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PT D LIU KH BNG CHNG TRNH MS-EXEL 1
B MN TON GVGD: Nguyn nh Huy
Chng 1
P DNG MS-EXCEL
TRONG THNG K M T
Tnh cc gi tr thng k m t
Xc nh v chnh xc
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PT D LIU KH BNG CHNG TRNH MS-EXEL 2
B MN TON GVGD: Nguyn nh Huy
A- TNH TON GI TR THNG K M T
3.1 Khi nim thng k
3.1.1 Gi tr trung bnh (Mean, Average)
Mt ngi t sn bn mt con vt bng hai lot n, mi lot gm 5 vin. Lot th nht
cch con vt mt mt v pha trc, lot th hai cch con vt mt mt v pha sau. Trn thc t
con vt cha cht nhng theo kt qu trung bnh th con vt cht. Ci m ngi th sn cn
bn mt pht trng con vt c nui mi, ci m nh khoa hc cn thng thng l s c
tnh c gi tr trung bnh.
Gi tr trung bnh l gi tr thng k m t hay c dng nht m t c tnh ca mt
mu t dn s. Gi s bn c mt mu gm N gi tr quan st c sp xp thnh mt chui
thng k: X1, X2, X3, , XN
Gi tr trung bnh ca mu c tnh bi biu thc:
Cng thc: N
X
X
N
i
i 1
Gi tr trung bnh ca mu, X , l tr s c tnh ca gi tr trung bnh thc s ca dn s .
Th d 3: Khi lng trung bnh (mg) ca 9 vin nn thuc l A
201, 203, 209, 204, 202, 206, 200, 207, 207
mgX 33,2049
1839
Th d 4: Khi lng trung bnh (mg) ca chnh vin nn thuc l B:
151, 153, 259, 154, 202, 256, 150, 257, 257
mgX 33,2049
18390
3.1.2 Gi tr trung v (Median)
Gi tr trung v din t khi nim trung tam ca chui d liu. Nu mt chui d liu c N
gi tr quan st c sp xp t nh n ln th gi tr trung v s th t (N + 1). Trong th d th
3, gi tr trung v l s th 5:
1 2 3 4 5 6 7 8 9
200, 201, 202, 203, 204, 256, 207, 207, 209
S th t th 2
)19(5
3.1.3 Khong kho st
L s khc bit gia hai gi tr quan st: ln nht v nh nht: r = Max Min
Trong th d 3: r = 209 200 = 9; trong th d 4: r = 259 150 = 109. Vy cc chui d
liu c th c khong quan st khc nhau cho d chng c cng gi tr trung bnh. Nu khong
quan st ln phn tn s cao.
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PT D LIU KH BNG CHNG TRNH MS-EXEL 3
B MN TON GVGD: Nguyn nh Huy
3.1.4 lch chun (Standarl Deviation)
phn tn d liu thng c din t bi phng sai (Variance) hai lch chun (cn
s bc 2 c phng sai):
)1(
)(1
2
N
XX
SD
N
i
i
Trong th d 3: S = 3,08; trong th d 4: S = 52,65. phn tn ca d liu trong th d 4
cao hn phn tn ca d liu trong th d 3:
3.1.5 Sai s chun gi tr trung bnh (Std. error of the mean)
Gi tr trung bnh ca mu gn bng gi tr trung bnh ca dn s hn l cc gi tr quan st
ring bit.
N
SSXSDSEM
X )(
Trong th d 3: SEM = 1,03; trong th d 4: SEM = 17,55
Khi c mu cng ln (N tng) th gi tr trung bnh cng gn
3.1.6 Gii hn v khong tin cy
Vi mt mc tin cy (Confidence level) nht nh l gii hn tin cy (confidence limits)
ca mt gi tr trung bnh c cho bi tch s:
XSt : (N < 30: phn phi Student)
X -X
St : Gii hn di (LCL: lower control limit)
X +X
St : Gii hn trn (LCL: upper control limit)
v khong tin cy (Confidence interval) ca gi tr trung bnh l:
XXXX
StXStXStXStX ,,( n XStX
Trong th d 3: 2,37X
t S ; Trong th d 4: 40,47Xt S
Gi tr thng k t (phn phi Student) cn c thay i bi gi tr thng k, z (phn phi
chun) trong trng hp mu ln (N > 30)
Lu : Cng c phn tch Deseriptive Statistics trong chng trnh MS-EXCEL ch p dng
cho mu nh. trong trng hp mu ln, bn phi tnh li tch s X
St , vi t c tra trong bng
tch phn Laplace.
3.1.7 H s phn tn (Coefficient of variatio)
H s phn tn cn c gi l sai s tng i (relative deviation): 100X
SCV
Trong th d 3: CV = 1,50%; trong th d 4: CV = 25,77%
H s phn tn c lin qujan n chun (cng nh chnh xc ca phng php o
lng) v gi tr trung bnh ca cc kt qu.
3.1.8 Gi tr yu v (Mode)
Gi tr yu v l gi tr c tn s cao nht trong mt chui d liu. trong th d 3: gi tr yu
v l 207; trong th d 4: gi tr yu v l 257.
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PT D LIU KH BNG CHNG TRNH MS-EXEL 4
B MN TON GVGD: Nguyn nh Huy
3.1.9 Gi tr KURT (Kurtosis)
Gi tr KURT din t c im thuc v nh ca dng phn phi d liu. Gi tr s dng d
liu phn phi tng i c nh. Ngc lai, c gi tr m khi d liu phn phi tng i phng.
)3)(2(
)1(3
)3)(2)(1(
)1( 21
NN
N
S
XX
NNN
NNKURT
3.1.10 Gi tr SKEW (Skewness)
Gi tr SKEW phn nh mc bt i xng ca dng phn phi d liu xung quanh gi
tr trung bnh. Gi tr SKEW c gi tr dng khi d liu phn phi bt i xng vi ui nm
lch v pha gi tr dng. Ngc li, n c gi tr m d liu phn phi bt i xng ui nm
lch v pha cc gi tr m.
S
XX
NN
NSKEM 1
)2)(1(
3.2 p dng MS-EXCEL
Hy tnh khong tin cy vi mc = 0,01, lch chun v h phn tn ca hai chui d liu
trong th d 3 v th d 4:
3.2.1 Nhp d liu vo bng tnh
A B C D E F G H I J
1 TD3 201 203 209 204 202 206 200 207 207
2 TD4 151 153 259 154 202 256 150 257 257
3.2.2 p dng Descriptive statistics
a- Nhp ln lt dn lch Tools v lch Data Analysis
b- Chn chng trnh Descriptive statistics trong hp thoi Data Analysis ri nhp nt OK
Hnh hp th thoi data Analysis
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PT D LIU KH BNG CHNG TRNH MS-EXEL 5
B MN TON GVGD: Nguyn nh Huy
c- Trong hp th thoi Data Analysis, n nh ln lt cc chi tit:
- Phm vi u vo (Input Range),
- Cch sp xp theo hng hay ct (Group By),
- Nhn d liu (Labels in Fisrt Row/Column),
- Mc tin cy (Confidence Level),
- Phm vi u ra (Output Range),
- Kt qu tm tc (Summary Satt.istics).
3.2.3 Tnh cc gi tr thng k
T u ra ca MS-EXCEL, bn phi tnh gii hn tin cy X
St ng thi tnh thm h s
phn tn 100X
SCV bng cch:
- Chn B18 trong bng tnh cha u ra ca MS-EXCEL, nhp biu thc = 2.306*B4 dng con
tr ko nt t iu n D18 (2,306: gi tr ca t vi = 0,05; B4: ta ca gi tr X
S ).
- Chn B19 trong bng tnh cha u ra ca MS-EXCEL, nhp biu thc 1003
7x
B
B
ri dng
con tr ko nt t iu n D19 (B7: ta ca gi tr S; B3: ta ca gi tr X ).
A B C D
1 TD3 TD4
2
3 Mean 204.3333333 Mean 204.3333333
4 Standard Error 1.027402334 Standard Error 17.54992877
5 Median 204 Median 202
6 Mode 207 Mode 257
7 Standard Deviation 3.082207001 Standard Deviation 52.64978632
8 Sample variance 9.5 Sample variance 2772
9 Kurtosis -1.330431342 Kurtosis -2.423671859
10 Skewness 0.058546077 Skewness 0.020438933
11 Range 9 Range 109
12 Minimum 200 Minimum 150
13 Maximum 209 Maximum 259
14 Sum 1839 Sum 1839
15 Count 9 count 9
16 Confidence Level (95.0 2.369189782 Confidence Level (95.0 4047020829
17
18
19
Kt qu:
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PT D LIU KH BNG CHNG TRNH MS-EXEL 6
B MN TON GVGD: Nguyn nh Huy
Gi tr thng k Th d 3 Th d 4
Gii hn tin cy 95% )(X
StX 204,33 2,37 204,33 40,47
lch chun (S) 3,08 52,65
H s phn tn 1,50% 25,77%
Lu : Trong thc t, d liu c khi khng ng nht nn lch chun S v h s phn
tan CV c gi tr ln. D liu c th c chuyn dng mt cch ph hp phn phi c
ng nht hn.
S chuyn dng Logrit (Log transformation)
Dng logarit (log, c s 10 hay ln, c s e) ca X hay 1/X thng c p dng khi d liu
c gi tr SKEW dng v gi tr trung bnh X t l thun vi lch chun S. Th d:
0,3 12 7 0,41 21 12 4 10 17 9 0,7 6 23 5,7;42,9( SX
D liu X S
Dng log (X) 0,71 -0,71
Dng log (1/X) 0,64 0,64
S chuyn dng cn s (Square-root transformation)
Dng cn s bc hai cu X ph hp hn dng logarit tng ng khi chui d liu c nhiu gi
tr nh. Nu chui d liu c cc s < 10 hay o th nn dng dng cn s ca (X + 1). Th d:
0 11 7 4 0 12 4 2 7 9 3 0 12 5 8 10 5,7;42,9( SX
D liu X S
Dng X 2,12 1,21
Dng 1X 2,14 0,92
Cc gi tr nh xc xut hay t s hoc t l (di hnh thc s l thp phn) c th c chuyn
Dng arcsin (Arcsine transformation), P
Cc gi thng k m t ca d liu c chuyn dng s khc vi d liu nguyn thy.
Bn nn thn trng khi chuyn dng v iu ny c th nh hng n kt qu ca cc trc
nghim thng k suy l (so snh hai gi tr trung bnh, so snh hai t s, s snh hai phng sai).
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PT D LIU KH BNG CHNG TRNH MS-EXEL 7
B MN TON GVGD: Nguyn nh Huy
B- XC NH NG V CHNH XC
3.3 Khi nim thng k
A: chnh xc, khng ng B: Khng chnh xc, khng ng
C: Chnh xc, ng D: Khng chnh xc, khng ng
chnh xc (Precision): lp li ca cc gi tr quan st
1001100
X
SCVP
ng (Accuracy): trng hp gia cc gi tr quan st (hay thc nghim) vi gi tr l thuyt.
100thuy h
ltriGi
bnhtrungtriGiA
chnh xc v ng phn nh cht lng ca mt phng php o lng. mt phng
php tt va chnh xc va ng.
p dng MS-EXCEL
Th d 5: ngi ta xc nh hm lng hot cht trong mt mu thuc bng cch tin hnh
song song 10 ln trong hai iu kin; mu khng c thm v c thm mt lng hot cht
bit trcl 10 mg
X 9,8 9,7 9,9 10,0 10,1 9,8 10,2 10,0 9,8 9,8
X 19,5 19,6 19,6 20,0 19,9 19,7 20,0 19,7 19,6 19,5
Tnh chnh xc v ng ca phng php: (X = X + 10mg)
A B
C D
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PT D LIU KH BNG CHNG TRNH MS-EXEL 8
B MN TON GVGD: Nguyn nh Huy
Nhp d liu vo bng tnh:
B3 21 BBfxX
A B C D E F G H I J K
1 X 19,5 19,6 19,6 20 19,9 19,7 20 19,7 19,6 19,5
2 X 9,8 9,7 9,9 10 10,1 9,8 10,2 10 9,9 9,8
3 Xo B2
4
Lm mt s php tnh
- Chn B3 ri nhp biu thc = B1 B2
- Dng con tr ko nt in t ng t B3 n K3.
A B C D E F G H I J K
1 X 19,5 19,6 19,6 20 19,9 19,7 20 19,7 19,6 19,5
2 X 9,8 9,7 9,9 10 10,1 9,8 10,2 10 9,9 9,8
3 Xo 9,7 9,9 9,7 10 9,8 9,9 9,8 9,7 9,7 9,7
p dng Descriptive Statistics
Tng t phn Tnh cc gi tr thng k m t
Kt qu:
%9,9710010
79,9
%5,9810092,9
15,01
A
P