L THUYT MUClick to edit Master subtitle style
Tng th v mup
Tng th: k hiu X l c tnh cn nghin cu. Tp hp gm tt c nhng phn t
mang c tnh X ca mt vn quan tm nghin cu gi l tng th. V d - C tri
trong mt cuc bu c. - Thu nhp ca cc h gia nh Tp.HCM - im trung bnh
ca sinh vin trong mt trng i hc. - Trng lng mt loi c di h.
p
Tng th v mup
S phn t ca tng th thng rt ln nn ta khng th chn ht nhng phn t thc
hin th nghim v nhng l do sau:n n n
S phn t qu ln. Thi gian v kinh ph khng cho php. C th lm h hi cc
phn t ca tng th.
p
V vy ngi ta s chn mt tp con ca tng th nghin cu, mt tp con nh vy
gi l Mu. S phn t ca mu gi l c mu.
Tng th v mup
V d n Thm d 1000 c tri. n Kho st 100 gia nh. n Cn trng lng 50
con c. Tham s: l mt c trng c th ca mt tng th. Thng k: l mt c trng c
th ca mt mu.
p
p
Tng th v muTng tha b cd o
Mub gi r y c n u
ef gh i jk l m n o p q rs t u v w x y z
Nhng gi tr c tnh ton bng s liu ca tng th gi l tham s.
Nhng gi tr c tnh ton bng s liu ca mu gi l thng k.
Chn mu ngu nhinCc phn t ca mu c chn ngu nhin t tng th. p Cc phn
t ca tng th c cng kh nng c chn lm mu. p Cc phn t ca mu c chn mt cch
c lp vi nhau. p Tt c nhng mu c n cng c cng kh nng c chn t tng th.
Mt mu c chn tha cc iu kin trn gi l mu ngu nhin.p
Chn mu ngu nhinp
p
p
K hiu Xi l gi tr quan st X trn phn t th i ca mu. Khi ta c mt b n
bin ngu nhin (X1, ..., Xn) gi l mu l thuyt ly t tng th. Tnh cht mu:
n Cc Xi c cng phn phi nh X. n Cc Xi c lp vi nhau. Khi ly mu c th ta
thu c b d liu (x1, .., xn) gi l mu thc nghim ly t X.
Phng php ly mu ngu nhin n ginnh s cc phn t ca tng th t 1 n N. V
lp cc phiu cng nh s nh vy.Trn u cc phiu, sau chn ln lt c hon li n
phiu. Cc phn t ca tng th c s th t trong phiu ly ra s c chn lm
mu.
Thng k m t v Thng k suy lunp
Hai nhnh ca Thng k:n
Thng k m t: Thu thp, tng hp, v x l d liu bin i d liu thnh thng
tin. Thng k suy lun: Cung cp nhng c s d on, d bo, v c lng bin i
thng tin thnh kin thc.n
Thng k m tp
Thu thp d liun
Vd: Phng vn Vd: Bng v th Vd: Trung bnh mu =
p
Trnh by d liun
p
Tng hp d liun
Thng k suy lunp
p
c lng n Vd: c lng cn nng trung bnh tng th s dng cn nng trung bnh
mu Kim nh gi thuyt n V d: kim nh tuyn b cn nng trung bnh bng 60
kg.Suy lun l mt qu trnh rt ra nhng kt lun hoc a ra nhng quyt nh v
mt tng th da trn cc kt qu ca mu.
Qu trnh ra quyt nhQuyt nh
Kin thcKinh nghim, l thuyt, tham kho, thng k suy lun Thng tnh m
my k
Thng tin B t
D liu
t, xc sut,my tnh
Cc dng d liuD liu
Phn loiV d:n
S Ri rcV d:n
n n
Tnh trng hn nhn ng k bu c? Mu mt
Lin tcV d:n n
n
S con trong 1 gia nh S ca cp cu trong 1 gi
Chiu cao in p
Cc thang o d liuVd: cn nng, chiu cao
Thang o t lD liu nh lng
Vd: mc hi lng (1 -> 5), nhit D liu phn loi c th t (xp hng, th
bc, )
Thang o khong Thang o th bcD liu nh tnh
D liu phn loi (v hng hoc khng c th t)
Thang o nh danh
Trnh by d liu bng thp p
D liu dng th thng kh s dng a ra cc quyt nh. Biu din d liu di
dngn n
Bng th
p
Cc dng ca th thng ph thuc vo bin c tng hp.
Trnh by d liu bng thp
Cc dng th:Bin s
Bin phn loi
Biu Biu Biu Biu
tn s ct trn Pareto
Biu ng Biu tn s Histogram v ogive Biu Stem-andleaf Biu phn
tn
Bng v th cho bin phn loiD liu phn loi
Biu din theo bng
Biu din bng th
Bng tn s
Biu ct
Biu trn
th pareto
Bng tn sTng hp d liu phn loi V d: D liu v bnh nhnKhoa nhn iu tr
Tim mch Cp cu K thut cao Sn Phu thut (Bin phn loi) S bnh 1,052
2,245 340 552 4,630
Biu ct v trnp
Biu ct v Biu trn thng c s dng biu din bin nh tnh (phn loi) Chiu
cao ca ct hoc ln ca cung trn biu din tn s hoc phn trm ca tng thnh
phn.
p
Biu ct V dKhoa iu tr bnh nhn Tim mch Cp cu K thut cao S n Phu
thut S 1,052 2,245 340 552 4,630
S bnh nhn12 10 8 6 4 2 0
Biu trn V dKhoa iu tr S % Tng bnh nhn cng 11.93 25.46 3.86 6.26
52.50
Tim mch 1,052 Cp cu 2,245 K thut cao 340 Sn 552 Phu thut
4,630
S bnh nhn
M t bin s bng thD liu s
Tn s v phn phi tch lu
Stem-&-Leaf
Histogram
Ogive
Phn b tn sp
Th no l mt phn b tn s?n n n
Mt phn b tn s l mt danh sch hoc bng cha cc nhm c chia khong(phn
loi hoc phm vi m d liu lt vo) v tn s tng ng vi d liu bn trong tng
khong vi mi khong hoc phn loi.
Chia khong v s khong chiap p
Chiu rng ca mi khong phi bng nhau. Xc nh chiu rng ca mi khong
bng
p p
t nht 5 khong nhng khng nhiu hn 15-20 khong. Cc khong khng trng
nhau.
Phn b tn sV d: o nhit ca 20 ngy ma ng c nhit cao c chn ngu
nhin.24, 35, 17, 21, 24, 37, 26, 46, 58, 30, 32, 13, 12, 38, 41,
43, 44, 27, 53, 27
Phn b tn sp58
Sp xp d liu theo th t tng dn12, 13, 17, 21, 24, 24, 26, 27, 27,
30, 32, 35, 37, 38, 41, 43, 44, 46, 53,
p p p p p
Xc nh min: 58 12 = 46 Chn s khong: 5 (thng thng chn t 5 n 15)
Chiu rng ca mi khong: 10 (lm trn 46/5) Xc nh bin ca mi khong:
[10,20), [20,30), , [60, 70). m s phn t nm trong mi khong tng
ng.
Phn b tn sD liu c sp xp:
12, 13, 17, 21, 24, 24, 26, 27, 27, 30, 32, 35, 37, 38, 41, 43,
44, 46, 53, 58
Khong [10, 20) [20, 30) [30, 40) [40, 50) [50, 60) 3 6 5 4 2
Tn s .15
Tn s quan h 15 .30 .25 .20 .10
% tch lu
30 25 20 10
Tng cng
20
1.00
100
Histogramp p
p p
Biu biu din s liu theo phn b tn s gi l histogram. Trc ngang biu
din gi tr ca cc khong chia. Trc ng biu din tn s, tn s quan h hoc
phn trm. Cc ct vi chiu cao thch hp biu din s quan st bn trong mt
khong.
HistogramKhong [10, [20, [30, [40, [50, 20) 30) 40) 50) 60) Tn s
3 6 5 4 2
0
10
20
30
40
50
60
70
(khng ckhong cch gia cc ct)
Dng iu phn phip
Dng iu ca phn phi c gi l i xng nu cc gi tr quan st cn bng, hoc
phn b xung quan trung tm.
Dng iu phn phip
Dng iu phn phi gi l bt i xng nu gi tr quan st khng phn b xung
quanh trung tm.
Biu Stem & Leafp
Mt dng biu n gin dng nhn dng phn phi t d liu.
PHNG PHP: chia d liu thnh hai thnh phn gm cc ch s dn u (stem) v
cc ch s ui (leaf).
V dD liu c sp xp:21, 24, 24, 26, 27, 27, 30, 32, 38, 41
p
S dng ch s hng chc lm stemStem Leafn n
21 c ghi l 38 c ghi l
2 3
1 8
V dp
S dng ch s hng trm lm stem:n
Lm trn ch s hng chc lm leafStemp p p p
Leaf 1 8 2
613 c ghi l 776 c ghi l 1224 c ghi l
6 7 12
V dp
S dng ch s hng trm lm stem:n
Biu stem & leaf hon chnh nh sauStem Leaves136 2258 346699
13368 356 47 2 6 7 8 9 10 11 12
D liu: 613, 632, 658, 717, 722, 750, 776, 827, 841, 859, 863,
891, 894, 906, 928, 933, 955, 982, 1034, 1047,1056, 1140,
1169, 1224
M t d liu sM t d liu s
tp trung Trung bnh Trung v Mode
bin thin Min d liu Min phn v Phng sai lch tiu chun H s bin
thin
o tp trung ca d liuTng quan tp trung
K vng
Trung v
Mode
Gi tr trung bnh
im chnh gia ca d liu c sp xp theo hng
Gi tr quan st thng gp nht
Trung bnhp
Trung bnh l gi tri thng c s dng o mc tp trung ca d liu.n
Vi mt tng th c N gi tr:Cc gi tr ca tng th S phn t ca tng th
n
Vi mt mu c n:Cc gi tr quan trc C mu
Trung bnhp p
o tp trung B nh hng bi nhng im ngoi lai (outliers).
0 1
2
3
4
5
6
7
8
9
10
0 1
2
3
4
5
6
7
8
9
10
Trung bnh = 3
Trung bnh = 4
Trung vp
Trong mt danh sch c th t, trung v l im chnh gia(50% bn trn, 50%
bn di)2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10
0 1
Trung v = 3
Trung v = 3
p
Khng b nh hng bi cc im outliers.
Xc nh trung vp
V tr ca trung v:
n n
Nu s gi tr quan trc l, trung v l im chnh gia. Nu s gi tr quan
trc chn, trung v l trung bnh ca hai gi tr chnh gia.
p
Lu rng
khng phi l gi tr ca trung v, n
ch l v tr ca trung v trong d liu c sp xp.
Modep p p p p
L mt i lng o tp trung. L gi tr thng xy ra nht. Khng b nh hng bi
cc im ngoi lai. C th s dng cho c d liu s v d liu phn loi. C th khng
tn ti mode hoc c nhiu mode.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
0 1 2 3 4 5 6
Khng c mode Mode = 9
Dng iu ca phn phip p
M t d liu phn b nh th no o ca dng iu (shape)n
i xng (Symmetric) hay bt i xng (skewed)
LeftMean < SkewedMedian
Symmetri Mean = cMedian
RightSkewed Median Sai s cng nh. Ch : khi n = 1 -> .
(1) C mu (n)
(2) bin thin ca tng th ( ) cng ln -> Sai s cng ln.
Phn phi mu ca trung bnhp p p
Theo nh l gii hn trung tm: phn phi ca trung bnh mu s hi t v phn
phi chun khi n tin ra v cng. (*) Khng nh trn ng ngay c khi mu c chn
t tng th khng phi l phn phi chun. Chn c mu nh th no?n n
n
Nu tng th c phn phi chun, mi n u tha. Nu tng th khng c phn phi
chun, nhng c phn phi i xng, c mu nh c th chp nhn c. Nu tng th khng
c phn phi chun v phn phi bt i xng, n phi ln, thng thng n 30.
Phn phi mu ca phng sai
Phn phi mu ca t lP = T l ca tng th c c tnh cn nghin cu. T l mu l
mt c lng ca t l P:
0
1c th xp x c phn phi
Phn phi ca chun.
Phn phi mu ca t lq
Tnh cht:
vq
Xp x chun:
q
Z ~ N(0,1) khi n .
Cc phn phi thng gp trong thng kp p p p
Phn phi chun. Phn phi Chi bnh phng. Phn phi Student. Phn phi
Fisher Snedecor.
Phn phi Chi bnh phngp
Xt Z1, Z2, ..., Zn l n bin ngu nhin c phn phi chun ha, tc l Zi ~
N(0,1) vi i=1,..,n. Z1, Z2, ..., Zn c lp vi nhau. t
p
p
i lng ngu nhin Y gi l c phn phi Chi bnh phng vi n bc t do. K
hiu:
p
Phn phi Chi bnh phng
Hm mt
Hm phn phi
Hm mt v hm phn phi ca phn phi Chi bnh phng vi cc bc t do Khc
nhau
Phn phi Studentp
p
Xt bin ngu nhin Z ~ N(0,1) v Y ~ 2(n); Z v Y c lp vi nhau. t
p p
i lng ngu nhin T gi l c phn phi Student vi n bc t do. K hiu: T ~
t(n)
Phn phi Student
Hm mt
Hm phn phi
Hm mt v hm phn phi ca phn phi Student vi cc bc t do Khc nhau
Phn phi Fisher - snedecorp
p
Xt bin ngu nhin Y1 ~ 2(m) v Y2 ~ 2(n); Y1 v Y2 c lp vi nhau.
t
p p
i lng ngu nhin F gi l c phn phi Fisher snedecor vi (m;n) bc t
do. K hiu: F ~ F (m;n)
Phn phi Fisher - snedecor
Hm mt
Hm phn phi
Hm mt v hm phn phi ca phn phi Fisher vi cc bc t do Khc nhau
