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N TP MN NGUYN L THNG KChng I: Cc khi nim vthut ng.
Phn tvi cc khong cch tbng nhau.
max mini i
i
X Xh
n
Trong :
ih : Trskhong cch t.
maxiX : Lng bin ln nht ca tiu thc phn t.
miniX : Lng bin nhnht ca tiu thc phn t.
n : Stcn chia.Cc bc phn tthng k:
Bc 1: La chn tiu thc phn t.Bc 2: Xc nh stcn phn v khong cch t.
Bc 3: Phn phi cc n vvo tng t.Chng II: nh gi thng k.
STT Tn Cng thcnv
Ch thch
1
Stngi ng
thi( T GT ),
(TLH
T )
1
0
T G
yT
y
1
iTLH
i
yT
y
%,pv
1y : Mc ca hin tng knghin cu.
0y : Mc ca hin tng kgc.
T GT : Stng i ng thi nh gc (Tc PT
nh gc).
TLH
T : Stng i ng thi lin hon (Tc PT
lin hon).
2
Stngi khoch( KHT ),
( TKT )
0
KHKH
yT
y
1TK
KH
yT
y
Hqu:
DT KH TKT T T
DTTK
KH
TT
T
DTKH
TK
TT
T
%,pv
KHT : Stng i nhim vkhoch.
TKT : Stng i hon thnh khoch.
KHy : Mc ca hin tng kkhoch.
0y : Mc thc tca chtiu kgc so snh.
1y : Mc ca hin tng kbo co.
3
Stngi kt
cu ( KCT )
bq
KC
TT
yT
y
%,pv
bqy : Mc ca bphn.
TTy : Mc ca tng th.
4
Stngi cng( CDT )
C
mT
n
% m : Mc ca hin tng cn nh gi phbin.n : Mc ca hin tng no c lin quan.
5
Stng
i khnggian( KGT )
1
2
KG
xT
x
%,
pv1x : Mc ca hin tng khng gian thnht
cn phn tch.2x : Mc ca hin tng khng gian thhai
dng lm c sso snh.
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6
Sbnhqun cnggin n
(X )
1
n
i
i
X
Xn
vti
X : Lng bin (i=1, 2, , n)
n : Sn vtrong tng th.
7
Sbnhqun cnggia quyn
(X )
1
1
n
i i
i
n
i
i
X f
Xf
vti
X : Lng bin (i=1, 2, , n)
i
f: Quyn s(Tn s)
i iX f : Gia quyn
8
Trsgia
( gX )
ax min
2m
g
X XX
(vi lng bin c khongcch t)
vtaxmX : Lng bin ln nht ca t.
minX : Lng bin nhnht ca t.
9
Sbnhqun
chung tcc s
bnh qunt(
tX )
1
1
k
i i
it k
i
i
X n
X
n
vti
X : Sbnh qun ti.
in : Quyn shoc sn vti.
K: Slng t.
10
Sbnhqun iuho giaquyn
(X )
1
1
n
i
i
ni
i i
M
XM
X
Khi c:
1 2 ... nM M M M
th:
1
1n
i i
nX
X
vti i iM X f : Gia quyn.
(Vn dng khi cha bit tn shay tn sn)
11
Sbnhqun nhngin n
(X )
1
1 2 3. . .....
n
ni
i
nn
X X
X X X X
vti
X : Lng bin (i=1, 2, 3,,n)
n : Sn v( Slng bin).
12
Sbnhqun nhngia quyn
(X )
1
21
1
1 2. .....
n
ii
i
n
i
ii
nff
i
i
ff f fn
n
X X
X X X
vti
X : Lng bin (i=1, 2, 3,,n)
if: Tn stngng.
13
Strung v(MEDIAN - eM)
+)Vi dy sclng bin khngc khong ccht:
*2 1, e qn k k N M x ( q l tgia) *2 ,
2
q p
e
x xn k k N M
( ,q p l tgia)
+)Vi dy slng bin ckhong cch t:
*Xc nh tcha eM : Cng dn tn sn khi no bng hoc vt qu2
if
th dng.
*Gi trgn ng ca strung vc xc nh theo cng thc:
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min
12
e
e e
e
i M
e M M
M
f SM X h
f
Trong :
mineMX : Gii hn di ca tcha trung v.
eM
h : Trskhong cch tca tcha trung v.
eMf :Tn sca tcha trung v.
1eMS : Tng tn sca tng trc tcha trung v.
1
n
i
i
f
: Tng tn s.
14
SMt (MODE - oM)
+)Vi dy slng bin khngc khong ccht:
axmo fM X
(Mt l lng bin ln nht trong dy lng bin)
+)Vi dy lngbin c khongcch t:
-)TH c khong cch tu nhau:
*Tcha mt l tc tn sln nht maxf
T .
*Gi trgn ng ca mt c tnh theo cng thc:
min1
1 1
o o
o o
o o o o
M M
o M M
M M M M
f fM X h
f f f f
Trong :
minoM
X :Gii hn di ca tcha Mt.
oMh : Trskhong cch tca tcha Mt.
oMf :Tn sca tcha Mt.
1oMf : Tn sca tng sau tcha Mt.
1oMf : Tn sca tng trc tcha Mt.
-)TH khong cch tkhng u nhau:
*Tcha Mt l tc mt phn phi l ln nht PPmax
MT .
i
iPP
i
fM
h
Trong :
iPPM : Mt phn phi ca ti.i
f: Tn sca ti.
ih : Trskhong cch tca ti.
*Gi trgn ng ca Mt c tnh:
min1
1 1
M Moo
o o
M M M Mo o o o
PP PP
o M M
PP PP PP PP
M MM X h
M M M M
Trong :
minoM
X :Gii hn di ca tcha Mt.
oM
h : Trskhong cch tca tcha Mt.
MoPPM : Mt phn phi tcha Mt.
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1MoPPM : Mt phn phi ttrn tcha Mt.
1MoPPM : Mt phn phi tdi tcha Mt.
15
Khongbin thin
(khong
chnh lch)(R )
ax minmR X X vt axmX : Lng bin ln nht.
minX : Lng bin nhnht.
16
lchtuyt i
bnh qun
( e )
+)TH khng c quyn s:
1
n
i
i
X X
en
+)TH c quyn s:
1
1
.n
i i
i
n
i
i
X X f
e
f
vti
X : Lng bin.
X : Trung bnh cng ca cc lng bin.
if: Tn s.
17Phng sai
( 2 )
+)TH khng c quyn s:
2
2 1
n
i
i
X X
n
+)TH c quyn s:
2
2 1
1
n
i i
i
n
i
i
X X f
f
iX : Lng bin.
X : Trung bnh cng ca cc lng bin.
if: Tn s.
18 lchchun ( )
2
19Hsbin
thin
100e
eV
X
100VX
20
Cc tham sbiu thhnh dng ca tham s:
Cch 1: So
snh 3 chtiu ctrng.
+)Nu ng cong phn phi i xng th:
e oX M M
+)Nu ng cong phn phi lch phi th:
e oX M M
+)Nu ng cong phn phi lch tri th:
e oX M M
Cch 2: Tnhhkhng ixng.
oA
X MK
*Khi AK >0 l phn phi lch phi.
*Khi AK
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Tng thchung vtng thmu
Chtiu Tng thchung Tng thmuQuy m N n
Sbnh qun X Tltheo mt tiu thc p f
Phng sai 2 2 2X 22 2
o X X
Phng sai ca tng thmu:
22
2 i i i i
o
i i
X n X n
n n
Cch chn ngu nhin slng n vca tng thmu ( n ):
+)Cch 1: Chn hon li (chn lp):
Slng mu khng hnh thnh: nQ N (mu)
+)Cch 2: Chn khng hon li (chn khng lp):
Slng mu c hnh thnh l:
!
! !
NQ
N n n
(mu)
-Vi 2, ,p l bnh qun, tl, phng sai ca tng thchung.
-Vi 2, ,i i iX f l bnh qun, tl, phng sai ca mu thi (i=1,2,3,,q)
Chn hon li(Chn nhiu ln) Chn khng hon li(Chn 1 ln)
Phng sai cc bnhqun mu
22
X n
22 1
X
n
n N
Phng sai cc tlmu
2 1f
p p
n
2 1 1fp p n
n N
-Kvng cc bnh qun mu: iE x
-Kvng cc tlmu: iE f p
Sai schn mu:
Cch chnSuy rng
Chn hon li(Chn nhiu ln)
Chn khng hon li(Chn 1 ln)
Bnh qun
Tng th2
X n
Tng th
2
1X
n
n N
Mu2
1
o
X n
Mu
2
11
o
X
n
n N
Tl Tng th 1
p
p p
n
Tng th
11
p
p p n
n N
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Mu 1
1f
f f
n
Mu
11
1f
f f n
n N
, pX : Cc sai sbnh qun chn mu khi c lng sbnh qun v tl.
Bi ton c bn ca iu tra chn mu.
*Cng thc tng qut:
. 2
. 2
X X
p p
P X z z
P f p z z
(*)
Vi.
..
X X
p f
zz
z
(**)
-i lng .X Xz v .p fz c gi l phm vi sai schn mu, zc gi l hstin cy.
-Nu 30n th ,i iX fc xem nh phn phi chun vi 2
2
0
1
2
tz
z e dt
. Cc gi trca hm c
cho bng tnh sn (Bng phn phi chun ho N(0:1)).
-Nu 30n thi
X c xem nh phn phi theo quy lut Student.
Dng T n Tm tt Cch gii
Biton 1
Suy rng tiliu iu trachn mu.
Bi ton tm&p bit
...P a
Tgithit tnh (*) v (**) :+)Suy rng bnh qun:
X XX X
+)Suy rng tl:
p pf p f
Bi
ton 2
Tm xc sut(tin cy)khi suy rngti liu iutra chnmu.
Bi ton tm
... ?P bit
&X p
Tcng thc (**) ta c:
? ... 2 ?
X
X
p
f
z
z P z
z
Trong :
X : Phm vi sai schn mu bnh qun.
p : Phm vi sai schn mu tl.
z: Hstin cy.
Biton 3
Tnh slng n vtng thmu( n )
Bi ton tm n
bit ...P av
Theo githit ta suy ra:
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2
2
2
2
... 2 ? ?
?
X X
p p
o
P z z z
n
f
Vi n c tnh nh sau:Suy rng Chn hon li Chn khng hon li
Bnhqun
2 2
2
X
zn
2 2
2 2 2
X
Nzn
N z
Tl 2
2
1
p
z p pn
2
2 2
1
1p
Nz p pn
N z p p
Nu hin tng nghin cu c phn phi chun th c thc tnh lch tiu chun theo khong bin thin:
Ta c: ax min 3 3mR X X
Theo quy tc 3 , nu 2,x N th hu ht cc gi trX sai lch vi khng qu 3 ln
ax min
6
mX X
Cc phng php chn mu ngu nhin
Chn mu ngu nhin n gin
Chn lp Chn khng lp Ch gii
22
X X n
2 1
X
n
N
n
2
o : Phng sai ca tng thmu iu tra.
2 : Phng sai ca tng thchung.n : Sn vca tng thmu.N : Sn vca tng thchung.2
1
o
X n
2 1
1
o
X
n
N
n
Chn mu hthng (chn my mc)
Nd
n
Trong :d: Khong cch chn.N : Slng n vtng thchung.n : Slng n vtng thmu.
Chn mu phn loi (phn loi)
Cng thc tnh sai sbnh qun chn mu:
Cch 1: Chia u slng cc n vca tng thmu cho st( in )
Chn lp Chn khng lp
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Suy rngbnh qun
2 21 i iX
i
N
N n
2 211i i i
X
i i
N n
N n N
Suy rngtl
211 i i if
i
p p N
N n
2111i i i i
f
i i
p p N n
N n N
Trong : i : Sai sbnh qun chn mu ca ti.
iN : Sn vtrong ti.
Cch 2: Chia slng n vca tng thmu theo tlslng n vca tng ttrong tng thchung.Slng n vtng thmu c chia cho stth i l:
ii
Nn n
N
Chn lp Chn khng lp ViSuy rng
bnh qun
2
X n
2
1X
n
n N
2
2 i i
i
N
N
Suy rngtl
1f
p p
n
11f
p p n
n N
11
i i
i
p p Np p
N
Cch 3: Chia slng n vca tng thmu theo tlslng n vca tng ttrong tng thchungv lch chun ca tng ttrong tng thchung. Slng n vtng thmu c chia cho stth il:
i ii
i i
Nn nN
Chn lp Chn khng lp
Suy rngbnh qun
2 21 i i
X
N
N n
2 21
1i i
X
N n
N n N
Suy rngtl
11 i i if
p p N
N n
111
i i i
f
p p N n
N n N
Chn mu ckhi (mu chm)
Cng thc Ch gii
Suyrngbnhqun
2
1
X
X
R r
r R
+) Nu sn vcc khi khng bng nhau:
2
2.i i i
X
i
x x n
n
+)Nu sn vcc khi bng nhau:
2
2 i
X
x x
r
2
X : Phng sai gia cc sbnh qun khi
c chn.
ix : Sbnh qun ca mi khi c chn
(i=1,2,,r).
x : Sbnh qun ca cc khi c chn.
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Suyrng t
l
11
r r
f
f f R r
r R
+)Nu sn vcc khi khng bng nhau:
i i
r
i
f nf
n
+)Nu sn vcc khi bng nhau:
i
r
ff
r
rf : Tlbnh qun ca cc khi c chn.
Vi 1,2,...,i r l tlca mi khi cchn.
Chng IV: KIM NH GITHUYT
Githuyt thng k.
Cp githuyt:
0
1 0
H : Gi thuyt gc
H : Gi thuyt i ca H
TH Cng thc Hnh minh ho Ni dungKimnh 2pha
0 0
1 0
:
:
H
H
Bc bgithuyt 0H khi tham sc trng
ca mu cao hn hoc thp hn so vi githit vtng thchung. Min bc bnm pha tri v pha phi ca ng phn phi.
Kimnhphatri
0 0
1 0
:
:
H
H
Bc bgithuyt 0H khi tham sc trng
ca mu nhhn mt cch ng kso vigi trca githuyt 0H . Min bc bnm
ph tri ca ng phn phi.Kim
nhphaphi
0 0
1 0
:
:
H
H
Bc bgithuyt0
H khi tham sc trng
ca mu ln hn mt cch ng kso vi gitrgithuyt 0H . Min bc bnm pha
phi ca ng phn phi.Sai lm v mc ngha trongkim nh.
Khi la chn gia 2 githuyt 0 1&H H ta c thmc phi 2 loi sai lm sau:
Sai lm loi 1: Bc bgithuyt 0H khi githuyt ny ng. Sai lm loi 2: Tha nhn gia thuyt 0H khi n sai. (nguy him hn v sai li tha nhn l ng).
Kt lunThc t
Chp nhn 0H Chp nhn 1H
0H ng Kt lun ng Sai lm loi 1
0H sai Sai lm loi 2 Kt lun ng
: Mc ngha (Xc sut mc sai lm loi 1).
: Mc ngha (Xc sut mc sai lm loi 2).
1 : Lc lng ca kim nh (Xc sut bc b 0H khi 0H sai)
Thng thng, c ly bng 0,01 (1%), 0,02 (2%), 0,05 (5%), Tmc ngha kim nh c thxc
nh min bc bgithuyt 0H v min tha nhn.
Mi n tha nhn
Mi n tha nhn
Mi n tha nhn
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CC BC TIN HNH KIM NH GITHUYT THNG K:
1. Xy dng cp githuyt: 0H v 1H .2. Xc nh mc ngha (Xc sut mc sai lm loi 1).3. Chn tiu chun kim nh.4. Tnh gi trtiu chun kim nh (z)
Kt lun:
Nu Z min bc b: Bc b 0H , chp nhn 1H . Nu Z min bc b: cha c sbc b 0H (chp nhn githuyt 0H ).
KIM NH V SO SNH STRUNG BNH
*)Kim nh githuyt vgi trtrung bnh ca 1 tng thchung.
1
Phng sai ca tng thchung bit (
2
bit)Tiu chun kim nh:
0
X nZ
i lng (Z) phn phi theo quy lut chun ho N(0,1), c cc TH sau:Kim nhpha phi
0 0
1 0
:
:
H
H
Nu 0,5Z Z Bc b 0H , chp
nhn 1H
Kim nhpha tri
0 0
1 0
:
:
H
H
Nu 0,5 Z Z Bc b 0H , chp
nhn 1H
Kim nhhai pha
0 0
1 0
:
:
H
H
Nu 0,5 2Z Z Bc b 0H , chp
nhn 1H
2
Phng sai ca tng thchung cha bit ( 2 cha bit), mu ln ( 30)n Tiu thc kim nh:
00
X nZ
Vi 20 01
n
n
0 : lch tiu chun mu
iu chnh.
Kt lun: (nh phn trn)
3
Phng sai ca tng thchung cha bit (
2
cha bit), mu nh ( 30)n Tiu thc kim nh:
0
X nt
S
Vi S(hay 0 ): lch
chun mu iu chnh.
i lng ( t) sphn phi theo quy lut Student vi 1n bc tdo, ccc TH sau:
Kim nhpha phi
0 0
1 0
:
:
H
H
Nu , 1 nt t Bc b 0H , chp
nhn 1H
Kim nhpha tri
0 0
1 0
:
:
H
H
Nu , 1 nt t Bc b 0H , chp
nhn 1H
Kim nhhai pha
0 0
1 0
:
:
H
H
Nu 2, 1 nt t Bc b 0H , chp
nhn 1H *)Kim nh 2 gi trtr ung bnh ca 2 tng thchung (2 mu c lp)
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1 bit phng sai ca 2 tng thchung ( 2 21 2
, bit)
Tiu thc kim nh:
1 2
2 2
1 2
1 2
X XZ
n n
2
1 1 1
2
2 2 2
,
,
X N
X N
, c cc TH sau:
Kim nh
pha phi
0 0
1 0
:
:
H
H
Nu 0,5Z Z Bc b 0H ,
chp nhn 1H
Kim nhpha tri
0 0
1 0
:
:
H
H
Nu 0,5 Z Z Bc b 0H ,
chp nhn 1H
Kim nhhai pha
0 0
1 0
:
:
H
H
Nu
0,5 2Z Z Bc b 0H ,
chp nhn 1H
2 bit phng sai ca 2 tng thchung, mu ln ( 2 21 2
, bit; 1 230, 30 n n )
Tiu thc kim nh:
1 2
1 2
2 2
0 0
1 2
X X
Z
n n
Kt lun: (nh phn trn)
3 Cha bit phng sai ca 2 tng thchung, mu nh( 2 21 2, cha bit; 1 230, 30 n n )
Tiu thc kim nh:
1 2
2 2
1 2
X Xt
s s
n n
1 2
2
1 2
1 1
X X
sn n
;
Vi 2s l gi trchung ca 2
phng sai mu1 2
2 2
0 0, :
1 2
2 2
1 0 2 02
1 2
1 1
2
n ns
n n
C2 tng thchung c phn phi chun th tc phn phi Student
vi 1 2 2 n n bc tdo, c cc TH sau:Kim nhpha phi
0 0
1 0
:
:
H
H
Nu
1 2, 2
n nt t
Bc b 0H ,
chp nhn 1H
Kim nh
pha tri0 0
1 0
:
:
H
H
Nu
1 2, 2 n nt t
Bc b 0H ,
chp nhn 1H
Kim nhhai pha
0 0
1 0
:
:
H
H
Nu
1 22, 2
n nt t
Bc b 0H ,
chp nhn 1H
*)Kim nh 2 gi trtr ung bnh ca 2 tng thchung ( 2 mu phthuc)
So snh 1 2, Xt lch trung bnh d .
Tiu chun kim nh: 0
0
d
d nt
Trong :22
2
0 0
.
1 1 1
d d
i
i
dd
n
dn n d
n n n
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2
1 1 1
2
2 2 2
,
,
X N
X N
, c cc TH sau:
Kim nhpha phi
0 0
1 0
:
:
H
H
Nu
, 1 nt t Bc b 0H , chp
nhn 1H Kim nhpha tri
0 0
1 0
:
:
H
H
Nu , 1 nt t Bc b 0H , chp
nhn 1H
Kim nhhai pha
0 0
1 0
:
:
H
H
Nu 2, 1
n
t t
Bc b 0H , chp
nhn 1H
*)Kim nh tl(p)
1 Kim nh githuyt vtlca tng thchung
K p dng: n ln 0 0. 5 1 5 n p n p Tiu thc kim nh:
0
0 01
f p nZ
p p
Vi xn
fn
Ta c cc TH sau:Kim nhpha phi
0 0
1 0
:
:
H
H
Nu 0,5Z Z Bc b 0H , chp
nhn 1H
Kim nhpha tri
0 0
1 0
:
:
H
H
Nu 0,5 Z Z Bc b 0H , chp
nhn 1H
Kim nhhai pha
0 0
1 0
:
:
H
H
Nu
0,5 2Z Z Bc b 0H , chp
nhn 1H
2 Kim nh 2 tlca 2 tng thchung
K p dng: Khi 1 2,n n ln 1 1 1 1 2 2 2 2; 1 ; ; 1 5 n f n f n f n f Zphn phi chun (0,1)N
Tiu thc kim nh:
1 2
1 2
1 11
f fZ
f fn n
Vi:
1 21 1 2 2
1 2 1 2
x x
n nn f n f f
n n n n
xk
k
k
nf
n
Zvn c phn phi xp xchun N(0,1). Vi mc ngha cho trc, tavn kt lun nh trn.
Chng V: Dy sthi gian
SBNH QUN CNG THEO THI GIAN
1
Dy sthi k
1
n
i
i
y
yn
Trong :( 1,2,..., )iy i n :Mc thi.
n : Sthi k.
2 Dy sthi im TH khong cch thi gian bng nhau
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12 1...
2 2
1
nn
yyy y
yn
Trong :( 1,2,..., )iy i n :Mc thi.
n : Sthi k.
TH khong cch thi gian khng bng nhau1
1
.n
i i
in
i
i
y t
y
t
Trong :( 1,2,..., )
i
y i n :Mc thi.
n : Sthi k.
it : khong thi gian c mc iy .
LNG TNG (GIM) TUYT I
1
Lng tng (gim) tuyt i lin hon
1i i iy y iy : Mc tuyt i thi gian
( 2,3,..., )i i n .
1iy : Mc tuyt i thi gian 1i
+) 1i iy y th 0i : Phn nh quy m
hin tng tng.+) 1i iy y th 0i : Phn nh quy m
hin tng gim.
2Lng tng (gim) tuyt i nh gc
1i iy y i
y : Mc tuyt i thi gian ( 2,3,..., )i i n .
1y : Mc tuyt i thi ku.
3
Lng tng (gim) tuyt i bnh qun
2 1
1 1 1
n
i
i n ny y
n n n
Chtiu ny c ngha khi cc lng tng (gim) tuyt i lin honxp xnhau, ngha l trong sut thi knghin cu, hin tng tng(gim) vi mt lng tng i u.
4
Mi lin hgia lng tng (gim) tuyt i lin hon v lng tng (gim) tuyt i nh gc.
1
n
i n
i
TC PHT TRIN
1
Tc pht trin lin hon
1
ii
i
yt
y i
y : Mc tuyt i thi gian ( 2,3,..., )i i n .
1iy : Mc tuyt i thi gian 1i
2
Tc pht trin nh gc
1
ii
yT
y i
y : Mc tuyt i thi gian ( 2,3,..., )i i n .
1y : Mc tuyt i thi ku.
3
Tc pht trin bnh qun
1 11 12 3
2 1
. .....n
nn nn ni n i n
i
yt t t t t T
y
Chtiu ny c ngha khi cc tc pht trin linhon xp xnhau, ngha l trong sut thi knghin cu,tc pht trin vi mt lng tng i u.
4
Mi lin hgia tc pht trin lin hon v tc pht trin nh gc.
2
n
i n
i
t T
5
Thng ca 2 tc pht trin nh gc lin nhau
1
ii
i
Tt
T
TC TNG (GIM) TNG I
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1 Tc tng (gim) tng i lin hon1
1 1
1i i ii ii i
y ya t
y y
100i ia t
2 Tc tng (gim) tng i nh gc1
1 1
1i ii iy y
A Ty y
100i iA T
3 Tc tng (gim) tng i bnh qun 1i ia t (ln) 100i ia t (%)
STNG (GIM) TUYT I NG VI 1% TC TNG (GIM) LIN HON
1
1
(%) 100.100
i i ii
ii
i
yg
a
y
STNG (GIM) TUYT I NG VI 1% TC TNG (GIM) NH GC
1 1
1
.ons
.100 100.100
i ii
i i
y yg c t
y
PHNG PHP SBNH QUN DI NG (SBNH QUN TRT)
-Nu tnh sbnh qun trt cho nhm 3 mc , sc:
1
1 2 32 2
2 3 43 3
2 11 1
( ) :
( ) :3
( ) :
3...
( ) :3
( ) :
n n nn n
n
y
y y yy y
y y yy y
y y yy y
y
-Nu tnh sbnh qun trt cho nhm 4 mc , sc:
1
2
1 2 3 43 3
2 3 4 54 4
4 3 2 12 2
3 2 11 1
( ) :
( ) :
( ) :4
( ) :4
...
( ) :4
( ) :4
( ) :
n n n nn n
n n n nn n
n
y
y
y y y yy y
y y y yy y
y y y yy y
y y y yy y
y
Tng tvi cc TH khc.
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PHNG PHP BIN NG THI V
Chsthi v:
0
i
TVi
y
I y
Trong :
TViI : Chsthi vca thi gian i .
iy : Strung bnh cc mc ca cc thi gian cng tn i .
0y : Strung bnh ca tt ccc mc trong dy s.
CC PHNG PHP DON THNG K NGN HN (di 3 nm)
1 Don da vo lng tng (gim) tuyt i bnh qunM hnh don:
.n L ny y L
Vi 11
ny y
n
Trong :
ny : Mc cui cng trong dy sthi gian
: Lng tng (gim) tuyt i bnh qun.L : Thi gian don (tm xa don).
2 Don da vo tc pht trin bnh qunM hnh don:
( )Ln L ny y t
Vi 11
nn
yt
y
Trong :
ny : Mc cui cng trong dy sthi gian
: Lng tng (gim) tuyt i bnh qun.L : Thi gian don (tm xa don).
t: Tc pht trin bnh qun.3 Don da vo hm xu th
-)T Ptr ng thng: xy a bx
-)Vn dng trong dy sthi gian ta c Ptr: ty a bt
-)Xc nh ,a b
CCH 1: p dng phng php bnh phng nhnht gii Hpt:
2
y na b t
ty a t b t
CCH 2:
2
.
t
a y bt
ty t yb
M hnh don: n Ly a b t L
PHN TCH CC THNH PHN CA DY STHI GIAN
+)Kt hp cng: t t t t y f s z .
+)Kt hp nhn: . .t t t t y f s z .
Trong :+) Xu th:
tf.
+) Thi v: ts .
+)Ngu nhin: tz .
+)Hm xu thc dng: . if t t T
0 1tf a a t Vi 1,2,3,...t thtthi gian trong dy s.
1 2
12 1
2.. 1
S na T
m mm n n
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n : Snm.
m : Squ trong nm 4m
0 1
. 1
. 2
T m na a
m n
1 Phn tch cc thnh phn theo kt hp cngSdng cc cng thc sau:
0 1
1
2t j j
ms s y y a j
vi 1,2,3,4j
t t t t z y f s
iT T . iS t T
04
iyy
i
i
yy
n
2 Phn tch cc thnh phn theo kt hp nhnSdng cc cng thc sau:
.t js s H
j
mH
s
tj
t
ys y
tt
t
yy
s
.
tt
t t
yz
f s
Chng VI: Chs
PHNG PHP CHS
+)Phng php chscc th i :
Chsc thvcht lng
1
0
p
pi
p
Stuyt i: 1 0p p p
Trong :
1p : Gi chng ho kbo co.
0p : Gi chng ho kgc.
1q : Lng hng ho bn ra kbo co.
0q : Lng hng ho bn ra kgc.Chsc thv
slng
1
0
q
qi
q
Stuyt i: 1 0q q q
+) Phng php chschung I :
Chstng hp vgi
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1
0
.
.P
p qI
p q
Trong :
PI : Chstng hp gi c.
1p : Gi bn bnh qun 1vsp knghin cu.
0p : Gi bn bnh qun 1vsp kgc.
q : Lng hng ha tiu th.
1.Chstng hp gi cLaspeyres 1 0
0 0
.
.
L
p
p qI
p q
Vi: 1
0
p
pi
p 1 0.pp i p nn ta c:
1 0
0 0
. .
.
pL
p
i p qI
p q
2.Chstng hp gi cPassche1 1
0 1
.
.
P
P
p qI
p q
Vi: 1
0
p
pi
p 10
p
ppi
nn ta c:
1 1
0 1
.
.P
P
p
p qI
p q
i
Chstng hp vlng hng ha tiu th
1
0
.
.q
q pI
q p
Trong :
qI : Chstng hp lng hng tiu th.
1q v 0q : Lng hng ha tiu thknghin cu v kgc.
p : Gi bn bnh qun 1 vhh.1.Chstng hp lng hng hatiu thLaspeyres
1 0
0 0
.
.
L
q
q pI
q p
2.Chstng hp lng hng hatiu thPassche
1 1
0 1
.
.
p
q
q pI
q p
Vi: 1
2
q
qi
q 10
q
qq
i nn ta c:
1 1
1 1
.
.q
q
q p
I q p
i
*)Phng php chslin hp:
1
0
.
.X
X YI
X Y
Trong :
XI : Chschung ca chtiu X.
1X : Chtiu knghin cu.
0X : Chtiu kgc so snh.
Y: Chtiu ghp to ra chtiu lin hp.Quy tc: Trong phn tch thng k, mun nghin cu sbin ng ca chtiu cht lng th quyn sthng l chtiu slng c lin quan c cnh knghin cu. Mun nghin cu sbin ng cachtiu slng th quyn sthng l chie tiu cht lng c lin quan c cnh kgc.
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-)Chslin hp cht lng:
1 1
0 1
.
.p
p qI
p q
1 1 0 0. .pq p q p q 1 1 0 00 0 0 0
. .%
. .
pq
pq
p q p q
p q p q
-)Chslin hp vslng:
0 1
0 0
.
.q
p qI
p q
0 1 0 0. .pq p q p q 0 1 0 00 0 0 0
. .%
. .
pq
pq
p q p q
p q p q
*)Phng php chstheo chtiu bnh qun:
1
0
X
XI
X
Trong :
XI : Chtiu bnh qun ca chtiu X.
1X : Mc bnh qun ca chtiu nghin cu knghin cu.
0X :Mc bnh qun ca chtiu nghin cu kgc.
-)Chtiu gi bnh qun ( p ):
1 1 01
0 0 0 1
.
.pp q qp
Ip p q q
Vi:
1 1 1
1
1 1
.p q pp
q q
; 0 0 00
0 0
.p q pp
q q
1 0p p p
0
% p
pp
Vi knghin cu:
1 0 1.pq p p q
1 0 10 0 0 0
.%
. .
pq
pq
p p q
p q p q
-)Chtiu sn lng bnh qun ( q ):
Mc gi ging nhau
11
00
q
qqI
qq
;
Vi:
1
1
qq
n
; 00
qq
n
Mc gi khc nhau:
1
0q
qI
q
Vi:
1 1
1
1
.p qq
p
; 0 00
0
.p qq
p
Kgc
1 0 0pq q q p 1 0 00 0 0 0
%. .
pq
pq
q q p
p q p q
HTHNG CHS
*)Phng trnh kinh t:
D P Q D : Doanh thu.P: Gi bn.
Q : Sn lng.WQ N Q : Sn lng sn xut.
W : Nng sut lao ng.
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N : Snhn cng, lao ng (ngi).F L N F : Qutin lng.
L : n gi lng trn 1 cng nhn.N : Snhn cng, lao ng (ngi).
C z Q C: Chi ph sn xut.z: Gi thnh n vsn phm.
Q : Sn lng sn xut.* )Hthng chsca chspht trin:
Chspht trin = Chshon thnh khoch Chsnhim vkhoch
Chspht trin doanh thu:
1 1 1 1 1
0 0 1 0 0
. . .
. . .
KH
KH
p q p q p q
p q p q p q
* )Hthng chsca chspht trin:
Chsdoanh thu = Chsgi cChslng bn ra.
.pq p qI I I
1 1 1 1 0 1
0 0 0 1 0 0
. . .
. . .
p q p q p q
p q p q p q
+)Stuyt i:
1 1 0 0 1 0 1 0 1 0 0. . . . . .pq p q p q p q p q p q p q
+)Stng i:
1 1 0 0 1 1 0 1 0 1 0 0
0 0 0 0 0 0
. .% pq
p q p q p q p q p q p q
p q p q p q
Xt TH Qutin lngc 2 nhn tnh hng ta c:
F L NI I I
1 11
0 0 0
.
.F
L NFI
F L N
Phn tch 2 nhn tnh hng:
011 1
0 01 0
F
FF FI
F F F
Vi: 01 0 1.F L N
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1 0 1 1 0 1
0 0 0 1 0 0
. . .
. . .F
L N L N L NI
L N L N L N
+)Stuyt i:
1 0 1 01 01 0F F F F F F F
+)Stng i:
1 0 1 01 01 0
0 0 0
% F F F F F F
FF F F
Xt TH Sn lng sn xut ra chu 3 nhn tnh hng:
1 1 1011
0 0 001 0
W . WW
W . W WQ
N NI
N N
Vi: 1 111
W .W
N
N
0 1
01
1
W .W
N
N
0 0
0
0
W .W
N
N
+)Stuyt i:
1 1 0 0 1 01 1 01 0 1 1 0 1W . W . W W . W W . .WQ N N N N N N
+)Stng i:
0 1 1 01 0 1 1 0 01 1 0 00 0 0 0 0 1 1 0
W W . W W . .WW . W .%
W . W . W . W .
N N N NN NQ
N N N N
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