

    nguyn k tip > i s ch v tr ca phn v pth.

    Nu i l s nguyn, phn v pth l trung bnh ca 2 gi tr d liu v tr i v i + 1

    n*i 100p

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 24

    CC I LNG V V TRCC I LNG V V TR

    S t phn

    S t phn ch n thun l cc s phn v c th, s

    70

    chia tp d liu ra lm 4 phn, c gi tn l:

    Q1 = s t phn th nht = P25%

    Q2 = s t phn th hai = P50% = Median

    Q3 = s t phn th ba = P75%

    CC I LNG V S BIN THINCC I LNG V S BIN THIN

    i lng v s bin thin c s dng m t xu hng ca cc gi tr d liu phn tnxung quanh gi tr trung bnh.Mt i l bi thi

    71

    Mt s i lng v s bin thin: Khong bin thin (Range) Khong bin thin ni t phn (Interquartile Range) Phng sai (Variance) lch chun (Standard Deviation) H s bin thin (Coefficient of variation)

    CC I LNG V S BIN THINCC I LNG V S BIN THIN

    Khong bin thin Range = Gi tr ln nht Gi tr nh nht

    hay Range = Max Min

    72

    Range Max Min

    Khong bin thin ni t phn (IQR) IQR = Q3 Q1

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 25

    CC I LNG V S BIN THINCC I LNG V S BIN THIN

    Phng sai

    Phng sai ca tng th:

    Nx 2i2

    73

    Phng sai ca mu:

    N

    1n

    xxs

    2i2

    CC I LNG V S BIN THINCC I LNG V S BIN THIN

    lch chun lch chun l cn bc hai ca phng sai. lch chun v phng sai c s dng ph bin o lng s bin thin

    74

    lng s bin thin

    H s bin thin

    22 ss

    100*XS100*

    MeanDeviation StandardCV

    CC I LNG V DNG PHN PHI, V TR CC I LNG V DNG PHN PHI, V TR TNG I V NHN DNG CC IM C BITTNG I V NHN DNG CC IM C BIT

    Dng phn phi lch (Skewness) l i lng v dng ca phn

    phi ca tp d liu

    75

    phi ca tp d liu i vi d liu lch v bn tri, lch s m i vi d liu lch v bn phi, lch s dng Nu d liu i xng, lch s bng 0

    i vi phn phi i xng, s trung bnh v s trung v s bng nhau

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 26

    CC I LNG V DNG PHN PHI, V TR CC I LNG V DNG PHN PHI, V TR TNG I V NHN DNG CC IM C BITTNG I V NHN DNG CC IM C BIT

    Tr thng k Z (Z-Scores)Tr thng k Z thng c gi l gi tr chun ha

    xxiZ

    76

    Zi: l s lch chun m Xi cch xa gi tr trungbnh

    si

    iZ

    CC I LNG V DNG PHN PHI, V TR CC I LNG V DNG PHN PHI, V TR TNG I V NHN DNG CC IM C BITTNG I V NHN DNG CC IM C BIT

    nh l Chebyshev

    nh l Chebyshev c s dng pht biu v phn

    77

    trm ca cc s hng s nm trong mt con s c th

    ca lch chun tnh t gi trung bnh

    CC I LNG V DNG PHN PHI, V TR CC I LNG V DNG PHN PHI, V TR TNG I V NHN DNG CC IM C BITTNG I V NHN DNG CC IM C BIT

    nh l Chebyshev

    Ti thiu (1-1/Z2) ca cc s hng c trong mi tp

    78

    ( ) g g

    d liu s phi nm trong Z lch chun tnh t

    s trung bnh, khi Z > 1.

    hay

    Prob 2z11zsxxzsx

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 27

    CC I LNG V DNG PHN PHI, V TR CC I LNG V DNG PHN PHI, V TR TNG I V NHN DNG CC IM C BITTNG I V NHN DNG CC IM C BIT

    nh l Chebyshev

    i vi mi tp d liu

    79

    p

    Prob

    Prob

    Prob

    %75 s2xx2s-x

    %89 s3xx3s-x

    %94 s4xx4s-x

    CC I LNG V DNG PHN PHI, V TR CC I LNG V DNG PHN PHI, V TR TNG I V NHN DNG CC IM C BITTNG I V NHN DNG CC IM C BIT

    Qui tc kinh nghim

    i vi mi tp d liu c phn phi dng hnh chung:

    80

    Prob

    Prob

    Prob

    %68 s1xx1s-x

    %95 s2xx2s-x

    %7.99 s3xx3s-x

    CC I LNG V DNG PHN PHI, V TR CC I LNG V DNG PHN PHI, V TR TNG I V NHN DNG CC IM C BITTNG I V NHN DNG CC IM C BIT

    MT PHN PHI DNG HNH CHUNG I XNG

    81

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 28

    CC I LNG V DNG PHN PHI, V TR CC I LNG V DNG PHN PHI, V TR TNG I V NHN DNG CC IM C BITTNG I V NHN DNG CC IM C BIT

    Nhn dng cc im c bit (outliers)

    Cc im c bit l cc gi tr thi cc (ln khc

    82

    thng hoc nh khc thng)

    S dng Z nhn dng im c bit: mi gi tr

    d liu vi Z nh hn 3 hoc ln hn +3 l im

    c bit

    PHN TCH D LIU KHM PHPHN TCH D LIU KHM PH

    M hnh 5-im Gi tr nh nht = Min

    S t phn th nht = Q1

    83

    1

    S t phn th hai = Q2 = Median

    S t phn th ba = Q3 Gi tr ln nht = Max

    Mt cch gn ng, 25% ca cc gi tr d liu gia cc s k nhau trong m hnh 5-im

    PHN TCH D LIU KHM PHPHN TCH D LIU KHM PH

    Biu hp (Box plot):

    Biu hp l tng kt d liu bng th

    84

    Biu hp l tng kt d liu bng th

    Outliers

    Whiskers

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 29

    PHN TCH D LIU KHM PHPHN TCH D LIU KHM PH

    Upper Limit Lower Limit Median Q1 Q3

    85

    0

    1

    2

    3

    4

    1900 2000 2100 2200 2300 2400 2500 2600 2700 2800 2900

    *

    Outlier

    IQR1.5(IQR) 1.5(IQR)

    I LNG V S LIN H I LNG V S LIN H GIA 2 BINGIA 2 BIN

    ng phng sai (Covariance) ng phong sai o lng s lin h tuyn tnh gia 2

    bin.

    86

    ng phng sai ca tng th:

    ng phng sai ca mu:

    N

    yx yixixy

    1nyyxx

    s iixy

    I LNG V S LIN H I LNG V S LIN H GIA 2 BINGIA 2 BIN

    ng phng sai

    sxy > 0 Quan h ng bin

    87

    sxy < 0 Quan h nghch bin

    Gi tr ca ng phng sai ph thuc n v o

    lng ca x v y

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 30

    I LNG V S LIN H I LNG V S LIN H GIA 2 BINGIA 2 BIN

    60

    65

    III . .0s) = 3x

    TH PHN TN IM C PHN CHIA

    I VI C HNG THIT B STEREO V M THANH

    88

    35

    4045

    50

    55

    0 1 2 3 4 5 6

    IVIII

    ....

    ...

    S thng v

    Doa

    nh s

    ($10

    0

    = 51y

    I LNG V S LIN H I LNG V S LIN H GIA 2 BINGIA 2 BIN

    . .yGII THCH V NG PHNG SAI CA MU

    89

    ....

    ....

    .

    .

    Sxy dng:(x v y c quan h tuyn

    tnh ng bin ) x

    I LNG V S LIN H I LNG V S LIN H GIA 2 BINGIA 2 BIN

    .Sxy gn bng 0:(x v y khng c quan h yGII THCH V NG PHNG SAI CA MU

    90

    . .. ..

    . .

    . ..

    ..

    . . . .

    (x v y khng c quan h tuyn tnh )

    x

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 31

    I LNG V S LIN H I LNG V S LIN H GIA 2 BINGIA 2 BIN

    y

    GII THCH V NG PHNG SAI CA MU

    ....Sxy m:(x v y c quan h tuyn

    91

    x

    ....

    . ..

    .

    (x v y c quan h tuyn tnh nghch bin )

    I LNG V S LIN H I LNG V S LIN H GIA 2 BINGIA 2 BIN

    H s tng quan (Correlation Coefficient) Mt i lng bng s o lng mi quan h

    tuyn tnh gia 2 bin H s tng quan Pearson

    92

    H s tng quan Pearson

    Tng th: Mu: yx

    xyxy

    yx

    xyxy ss

    sr

    2i

    2i

    iixy

    yyxx

    yyxxrr

    I LNG V S LIN H I LNG V S LIN H GIA 2 BINGIA 2 BIN

    H s tng quanCc tnh cht quan trng ca r: -1 r 1

    93

    r cng ln th mi quan h tuyn tnh cng mnh.

    r = 0 -> khng c quan h tuyn tnh gia X vY

    r = 1 hoc r = -1 X v Y tng quan tuyn tnh hon ton

    Du ca r cho thy mi quan h gia X v Y l ng bin hay nghch bin

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 32

    I LNG V S LIN H I LNG V S LIN H GIA 2 BINGIA 2 BIN

    25

    30

    35

    dred

    s)

    ..

    . .y

    25

    30

    35

    dred

    s)

    ..

    . .y

    94

    0

    5

    10

    15

    20

    25

    10 20 30 40 50 60 70

    Income (thousand)

    Squa

    re fo

    otag

    e (h

    und

    . ..

    . ..

    .

    x0

    5

    10

    15

    20

    25

    10 20 30 40 50 60 70

    Income (thousand)

    Squa

    re fo

    otag

    e (h

    und

    . ..

    . ..

    .

    x

    I LNG V S LIN H I LNG V S LIN H GIA 2 BINGIA 2 BIN

    . ..... .

    ..

    . .

    y y y

    th phn tn im i vi cc gi tr r khc nhau

    95

    .

    .

    ... . .

    .... .. .

    ..

    .. . . .

    . .x x xr = 0 r = 1 r = -1

    I LNG V S LIN H I LNG V S LIN H GIA 2 BINGIA 2 BIN

    yy y

    th phn tn im i vi cc gi tr r khc nhau

    96

    ... .

    . .. . . .

    . ... .

    ... ..

    ... .

    .

    .. .

    ... .

    . . .....

    . .

    y

    x

    y

    x

    y

    xr = .5r = -.8r = 0.9

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 33

    TRUNG BNH C TRNG S V TRUNG BNH C TRNG S V X L D LIU NHMX L D LIU NHM

    Trung bnh c trng s (The weighted Mean)

    Trung bnh ca tp d liu c c bng cch

    97

    gn mi gi tr d liu mt trng s phn nh

    tm quan trng ca n trong tp d liu

    i

    ii

    wx*w

    x

    TRUNG BNH C TRNG S V TRUNG BNH C TRNG S V X L D LIU NHMX L D LIU NHM

    D liu nhm (Grouped data)

    D liu c sn trong cc lp c tng kt bng

    98

    D liu c sn trong cc lp c tng kt bng

    phn phi tn s. Cc gi tr ring ca tp d liu gc

    s khng c ghi nhn

    TRUNG BNH C TRNG S V TRUNG BNH C TRNG S V X L D LIU NHMX L D LIU NHM

    D liu nhm

    Trung bnh ca d liu nhm

    99

    Tng th

    Mu

    NM*f ii

    nM*f

    x ii

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 34

    TRUNG BNH C TRNG S V TRUNG BNH C TRNG S V X L D LIU NHMX L D LIU NHM

    D liu nhm

    Phng sai ca d liu nhm

    100

    Tng th

    Mu

    NM*f 2ii2

    1n

    xM*fs

    2ii2

    CHNG 4CHNG 4

    GII THIU GII THIU

    101

    vvXC SUTXC SUT

    NI DUNG CHNHNI DUNG CHNH

    Th nghim, qui tc m v xc nh xc sut Bin c v xc sut ca bin c Mt s mi quan h cn bn ca xc sut

    102

    Xc sut c iu kin nh l Bayes

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 35

    TH NGHIM, QUI TC M v TH NGHIM, QUI TC M v XC NH XC SUTXC NH XC SUT

    Th nghim (Experiment) Th nghim l mi qu trnh to ra kt qu c nh ngha r rng

    103

    Khng gian mu (Sample space) im ca mu l mt kt qu c th ca mt th

    nghim

    Khng gian mu l tp hp ca tt c cc im c th c ca mu (cc kt qu ca th nghim)

    TH NGHIM, QUI TC M v TH NGHIM, QUI TC M v XC NH XC SUTXC NH XC SUT

    Qui tc m S cy l mt phng tin th rt hu ch trong

    vic xc nh cc im ca mu ca mt th nghim c lin quan n nhiu bc.

    104

    Qui tc m i vi th nghim nhiu bc

    S kt qu ca th nghim = (n1)x(n2)x.. x(nk) Qui tc m i vi t hp

    S t hp ca N phn t c chn n trong mt ln l:

    !nN!n!N

    nN

    TH NGHIM, QUI TC M v TH NGHIM, QUI TC M v XC NH XC SUTXC NH XC SUT

    Yu cu cn bn ca xc sutGi Ei l kt qu ca th nghim 0 P(Ei) 1

    105

    P(Ei) = 1

    Cc phng php xc nh xc sut Phng php c in Phng php tn s tng i Phng php ch quan

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 36

    TH NGHIM, QUI TC M v TH NGHIM, QUI TC M v XC NH XC SUTXC NH XC SUT

    Phng php c in

    Mt phng php xc nh xc sut thch hp khi tt c cc

    kt qu ca th nghim c cng kh nng xy ra

    106

    Phng php tn s tng i

    Mt phng php xc nh xc sut thch hp khi c sn

    d liu (d liu lch s) c lng t l ca s ln kt

    qu th nghim s xy ra nu th nghim c lp li vi

    mt s ln ln

    TH NGHIM, QUI TC M v TH NGHIM, QUI TC M v XC NH XC SUTXC NH XC SUT

    Phng php ch quan

    Mt phng php xc nh xc sut da trn c s

    h

    107

    phn on

    Mt xc sut ch quan l mt mc tin tng ca c

    nhn i vi vic xy ra mt kt qu ca th nghim

    BIN C v BIN C v XC SUT CA BIN CXC SUT CA BIN C

    Bin cMt bin c l mt tp hp ca cc kt qu ca th nghim

    108

    g

    Xc sut ca bin cXc sut ca mt bin c bt k s bng vi tngcc xc sut ca cc kt qu ca th nghim

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 37

    MT S MI QUAN H CN BN MT S MI QUAN H CN BN CA XC SUTCA XC SUT

    Phn b/ph ca bin c

    Phn ph ca bin c A l bin c cha tt c kt

    qu ca mu m khng thuc v A

    109

    qu ca mu m khng thuc v A

    P(A) = 1 P(Ac)

    Bin c Bin c AA AAcc

    Khng gian mu SKhng gian mu S

    MT S MI QUAN H CN BN MT S MI QUAN H CN BN CA XC SUTCA XC SUT

    BIn c HI ca 2 bin c: A BA B l bin c cha tt c cc kt qu ca th nghim thuc A hoc B, hoc c hai

    110

    Bin c Bin c AA Bin cBin cBB

    Khng gian mu SKhng gian mu S

    MT S MI QUAN H CN BN MT S MI QUAN H CN BN CA XC SUTCA XC SUT

    Bin c GIAO ca 2 bin c: A B A B l bin c cha tt c cc kt qu ca th nghim thuc A v B

    Khng gian mu SKhng gian mu S

    111

    Phn giaoPhn giao

    Bin c Bin c AA Bin c Bin c BB

    Khng gian mu SKhng gian mu S

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 38

    MT S MI QUAN H CN BN MT S MI QUAN H CN BN CA XC SUTCA XC SUT

    Php cng xc sut P(A B) = P(A) + P(B) P(A B) BIn c cch bit

    112

    Hai bin c dc gi l cch bit nu hai bin c khng c cc im phn giao.

    A v B l hai bin c cch bit: P(A B) = 0

    Php cng xc sut i vi hai bin c cch bit

    P(A B) = P(A) + P(B)

    XC SUT C IU KINXC SUT C IU KIN

    Xc sut c iu kin

    hay

    )B(PBAP)B\A(P

    BAP

    113

    Cc bin c c lpNu A v B l hai bin c c lp th:

    P(A\B) = P(A) hay P(B\A) = P(B)

    )A(PBAP)A\B(P

    XC SUT C IU KINXC SUT C IU KIN

    Php nhn xc sut

    P(A B) = P(B). P(A\B) = P(A). P(B\A)

    114

    Php nhn xc sut i vi hai bin c c lp

    P(A B) = P(A). P(B)

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 39

    NH L BAYESNH L BAYES

    Cc xc sut tin nghim: Cc c lng ban u v xc sut ca cc bin c

    Xc sut hu nghim: Cc xc sut c sa li

    115

    g ca cc bin c da trn cc thng tin b sung

    nh l Bayes

    )B(P)BA(P

    )A\B(P)A(P)A\B(P)A(P)A\B(P)A(P)B\A(P 1

    2211

    111

    CHNG 5CHNG 5

    PHN PHI XC SUTPHN PHI XC SUT

    116

    PHN PHI XC SUTPHN PHI XC SUTRI RCRI RC

    NI DUNG CHNHNI DUNG CHNH

    Cc bin ngu nhin

    Cc phn phi xc sut ri rc

    117

    Gi tr k vng v phng sai ca bin ri rc

    Phn phi xc sut nh thc

    Phn phi xc sut Poisson

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 40

    BIN NGU NHINBIN NGU NHIN

    Bin ngu nhin

    Mt bin ngu nhin l mt m t bng s ca kt qu ca th nghim

    118

    q g

    Bin ngu nhin ri rc

    Mt bin ngu nhin ri rc c th nhn mt s m c ca cc gi tr trong mt khong

    BIN NGU NHINBIN NGU NHIN

    Bin ngu nhin lin tc

    Mt bin ngu nhin lin tc c gi nh c th nhn mi gi tr trong mt khong

    119

    th nhn mi gi tr trong mt khong

    Mi gi tr c th c trong khong ny

    2 3 4 5 6 7 8 X

    X: height, in feet

    PHN PHI XC SUT RI RCPHN PHI XC SUT RI RC

    Phn phi xc sut i vi mt bin ngu nhin s m t lm th no cc xc sut c phn phi theo cc gi tr ca bin ngu nhin

    120

    Mt phn phi xc sut i vi mt bin ngu nhin ri rc X l mt danh sch cc gi tr c th c ca bin X v cc xc sut tng ng

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 41

    PHN PHI XC SUT RI RCPHN PHI XC SUT RI RC

    Mt phn phi xc sut c th c trnh by di dng: Bng th ( th t )

    121

    th ( th tn s) Cng thc (Hm s)

    x 1 2 3 4 5 6P (x) 1/6 1/6 1/6 1/6 1/6 1/6

    1 2 3 4 5 6

    1/6X

    c sut

    PHN PHI XC SUT RI RCPHN PHI XC SUT RI RC

    Hm xc sut ri rc f(x) l mt hm xc nh xc sut i vi mi gi tr ca bin X

    f(x) = Prob (X=x)

    122

    Cc iu kin yu cu i vi hm xc sut ri rc

    0 f(x) 1

    f(x) = 1

    PHN PHI XC SUT RI RCPHN PHI XC SUT RI RC

    Hm phn phi xc sut ri rc u

    f(x) = 1/n

    123

    n = s cc gi tr c th c ca bin ngu nhin ri rc

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 42

    GI TR K VNG v PHNG SAI GI TR K VNG v PHNG SAI ca BIN NGU NHIN RI RCca BIN NGU NHIN RI RC

    Gi tr k vngE (x) = = x * f(x)

    Phng sai

    124

    Var (x) = 2 = (x - )2 * f(x)or

    2 = x2 * f(x) - 2

    lch chun

    2

    PHN PHI XC SUT NH THCPHN PHI XC SUT NH THC

    Mt th nghim nh thcMt th nghim nh thc c 4 tnh cht:

    Th nghim gm c mt chui n ln th tng t

    125

    Hai kt qu c th c cho mi ln th: thnh cng v tht bi

    Xc sut ca thnh cng, p, khng thay i ln th ny sang ln th khc. V vy, xc sut ca tht bi, 1-p, khng thay i ln th ny sang ln th khc

    Cc ln th c lp vi nhau

    PHN PHI XC SUT NH THCPHN PHI XC SUT NH THC

    Hm xc sut nh thc

    xnx p1pxn

    )x(f

    126

    Gi tr k vng v phng sai ca phn phi xc sut nh thc

    Gi tr k vng: E(x) = = np

    Phng sai: 2 = np (1-p)

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 43

    PHN PHI XC SUT POISSONPHN PHI XC SUT POISSON

    Cc tnh cht ca Th nghim Poisson

    Xc sut ca mt s kin s ging nhau cho bt k

    2 kh di

    127

    2 khong c cng di

    Vic xy ra hay khng xy ra trong 1 khong bt k

    s c lp vi vic xy ra hay khng xy ra trong 1

    khong bt k khc

    PHN PHI XC SUT POISSONPHN PHI XC SUT POISSON

    Hm xc sut Poisson

    = Gi tr k vng hay s trung bnh ca s kin trong

    !xe)x(f

    x

    128

    g y g gmt khong.

    Gi tr k vng v phng sai ca phn phi xc sut Poisson Gi tr k vng: E(x) =

    Phng sai: Var(x) =

    CHNG 6CHNG 6

    PHN PHI XC SUTPHN PHI XC SUT

    129

    PHN PHI XC SUTPHN PHI XC SUTLIN TCLIN TC

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 44

    NI DUNG CHNHNI DUNG CHNH

    Gii thiu

    Phn phi xc sut u

    130

    Phn phi xc sut chun

    Tnh gn ng phn phi chun cho phn phi

    nh thc

    GII THIUGII THIU

    Mt bin ngu nhin lin tc l mt gi tr ngu nhin c th nhn bt k gi tr no trong mt khong hay tp hp cc khong

    131

    Mt Phn phi xc sut i vi mt bin ngu nhin lin tc c c trng bi mt Hm mt xc sut (Probability Density Function PDF)

    GII THIUGII THIU

    Cc din tch di ng cong mt xc sut l cc xc sut f(x)

    ty

    132

    a bx

    SDen

    si

    b

    a

    dx)x(fS)bXa(P

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 45

    GII THIUGII THIU

    Mt s cc phn phi xc sut ph bin i vi

    bin lin tc:

    Phn phi u (Uniform Distribution)

    133

    Phn phi u (Uniform Distribution)

    Phn phi chun (Normal Distribution)

    PHN PHI XC SUT UPHN PHI XC SUT U

    Hm mt xc sut ca phn phi u

    elsewhere0

    bxa forab

    1)x(f

    f(x)

    134

    elsewhere0( )

    x

    Den

    sity

    h

    a b

    PHN PHI XC SUT UPHN PHI XC SUT U

    Gi tr k vng v phng sai ca phn phi u

    bab

    135

    12

    abdx)x(fx)x(Var

    2badx)x(f.x)x(E

    2b

    a

    22

    a

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 46

    PHN PHI XC SUT CHUNPHN PHI XC SUT CHUN

    Hm mt xc sut ca phn phi chun

    2

    2

    2x

    e21)x(f

    136

    Vi = Trung bnh = lch chun = 3.14159e = 2.71828X N (, 2)

    2

    PHN PHI XC SUT CHUNPHN PHI XC SUT CHUN

    ng cong chun

    Dng ca f(x) i xng, ging dng hnh chung

    137

    ng cong chun c 2 tham s, v . Chng

    xc nh v tr v dng ca phn phi

    PHN PHI XC SUT CHUNPHN PHI XC SUT CHUN

    1 2 3

    138

    1 2 3

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 47

    PHN PHI XC SUT CHUNPHN PHI XC SUT CHUN

    1

    139

    X

    2

    1 < 2

    PHN PHI XC SUT CHUNPHN PHI XC SUT CHUNf(x)

    S

    140

    a b x

    S

    P( a < X < b) = S

    P ( - < X < + ) = 68.26%

    P ( - 2 < X < + 2) = 95.44%

    P ( - 3 < X < + 3) = 99.72%

    PHN PHI XC SUT CHUNPHN PHI XC SUT CHUN

    Phn phi xc sut chun chun ha

    Phn phi xc sut chun chun ha l mt phn phi chun

    c trung bnh bng 0 v phng sai bng 1

    141

    Mt bin ngu nhin chun chun ha Z l mt bin tun

    theo phn phi xc sut chun chun ha

    Z N (0,12)

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 48

    PHN PHI XC SUT CHUNPHN PHI XC SUT CHUN

    Mt bin chun chun ha Nu X N (, 2) th bin chun chun ha Z c trung bnh bng 0, phng sai bng 1 v Z N (0, 12)

    142

    XZ

    a b x

    f(x)

    S

    - 3 - 2 - + +2 +3

    PHN PHI XC SUT CHUNPHN PHI XC SUT CHUNf(x)

    143

    Z

    S

    -3 -2 -1 Za 0 1 Zb 2 3

    PHN PHI XC SUT CHUNPHN PHI XC SUT CHUN

    X N(, 2) Z N (0, 12)

    XZ

    144

    P (a < X < b) = P (Za < Z < Zb) = S

    aZa

    bZb

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 49

    PHN PHI XC SUT CHUNPHN PHI XC SUT CHUN

    S dng bng din tch ca ng cong chun tm gi tr ca S f(x)

    145

    Z S or S Z

    z

    S

    -3 -2 -1 0 1 2 3

    Using table Using table

    TNH GN NG PHN PHI CHUN TNH GN NG PHN PHI CHUN CHO PHN PHI NH THCCHO PHN PHI NH THC

    Khi chng ta gp mt vn ca phn phi nh thc vi s ln th ln, chng ta c th mun tnh gn ng xc sut ca phn phi nh thc

    146

    n > 20

    np 5

    n(1-p) 5

    Vi n cho trc, tnh gn ng phn phi chun cho phn phi nh thc s tt nht khi p= 0.5

    TNH GN NG PHN PHI CHUN TNH GN NG PHN PHI CHUN CHO PHN PHI NH THCCHO PHN PHI NH THC

    Khi s dng phn phi chun tnh gn ng cho phn phi nh thc, chng ta t

    = np

    147

    Vo trong nh ngha ca ng cong chun

    )p1(np

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 50

    TNH GN NG PHN PHI CHUN TNH GN NG PHN PHI CHUN CHO PHN PHI NH THCCHO PHN PHI NH THC

    Nhn t iu chnh lin tc l gi tr 0.5, ngha l

    cng hoc tr vo gi tr ca X khi s dng

    148

    phn phi xc sut chun lin tc tnh gn

    ng cho phn phi xc sut nh thc ri rc

    CHNG 7CHNG 7

    LY MULY MU

    149

    LY MULY MUvv

    PHN PHI MUPHN PHI MU

    NI DUNG CHNHNI DUNG CHNH

    Gii thiu vn ly mu Ly mu ngu nhin n gin c lng im

    150

    Gii thiu phn phi mu Phn phi mu ca trung bnh mu Phn phi mu ca t l mu Cc tnh cht ca c lng im Cc phng php ly mu khc

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 51

    GII THIU VN LY MUGII THIU VN LY MU

    Mt Tng th l tp hp tt c cc phn t cn

    quan tm trong mt nghin cu.

    151

    Mt Mu l mt tp hp con ca tng th.

    Mc ch ca thng k suy din l thu thp

    thng tin v tng th t cc thng tin c trong

    mu.

    GII THIU VN LY MUGII THIU VN LY MU

    Ly mu ngu nhin

    Tng thN (C) Mu

    152

    c lngKim nh Gi thuyt

    N (C) (Trung bnh) ( lch chun)p (T l)

    Mun

    s x

    p

    GII THIU VN LY MUGII THIU VN LY MU

    Cc tr thng k mu: Mt c trng ca mu,

    nh l trung bnh mu , lch chun mu s, x

    153

    t l mu .Gi tr ca tr thng k mu c

    dng c lng gi tr tham s ca tng th

    p

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 52

    LY MU NGU NHIN N GINLY MU NGU NHIN N GIN

    nh ngha ca mu ngu nhin n gin v qu trnh la chn mt the mu ngu nhin n gin ty thc vo tng th l hu hn hay v hn.

    154

    Tng th hu hn thng c nh ngha bng mt danh sch.

    Tng th v hn thng c nh ngha l mt qu trnh ang din ra. Cc phn t ca tng th v hn c th khng lit k c

    LY MU NGU NHIN N GINLY MU NGU NHIN N GIN

    Ly mu t tng th hu hn Mt mu ngu nhin n gin c mu n t tng th

    hu hn c N l mt mu c chn sao cho mi mu c th vi c mu n u c cng xc sut c

    155

    mu c th vi c mu n u c cng xc sut c chn

    S mu ngu nhin n gin c mu n khc nhau t tng th hu hn c N l:

    )!nN(!n!N

    LY MU NGU NHIN N GINLY MU NGU NHIN N GIN

    Ly mu t tng th hu hn Ly mu khng thay th: Khi mt phn t c

    chn vo mu th n c ly ra khi tng th v khng th c chn ln th hai

    156

    khng th c chn ln th hai

    Ly mu c thay th : Khi mt phn t c chn vo mu th n c b tr li tng th. Mt phn t c la chn ln trc th n c th c la chn ln na v v vy phn t c th xut hin trong mu hn mt ln

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 53

    LY MU NGU NHIN N GINLY MU NGU NHIN N GIN

    Ly mu t tng th v hnMt mu ngu nhin n gin t mt tng th

    v hn l mt mt c chn phi tha mn

    157

    v hn l mt mt c chn phi tha mn

    cc iu kin sau:

    Mi phn t c chn phi n t cng mt tng

    th

    Mi phn t c chn mt cch c lp

    C LNG IMC LNG IM

    Trong c lng im chng ta s dng d liu t mu tnh mt gi tr ca tr thng k mu v da vo cung cp mt c lng v mt tham s ca tng th

    158

    ca tng th c lng im l mt tr thng k mu, nh l ,

    s hay cung cp c lng im v tham s ca tng th, , v p.

    xp

    GII THIU PHN PHI MUGII THIU PHN PHI MU

    Phn phi xc sut ca bt k tr thng k mu c th c gi l phn phi mu ca tr thng k.

    Phn phi xc sut ca c gi l phn phi mu ca .Kin thc v phn phi mu ny v

    xx

    159

    mu ca .Kin thc v phn phi mu ny v cc tnh cht ca n s cho php chng ta pht biu v xc sut cho trung bnh ca mu gn bng vi trung bnh ca tng th .

    Trong thc t, chng ta ch chn mt mu ngu nhin n gin t tng th

    x

    x

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 54

    PHN PHI MU CAPHN PHI MU CA

    Phn phi mu ca

    Phn phi mu ca l phn phi xc sut ca

    xx

    x

    160

    tt c cc gi tr c th ca trung bnh mu

    Gi tr k vng ca

    E( ) =

    x

    x

    x

    PHN PHI MU CAPHN PHI MU CA x

    Tng th vi trung

    Mt mu ngu nhin n gin vi n phn t c

    h t t th

    161

    gbnh = ? chn t tng th

    Tng kt ca d liu mu cung cp mt gi tr trung bnh mu X

    Gi tr c dng suy din v gi tr

    X

    PHN PHI MU CAPHN PHI MU CA

    lch chun ca Tng th v hn hay khng bit N

    xx

    nX

    162

    Tng th hu hn hay bit N

    Vi l nhn t iu chnh tng th hu hn

    1NnN

    nx

    1NnN

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 55

    lch chun ca B qua nhn t iu chnh tng th hu hn khi

    n/N 0.05Sai s chun l lch chun ca mt c lng

    PHN PHI MU CAPHN PHI MU CA xx

    163

    Sai s chun l lch chun ca mt c lng im

    xbar c xem nh sai s chun ca trung bnh

    Phn phi ca Cu hi: Phn phi xc sut ca l g?

    PHN PHI MU CAPHN PHI MU CA xx

    x

    164

    nh l gii hn trung tm Phn phi ca tng th c bit l phn phi

    chunX N (, 2) N (, 2/n) x

    nh l gii hn trung tm Trong vic chn cc mu ngu nhin n gin c

    mu n t mt tng th, phn phi mu ca trung bnh mu c th gn ng tun theo phn phi

    PHN PHI MU CAPHN PHI MU CA x

    x

    165

    bnh mu c th gn ng tun theo phn phi chun khi c mu ln.

    X ~ Bt k phn phi no Khng bit phn phi

    xc sut tng th C mu ln

    (N>30)

    x

    N (, 2/n)X

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 56

    N (, 2/n) Z N (0,12)vi

    PHN PHI MU CAPHN PHI MU CA xX

    x

    166

    n/x

    PHN PHI MU CAPHN PHI MU CA

    Phn phi mu ca

    Phn phi mu ca l phn phi xc sut

    pp

    p

    167

    ca tt c cc gi tr c th ca t l mu

    Gi tr k vng ca

    E( ) = p

    p

    p

    p

    PHN PHI MU CAPHN PHI MU CA p

    Tng th vi t l p

    = ?

    Mt mu ngu nhin n gin vi n phn t c

    chn t tng th

    168

    Tng kt ca d liu mu cung cp mt gi tr trung bnh mu p

    Gi tr c dng suy din v gi tr

    p

    p

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 57

    lch chun ca Tng th v hn:

    PHN PHI MU CAPHN PHI MU CA pp

    n)p1(p

    p

    169

    Tng th hu hn:

    B qua nhn t iu chnh tng th hu hn

    khi n/N < 0.05

    1NnN

    n)p1(p

    p

    1NnN

    Dng phn phi mu ca

    Phn phi mu ca c th gn ng tun

    PHN PHI MU CAPHN PHI MU CA p

    p

    p

    170

    theo phn phi xc sut chun khi c mu ln np 5 n(1 p) 5

    TNH CHT CA C LNG IMTNH CHT CA C LNG IM

    Gi = tham s tng th c quan tm

    = tr thng k mu hay c lng im ca Kh thi l h

    171

    Khng thin lchTr thng k mu l mt c lng khng thin lch ca tham s tng th nu

    E( ) = thin lch (Bias)

    Bias ( ) = E( ) -

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 58

    TNH CHT CA C LNG IMTNH CHT CA C LNG IM

    hu hiuCho hai c lng im khng thin lch ca tham s tng th, c lng im vi lch chun nh hn c xem l hiu qu hn nu:

    12

    172

    qVar ( ) < Var ( )

    nht qunMt tnh cht ca c lng im c trnh by khi cc c mu ln hn s cung cp cc c lng im gn vi tham s ca tng th

    2

    21

    CC PHNG PHP LY MU KHCCC PHNG PHP LY MU KHC

    Ly mu h thngMt phng php ly mu xc sut theo chng ta s chn mt cch ngu nhin mt trong k phn t u tin v sau chn mi phn t th k k tip

    173

    v sau chn mi phn t th k k tip

    Ly mu thun tinMt phng php ly mu phi xc sut theo cc phn t c chn vo mu da trn c s thun tin

    CC PHNG PHP LY MU KHCCC PHNG PHP LY MU KHC

    Ly mu phn onMt phng php ly mu phi xc sut theo cc phn t c chn vo mu da trn s phn on ca ngi thc hin nghin cu

    174

    ngi thc hin nghin cu

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 59

    CHNG 8CHNG 8

    C G O GC G O G

    175

    C LNG KHONGC LNG KHONG

    NI DUNG CHNHNI DUNG CHNH

    c lng khong ca trung bnh tng th: bit c lng khong ca trung bnh tng th: khng

    176

    bit Xc nh c mu c lng khong ca t l tng th

    C LNG KHONG CA C LNG KHONG CA TRUNG BNH TNG TH: BIT TRUNG BNH TNG TH: BIT

    c lng khong l mt c lng ca mt

    tham s ca tng th theo cung cp mt

    177

    khong c tin l s cha gi tr ca tham s

    Trng hp c mu ln: n 30

    Trng hp c mu nh: n < 30

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 60

    C LNG KHONG CA C LNG KHONG CA TRUNG BNH TNG TH: BIT TRUNG BNH TNG TH: BIT

    Dng tng qut ca c lng khong l:

    c lng im Bin ca sai s

    178

    Bin ca sai s l gi tr cng v tr vo c lng im to ra mt khong tin cy

    to ra mt khong tin cy ca , th c v s phi c s dng tnh bin ca sai s

    f(x)

    S /21-

    C LNG KHONG CA C LNG KHONG CA TRUNG BNH TNG TH: BIT TRUNG BNH TNG TH: BIT

    179

    P( Z > Z/2) = /2P( Z < -Z/2) = /2P( -Z/2 < Z < Z/2) = 1-

    Z/2: l gi tr ca bin phn phi chun chun ha tng ng vi mt din tch /2 di ui pha trn ca phn phi

    -z/2 z/2x

    S /2

    C LNG KHONG CA C LNG KHONG CA TRUNG BNH TNG TH: BIT TRUNG BNH TNG TH: BIT

    1Z

    n/xZP

    22

    180

    1n

    Zxn

    ZxP

    n/

    22

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 61

    Tnh c lng khong: bit

    Vi

    C LNG KHONG CA C LNG KHONG CA TRUNG BNH TNG TH: BIT TRUNG BNH TNG TH: BIT

    Zx2

    181

    Vi: (1-) l tin cy x l c lng im ca

    l bin ca sai s

    C mu ln (n 30) dng cng thc ny

    n2

    nZ

    2

    CC GI TR CA Z/2 I VI CC MC TIN CY C S DNG PH BIN NHT

    M ti

    /2

    Z

    C LNG KHONG CA C LNG KHONG CA TRUNG BNH TNG TH: BIT TRUNG BNH TNG TH: BIT

    182

    Mc tin cy /2 Z/2 90% 95% 99%

    .10

    .05

    .01

    .050 .0.25 .005

    1.645 1.960 2.576

    Tnh c lng khong: bit Bin ca sai s l gi tr cng v tr vo c lng im to ra mt khong tin cy

    C LNG KHONG CA C LNG KHONG CA TRUNG BNH TNG TH: BIT TRUNG BNH TNG TH: BIT

    183

    Khong tin cy: Mt khong tin cy 100(1 - )% i vi trung bnh ca phn phi chun l

    n

    Zx,n

    Zx22

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 62

    C LNG KHONG CA C LNG KHONG CA TRUNG BNH TNG TH: KHNG BIT TRUNG BNH TNG TH: KHNG BIT

    Nu khng bit , lch chun ca mu s c dng c lng lch chun ca tng th v khong tin cy thch hp s da trn mt phn phi xc sut c gi l phn

    184

    trn mt phn phi xc sut c gi l phn phi t

    Tr thng k t:

    n/sxt

    Tr thng k t s tun theo mt Phn phi Students t, vi t do df

    df = n - 1

    C LNG KHONG CA C LNG KHONG CA TRUNG BNH TNG TH: KHNG BIT TRUNG BNH TNG TH: KHNG BIT

    185

    Phn phi t thng c c dng vi phn phi c mu nh ca

    If n N then t # Z

    x

    Phn phi chun chun ha Z

    ng cong t vi bc t do l 20

    C LNG KHONG CA C LNG KHONG CA TRUNG BNH TNG TH: KHNG BIT TRUNG BNH TNG TH: KHNG BIT

    186

    t

    t do l 20ng cong t vi bc t do l 10

    Phn phi t

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 63

    c lng khong ca mt trung bnh tng th: khng bit

    C LNG KHONG CA C LNG KHONG CA TRUNG BNH TNG TH: KHNG BIT TRUNG BNH TNG TH: KHNG BIT

    stx

    187

    C mu nh (n < 30) v tng th tun theo mt phn phi chun hoc gn chun cng dng cng thc ny

    ntx

    2

    TNG KT CC TH TC C LNG KHONG I VI TNG KT CC TH TC C LNG KHONG I VI TRUNG BNH TNG THTRUNG BNH TNG TH

    C th gi s lch chun ca tng th

    bit?C Khng

    Dng lch chun ca mu s c

    188

    lng

    nstx 2/

    Dng

    Trng hp khng bit

    x zn

    /2

    Dng

    Trng hp bit

    XC NH C MUXC NH C MU

    Gi E = bin ca sai s k vng

    nZE

    2

    189

    C mu i vi c lng khong ca mt trung bnh ca tng th

    C mu i vi khng bit

    2

    22

    EZ

    n 2

    2

    22

    EsZ

    n 2

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 64

    C LNG KHONG CA C LNG KHONG CA T L TNG THT L TNG TH

    n/)p1(p

    p)p(E

    p

    190

    c lng khong ca t l tng th

    hayp2

    Zp

    n/)p1(pZp2

    Xc nh c muGi E = bin ca sai s k vng

    C LNG KHONG CA C LNG KHONG CA T L TNG THT L TNG TH

    n/)p1(pZE

    191

    2

    2

    E)p1(pZ

    n

    n/)p1(pZE

    2

    2

    CHNG 9CHNG 9

    KIM NH GI THUYT

    192

    KIM NH GI THUYT

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 65

    NI DUNG CHNHNI DUNG CHNH

    Pht trin gi thuyt khng v gi thuyt khc Cc sai lm loi I v loi II

    193

    Kim nh mt-pha v trung bnh ca tng th: bit Kim nh hai-pha v trung bnh ca tng th: bit Kim nh v trung bnh ca tng th: khng bit Kim nh v t l ca tng th

    PHT TRIN GI THUYT PHT TRIN GI THUYT KHNG v GI THUYT KHCKHNG v GI THUYT KHC

    Gi thuyt

    Gi thuyt l mt gi s hay pht biu v cc tham s ca tng th; N c th ng hoc sai

    194

    Gi thuyt Khng (H0)

    H0 l mt pht biu (ng thc hoc bt ng thc) lin quan n tham s ca tng th

    H0 l mt gi nh ng trong th tc kim nh gi thuyt

    Mt tuyn b ca nh sn xut thng b nghi ng v c pht biu trong H0

    PHT TRIN GI THUYT KHNG PHT TRIN GI THUYT KHNG v GI THUYT KHCv GI THUYT KHC

    Gi thuyt khc (Ha)Ha l pht biu ngc vi H0Ha c kt lun l ng nu H0 b bc b

    195

    a g 0

    Nh nghin cu mong mun ng h Ha v nghi ng H0

    Tng kt cc dng ca gi thuyt Khng v gi thuyt khc H0 : = 0 or H0 : 0 or H0 : 0 Ha : 0 Ha : 0 Ha : 0

    Nhim v ca tt c kim nh gi thuyt hoc l bc b H0 hay khng bc bH0 ( Accept H0 )

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 66

    CC SAI LM LOI I V LOI IICC SAI LM LOI I V LOI II

    Sai lm loi I l sai lm ca vic bc b H0 khi n ngSai lm loi II l sai lm ca vic khng bc b H0 khi n sai

    196

    CC KT LUN NG V SAI TRONG KIM NH GI

    THUYT

    iu kin ca tng th

    H0 ng H0 sai

    CC SAI LM LOI I V LOI IICC SAI LM LOI I V LOI II

    l xc sut ca sai lm loi I = P( Bc b H0 / H0 ng ) = P(Sai lm loi I ) c gi l mc ngha ca kim nh, 0.01 < < 0.1

    197

    Thng chn = 0.05

    l xc sut ca sai lm loi II = P( Khng bc b H0 / H0 sai ) = Sai lm loi II )(1-) = P(Bc b H0 / H0 sai) = Nng lc ca kim nh cng nh th cng ln

    MIN BC BMIN BC B

    Mt min bc b R nh r cc gi tr ca tr thng ks ch dn cho chng ta bc b H0

    198

    Kim dnh 2-pha

    H0 : = 0Ha : 0

    Khng bc b

    H0Bc b H0 Bc b H0

    -Z/2

    Z

    Z/2

    /2 /2

    f(x)

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 67

    MIN BC BMIN BC B

    Kim nh 1-phaH0 : 0 H0 : 0Ha : 0 Ha : 0

    199

    Bc b H0 Khng bc b H0

    -Z

    Z

    Bc b H0

    Z

    Z

    Khng bc b H0

    KIM NH 1KIM NH 1--PHA V TRUNG BNH PHA V TRUNG BNH CA TNG TH: BIT CA TNG TH: BIT

    Gi thuytTrng hp 1 Trng hp2H : H :

    200

    H0 : 0 H0 : 0Ha : 0 Ha : 0

    Tr thng k

    n/

    XZ 0

    KIM NH 1KIM NH 1--PHA V TRUNG BNH PHA V TRUNG BNH CA TNG TH: BIT CA TNG TH: BIT

    Phng php p-valuep-value

    201

    p-value l xc sut, c tnh t tr thng k, o lng mc ng h (hay khng ng h) cung cp bi mu i vi gi thuyt H0

    Tiu ch p-value i vi kim nh gi thuyt

    Bc b H0 nu p-value <

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 68

    KIM NH 1KIM NH 1--PHA V TRUNG BNH PHA V TRUNG BNH CA TNG TH: BIT CA TNG TH: BIT

    Phng php gi tr ti hn(Qui tc bc b)Bc b H0 nu Z < -Z Bc b H0 nu Z >Z

    202

    Bc b H0 nu Z < Z Bc b H0 nu Z >Z

    Bc b H0 Khng bc b H0

    -Z

    Z

    Bc b H0

    Z

    Z

    Khng bc b H0

    KIM NH 2KIM NH 2--PHA V TRUNG BNH PHA V TRUNG BNH CA TNG TH: BIT CA TNG TH: BIT

    Gi thuyt:H0 : = 0Ha : 0

    203

    a 0

    Tr thng k:

    n/X

    Z 0

    KIM NH 2KIM NH 2--PHA V TRUNG BNH PHA V TRUNG BNH CA TNG TH: BIT CA TNG TH: BIT

    p-value i vi kim nh 2-phaTrong kim nh 2-pha, p-value c tnh bng cch nhn i din tch phn ui ca phn phi

    204

    i din tch phn ui ca phn phi

    V din tch c nhn i nn p-value c th so snh trc tip vi v qui tc bc b vn ging nh trc

    Bc b H0 nu p-value <

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 69

    KIM NH 2KIM NH 2--PHA V TRUNG BNH PHA V TRUNG BNH CA TNG TH: BIT CA TNG TH: BIT

    Phng php gi tr ti hn(Qui tc bc b)

    205

    Bc b Ho nu Z < -Z/2 Bc b Ho nu Z > Z/2

    /2 /2

    f(x)

    - Z/2 Z/2

    Khng bc b H0Bc b H0Bc b H0

    Z

    KIM NH 2KIM NH 2--PHA V TRUNG BNH PHA V TRUNG BNH CA TNG TH: BIT CA TNG TH: BIT

    Mi lin h gia c lng khong v kim nh gi thuytMt phng php khong tin cy kim nh gi thuyt di dng:

    H0 : = 0

    206

    0 0Ha : 0

    Chn mt mu ngu nhin n gin t tng th v dng gi tr ca trung bnh ca mu pht trin khong tin cy i vi .

    Nu khong tin cy cha gi tr c gi thuyt 0, th khng bc b H0. Nu khng cha th bc b H0

    nZX /2

    CC BC KIM NH GI THUYT CC BC KIM NH GI THUYT

    Bc 1: Pht trin H0 v HaBc 2: nh mc ngha Bc 3: Thu thp d liu mu v tnh tr thng k kim nh

    207

    Phng php p-valueBc 4: Dng gi tr ca tr thng k kim nh tnh p-valueBc 5: Bc b H0 nu p-value < Phng php gi tr ti hnBc 4: Dng xc nh gi tr ti hn v qui tc bc bBc 5: Dng gi tr ca tr thng k kim nh v qui tc bc b

    xc nh xem c bc b H0 hay khng

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 70

    KIM NH V TRUNG BNH CA KIM NH V TRUNG BNH CA TNG TH: KHNG BIT TNG TH: KHNG BIT

    s c dng c lng Phn phi t c th c dng suy din v Tr thng k kim nh l

    208

    Tr thng k kim nh l

    df = n-1 C mu nh (n < 30) v tng th tun theo mt phn phi

    chun hoc gn chun cng dng cng thc ny

    ns/ - Xt 0

    KIM NH V TRUNG BNH CA KIM NH V TRUNG BNH CA TNG TH: KHNG BIT TNG TH: KHNG BIT

    Kim nh 1-phaH0 : 0 H0 : 0H : < H : >

    209

    Ha : < 0 Ha : > 0Bc b H0 nu t < -t, n-1 Bc b H0 nu t > t, n-1

    Kim nh 2-phaH0 : = 0Ha : 0Bc b H0 nu t < -t/2, n-1 hay nu t > t/2, n-1

    KIM NH V TRUNG BNH CA KIM NH V TRUNG BNH CA TNG TH: KHNG BIT TNG TH: KHNG BIT

    p-value v phn phi t X Dng bng t l

    210

    Bc b H0 nu p-value <

    ns/Xt 0

    g gp-value

    df = n-1

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 71

    KIM NH V T L CA TNG THKIM NH V T L CA TNG TH

    Gi p : t l ca tng thp0 : gi tr c th ca gi thuyt i vi t l ca tng th

    211

    Gi thuytHo : p p0 H : p p0 H0 : p = pHa : p < p0 H : p > p0 Ha : p p0

    Tr thng k kim nh

    p

    0

    ppZ

    n)p(1p 00p

    KIM NH KIM NH V T L CA V T L CA TNG THTNG TH

    Qui tc bc b

    212

    HI QUI TUYN TNH N

    CHNG 10

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 72

    HI QUI TUYN TNH NHI QUI TUYN TNH N

    M hi qui tuyn tnh n

    Phng php bnh phng ti thiu

    H s c nh

    214

    H s xc nh

    Cc gi nh ca m hnh

    Kim nh mc ngha

    S dng m hnh hi qui c lng c

    lng v d on

    M HNH HI QUI TUYN TNHM HNH HI QUI TUYN TNH

    M hnh hi qui tuyn tnh n l:

    Phng trnh m t y lin h vi x nh th no v mt

    s hng sai s c gi l m hnh hi qui.

    215

    yy = = 00 + + 11xx ++

    Vi:

    0 v 1 c gi l cc tham s ca m hnh,

    l bin ngu nhin c gi l s hng sai s.

    PHNG TRNH

    HI QUI TUYN TNH N

    Phng trnh hi qui tuyn tnh nPhng trnh hi qui tuyn tnh n l: l:

    EE((yy) = ) = 00 + + 11xx

    216

    EE((yy) ) l gi tr k vng ca l gi tr k vng ca yy i vi gi tr i vi gi tr xx cho trc.cho trc. 11 l dc ca ng hi quil dc ca ng hi qui 00 l tung gc ca ng hi quil tung gc ca ng hi qui

    th ca phng trnh hi qui l ng thng. th ca phng trnh hi qui l ng thng.

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 73

    PHNG TRNH PHNG TRNH HI QUI TUYN TNH NHI QUI TUYN TNH N

    Quan h tuyn tnh ng binQuan h tuyn tnh ng bin

    EE((yy))EE((yy))

    217xxxx

    dc dc 11

    dngdng

    ng hi quing hi qui

    Tung gcTung gc

    00

    PHNG TRNH PHNG TRNH

    HI QUI TUYN TNH NHI QUI TUYN TNH N Quan h tuyn tnh nghch binQuan h tuyn tnh nghch bin

    EE((yy))EE((yy))

    hi i hi i

    218

    xxxx

    dc dc 11

    mm

    ng hi quing hi quiTung gcTung gc

    00

    PHNG TRNH

    HI QUI TUYN TNH N Khng quan hKhng quan h

    EE((yy))EE((yy))

    219

    xxxx

    dc dc 11

    Bng 0Bng 0

    ng hi quing hi quiTung gcTung gc

    00

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 74

    PHNG TRNH HI QUI

    TUYN TNH N C LNG

    Phng trnh hi qui tuyn tnh n c lng Phng trnh hi qui tuyn tnh n c lng

    ^ b b

    220

    y^ = b0 + b1x

    y^ y^ l gi tr c lng ca y i vi gi tr x cho trc.l gi tr c lng ca y i vi gi tr x cho trc. bb11 l dc ca ngl dc ca ng bb00 l tung gc ca ng.l tung gc ca ng. th c gi l ng hi qui c lng. th c gi l ng hi qui c lng.

    QU TRNH C LNGQU TRNH C LNG

    M hnh hi quiM hnh hi quiyy = = 00 + + 11xx ++

    Phng trnh hi quiPhng trnh hi quiEE((yy) = ) = 00 + + 11xx

    Tham s cha bitTham s cha bit

    D liu muD liu mux yx y

    xx11 yy11. .. .. .. .

    221

    00, , 11. .. .xxnn yynn

    bb00 vv bb11

    c lng cac lng ca

    00 vv 11

    Phng trnh Phng trnh

    hi qui c lnghi qui c lng

    Tr thng k muTr thng k mu

    bb00, , bb11

    0 1y b b x

    PHNG PHP PHNG PHP BNH PHNG TI THIUBNH PHNG TI THIU

    Tiu ch bnh phng ti thiu

    min (y yi i )2

    222

    Vi:Vi:

    yyii = gi tr = gi tr quan stquan st ca bin ph thuc ca bin ph thuc

    i vi quan st th ii vi quan st th iyyii ^ = = gi tr gi tr c lngc lng ca bin ph thuc ca bin ph thuc

    i vi quan st th I i vi quan st th I

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 75

    dc ca phng trnh hi qui c lng

    PHNG PHP PHNG PHP BNH PHNG TI THIUBNH PHNG TI THIU

    223

    1 2

    ( )( )( )

    i i

    i

    x x y yb

    x x

    Tung gc ca phng trnh hi qui c lngTung gc ca phng trnh hi qui c lng

    PHNG PHP PHNG PHP

    BNH PHNG TI THIUBNH PHNG TI THIU

    0 1b y b x

    224

    Vi:Vi:xxii = gi tr ca bin c lp i vi quan st th i= gi tr ca bin c lp i vi quan st th i

    nn = tng s quan st = tng s quan st

    __yy = gi tr trung bnh ca bin ph thc = gi tr trung bnh ca bin ph thc

    __xx = gi tr trung bnh ca bin c lp = gi tr trung bnh ca bin c lp

    yyii = gi tr ca bin ph thuc i vi quan st th i= gi tr ca bin ph thuc i vi quan st th i

    HI QUI TUYN TNH NHI QUI TUYN TNH N

    V d: Doanh s xe hiV d: Doanh s xe hi

    225

    Qung co Qung co

    TVTV

    Doanh s Doanh s

    xe hixe hi11

    33

    22

    11

    1414

    2424

    1818

    1717

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 76

    PHNG TRNH PHNG TRNH HI QUI C LNGHI QUI C LNG

    1 2

    ( ) ( ) 2 0 5( ) 4

    i i

    i

    x x y yb

    x x

    dc ca phng trnh hi qui c lng

    226

    10 5y x

    0 1 2 0 5 ( 2 ) 1 0b y b x Tung gc ca phng trnh hi qui c lng

    Phng trnh hi qui c lng

    TH PHN TN IM V TH PHN TN IM V NG XU HNGNG XU HNG

    20

    25

    30

    hi

    227

    y = 5x + 10

    0

    5

    10

    15

    20

    0 1 2 3 4Qung co TV

    Doa

    nh s

    xe

    H S XC NHH S XC NH

    Mi lin h gia SST, SSR, SSE

    228

    Vi:Vi:SST = Tng bnh phng ton phnSST = Tng bnh phng ton phnSSR = SSR = Tng bnh phng hi quiTng bnh phng hi quiSSE = SSE = Tng bnh phng sai sTng bnh phng sai s

    SST = SSR + SSESST = SSR + SSE

    2( )iy y 2( )iy y 2( )i iy y

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 77

    H s xc nhH s xc nh l:l:

    H S XC NH

    229

    Vi:Vi:

    SSR = Tng bnh phng hi quiSSR = Tng bnh phng hi qui

    SST = Tng bnh phng ton phnSST = Tng bnh phng ton phn

    rr22 = SSR/SST= SSR/SST

    H S XC NHH S XC NH

    rr22 = SSR/SST = 100/114 = .8772= SSR/SST = 100/114 = .8772Mi h hi i h 88%Mi h hi i h 88%

    230

    Mi quan h hi qui rt mnh; 88% Mi quan h hi qui rt mnh; 88% s bin thin ca doanh s xe hi c th c s bin thin ca doanh s xe hi c th c gii thch bi mi quan h tuyn tnh gia gii thch bi mi quan h tuyn tnh gia s qung co trn TV v doanh s xe hi.s qung co trn TV v doanh s xe hi.

    H S TNG QUAN MUH S TNG QUAN MU

    ionDeterminat oft Coefficien ) of(sign 1brxy

    231

    21 ) of(sign rbrxy

    ViVi

    bb11 = dc ca phng trnh hi qui c lng= dc ca phng trnh hi qui c lngxbby 10

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 78

    21 ) of(sign rbrxy

    10 5y x

    H S TNG QUAN MUH S TNG QUAN MU

    232

    Du ca Du ca bb11 trong phng trnhtrong phng trnh

    l +.l +.

    10 5y x

    = + .8772xyr

    rrxyxy = +.9366= +.9366

    CC GI NH V S HNG SAI S CC GI NH V S HNG SAI S

    1.1. Sai s l bin ngu nhin vi trung bnh bng 0

    2.2. Phng sai ca , k hiu 2, s ging nhau

    233

    i vi tt c cc gi tr ca bin c lp.

    3.3. Cc gi tr ca l c lp.

    4. Sai s l bin ngu nhin tun theo

    phn phi chun

    KIM NH NGHAKIM NH NGHA

    kim nh ngha ca mi quan h hi qui, chng

    Ta phi tin hnh kim nh gi thuyt xc nh xem

    gi tr ca 1 c bng 0 hay khng.

    234

    gi tr ca 1 c bng 0 hay khng.Hai kim nh c dng ph bin l:

    t Test v F Test

    C kim nh t v F u yu cu mt c lng ca

    2, phng sai ca trong m hnh hi qui

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 79

    c lng ca

    KIM NH NGHAKIM NH NGHA

    Trung bnh ca sai s bnh phng (MSE) s cung cp Trung bnh ca sai s bnh phng (MSE) s cung cp

    235

    2102 )()(SSE iiii xbbyyyViVi

    ss 22 = MSE = SSE/(= MSE = SSE/(n n 2)2)

    c lng cac lng ca 22, v , v ss22 cng c s dng.cng c s dng.

    KIM NH NGHAKIM NH NGHA

    c lng ca

    c lng c lng chng ta ly cn bc hai cachng ta ly cn bc hai ca 22..

    236

    2SSEMSE

    n

    s

    Kt qu Kt qu ss c gi l c gi l sai s chun ca c lngsai s chun ca c lng

    Gi thuyt

    KIM NH NGHA: KIM NH KIM NH NGHA: KIM NH tt

    0 1: 0H : 0H

    237

    Tr thng k

    1: 0aH

    1

    1

    b

    bts

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 80

    Qui tc bc bQui tc bc b

    KIM NH NGHA: KIM NH KIM NH NGHA: KIM NH tt

    238

    ViVi

    tt c da trn phn phi tc da trn phn phi t

    vi bc t do l n vi bc t do l n --2 2

    Bc bBc b HH00 nu nu pp--valuevalue tt

    1. Xc nh gi thuyt.1. Xc nh gi thuyt.

    KIM NH NGHA: KIM NH KIM NH NGHA: KIM NH tt

    0 1: 0H

    1: 0aH

    239

    2. Xc nh mc ngha2. Xc nh mc ngha..

    3. La chn tr thng k kim nh.3. La chn tr thng k kim nh.

    = .05= .05

    4. Qui tc bc b.4. Qui tc bc b. Bc b Bc b HH00 nu nu pp--valuevalue 3.182 (> 3.182 (vi t do l 3vi t do l 3))

    1

    1

    b

    bts

    KIM NH NGHA: KIM NH t

    5. Tnh gi tr ca tr thng k kim nh.5. Tnh gi tr ca tr thng k kim nh.

    1 5 4.631 08b

    bts

    240

    6. Xc nh c bc b 6. Xc nh c bc b HH00 hay khnghay khng

    tt = 4.541 cho mt din tch .01 phn ui= 4.541 cho mt din tch .01 phn ui

    pha trn. V vy, pha trn. V vy, pp--value nh hn .02. (Cng vy,value nh hn .02. (Cng vy,

    tt = 4.63 > 3.182.) chng ta c th bc b = 4.63 > 3.182.) chng ta c th bc b HH00..

    11.08bs

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 81

    KHONG TIN CY CA KHONG TIN CY CA 11

    Chng ta c th dng mt khong tin cy 95% ca Chng ta c th dng mt khong tin cy 95% ca 11

    kim nh cc gi th t a mi dng trong kim nh cc gi th t a mi dng trong

    241

    HH00 b bc b nu gi tr c gi thuyt cab bc b nu gi tr c gi thuyt ca 11

    khng nmkhng nm trong khong tin cy catrong khong tin cy ca 11..

    kim nh cc gi thuyt va mi dng trong kim nh cc gi thuyt va mi dng trong

    kim nh t.kim nh t.

    Cng thc ca khong tin cy i vi 1 l:

    KHONG TIN CY CA KHONG TIN CY CA 11

    1/2 bt s

    242

    11 /2 bb t s

    ViVi l gi tr l gi tr tt cho mt din tch lcho mt din tch l

    /2 /2 trong phn ui pha trn ca phn phi trong phn ui pha trn ca phn phi tt

    Vi t do l n Vi t do l n -- 22

    2/t

    bb11 l l

    c c

    lng lng

    imim

    l bin l bin

    ca sai ca sai

    ss

    KHONG TIN CY CA KHONG TIN CY CA 11

    Bc b Bc b HH00 nu 0 khng nm trong nu 0 khng nm trong

    khong tin cy cakhong tin cy ca 11..

    Qui tc bc b

    243

    0 0 khng nm trong khong tin cy khng nm trong khong tin cy . .

    Bc b Bc b HH00

    = 5 +/= 5 +/-- 3.182(1.08) = 5 +/3.182(1.08) = 5 +/-- 3.443.4412/1 bstb

    or 1.56 to 8.44or 1.56 to 8.44

    Khong tin cy 95% ca 1

    Kt lun

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 82

    Gi thuyt

    KIM NH NGHA: KIM NH F

    0 1: 0H

    1: 0aH

    244

    Tr thng kFF = MSR/MSE= MSR/MSE

    1a

    Qui tc bc b

    KIM NH NGHA: KIM NH F

    B bB b HH

    245

    ViVi::

    FF da trn phn phi F vi t do l 1da trn phn phi F vi t do l 1

    t s v t s v t do l n t do l n -- 2 mu s2 mu s

    Bc bBc b HH00 nunu

    pp--valuevalue > FF

    1. Xc nh gi thuyt.1. Xc nh gi thuyt.

    KIM NH NGHA: KIM NH F

    0 1: 0H 1: 0aH

    246

    2. Xc nh mc ngha.2. Xc nh mc ngha.

    3. La chn tr thng k kim nh.3. La chn tr thng k kim nh.

    = .05= .05

    4. Qui tc bc b.4. Qui tc bc b. Bc b Bc b HH00 nu nu pp--valuevalue > 10.13 (vi 10.13 (vi d.fd.f t s t s

    l l 1 v d.f mu s l 3)1 v d.f mu s l 3)

    FF = MSR/MSE= MSR/MSE

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 83

    KIM NH NGHA: KIM NH F

    5. Tnh gi tr ca tr thng k kim nh.5. Tnh gi tr ca tr thng k kim nh.

    6 X h b b6 X h b b HH h khh kh

    FF = MSR/MSE = 100/4.667 = 21.43= MSR/MSE = 100/4.667 = 21.43

    247

    6. Xc nh c bc b 6. Xc nh c bc b HH00 hay khnghay khng

    FF = 17.44 cho mt din tch l .025 phn ui = 17.44 cho mt din tch l .025 phn ui

    pha trn. V vy, pha trn. V vy, pp--value tng ng vi value tng ng vi FF = 21.43 = 21.43

    s nh hn 2(.025) = .05. V vy, chng ta bc b s nh hn 2(.025) = .05. V vy, chng ta bc b

    HH00..Chng c thng k kt lun c mi quan h Chng c thng k kt lun c mi quan h

    c ngha gia s lng qung co TV v doanh s c ngha gia s lng qung co TV v doanh s xe hixe hi

    MT VI LU V MT VI LU V GII THCH CC KIM NH NGHAGII THCH CC KIM NH NGHA

    Bc b Bc b HH00: : 11 = 0 v kt lun rng mi quan h = 0 v kt lun rng mi quan h

    giagia xx vv yy c ngha chng ta khng th ktc ngha chng ta khng th kt

    248

    Bi v chng ta c th bc b Bi v chng ta c th bc b HH00: : 11 = 0 v= 0 v

    chng t c ngha v thng k chng t c ngha v thng k , chng ta khng th kt, chng ta khng th kt

    lun c lun c mi quan h tuyn tnhmi quan h tuyn tnh gia gia xx v v yy

    gia gia xx v v yy c ngha, chng ta khng th kt c ngha, chng ta khng th kt

    lun c lun c mi quan h nhn qumi quan h nhn qu gia gia xx v v yy

    S DNG PHNG TRNH HI QUI C LNGS DNG PHNG TRNH HI QUI C LNG

    C LNG V D ON C LNG V D ON

    / y t sp yp 2

    Khong tin cy ca E(yp)

    249

    Vi:Vi:h s tin cy l 1h s tin cy l 1 -- vvtt/2 /2 da trn phn phi tda trn phn phi tvi t do l n vi t do l n -- 22

    /2 indpy t s

    D on khong tin cy ca yp

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 84

    Nu 3 qung co TV c tin hnh trc khi bn, chng ta k vng trung bnh doanh s xe hi l:

    C LNG IMC LNG IM

    250

    yy = 10 + 5(3) = 25 xe h= 10 + 5(3) = 25 xe hii

    Kt qu khong tin cy t Excel D E F G1 CONFIDENCE INTERVAL2 x p 33 xbar 2.04 x -xbar 1 0

    KHONG TIN CY CA KHONG TIN CY CA EE((yypp))

    251

    4 x p -xbar 1.05 (x p -xbar)2 1.06 (x p -xbar)2 4.07 Variance of yhat 2.10008 Std. Dev of yhat 1.44919 t Value 3.1824

    10 Margin of Error 4.611811 Point Estimate 25.012 Lower Limit 20.3913 Upper Limit 29.61

    c lng khong tin cy 95% ca trung bnh doanh s c lng khong tin cy 95% ca trung bnh doanh s xe hi khi 3 qung co TV c thc hin l:xe hi khi 3 qung co TV c thc hin l:

    KHONG TIN CY CA E(yp)

    252

    25 25 ++ 4.61 = 20.39 to 29.61 xe hi4.61 = 20.39 to 29.61 xe hi

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 85

    Kt qu khong d on t Excel

    H I1 PREDICTION INTERVAL

    KHONG D ON CA yp

    253

    2 Variance of y ind 6.766673 Std. Dev. of y ind 2.601284 Margin of Error 8.278455 Lower Limit 16.726 Upper Limit 33.287

    c lng khong d on 95% ca doanh s xe hi c lng khong d on 95% ca doanh s xe hi

    trong 1 tun c th khi 3 qung co TV c thc hin l:trong 1 tun c th khi 3 qung co TV c thc hin l:

    KHONG D ON CA yp

    254

    g q gg q g

    25 25 ++ 8.28 = 16.72 to 33.28 xe h8.28 = 16.72 to 33.28 xe hii

    PHN TCH PHN D

    Nu cc gi nh v s hng sai s khng m bo

    th cc kim nh gi thuyt v ngha ca mi quan h

    hi qui v cc kt qu c lng khong khng cn

    255

    i iy y

    Rt nhiu phn tch phn d da trn Rt nhiu phn tch phn d da trn

    vic kho st th phn dvic kho st th phn d

    Phn d ca quan st th Phn d ca quan st th ii

    Cc phn d s cho thng tin tt nht vCc phn d s cho thng tin tt nht v ..hiu lc

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 86

    TH PHN D THEO X

    Nu gi nh phng sai ca ging nhau i vi tt

    c cc gi tr ca x c tha, v m hnh hi qui gi

    nh l mt biu din y ca mi quan h gi cc

    256

    nh l mt biu din y ca mi quan h gi cc

    bin, th th phn d s cho mt n tng tng th v gii bng cc im nm ngang

    y y

    Dng ttDng tt

    TH PHN D THEO X

    257

    xx

    00

    Ph

    n d

    Ph

    n d

    TH PHN D THEO X TH PHN D THEO X

    y y

    Phng sai thay iPhng sai thay i

    258

    xx

    00

    Ph

    n d

    Ph

    n d

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  • Trng HBK Tp.HCM Thng K - Chng 1

    TS. Cao Ho Thi 87

    TH PHN D THEO X

    y y

    Dng m hnh khng thch hpDng m hnh khng thch hp

    259

    xx

    00

    Ph

    n d

    Ph

    n d

    Phn d

    Observation Predicted Cars Sold Residuals1 15 -1

    TH PHN D THEO X

    260

    1 15 12 25 -13 20 -24 15 25 25 2

    TH PHN D THEO X TH PHN D THEO X

    th phn d

    2

    3

    261

    -3

    -2

    -1

    0

    1

    0 1 2 3 4Qung co TV

    Phn

    d

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