chuong_1.pdf

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



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.



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.



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



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:



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).



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



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

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