3. principles of statistics 16 feb 2012

8/2/2019 3. Principles of Statistics 16 Feb 2012

1/19

Principles of Statistics

Univariable and Bivariables


2/19

Frequency Distribution

i

Ri

ff

n

CLASS FREQUENCY VALUES FOR NUMERICAL EXAMPLE 2.1

Class i fi fri Fi0.10 < < 0.12 1 5 0.1 0.1

0.12 < < 0.14 2 9 0.18 0.28

0.14 < < 0.16 3 20 0.4 0.68

0.16 < < 0.18 4 10 0.2 0.88

0.18 < < 0.2 5 6 0.12 1.0

iifRifiF


3/19

Total frequency distribution

Comulative Distribution Function (cdf)

Relative frequency fR3

Cdf F3

1

1N

Ri

i

f

j

i

Rij fF1

33

20 0.40.50

Rffn

3

3

1

0.1 0.18 0.4 0.68.Ri

i

F f


4/19

0.000.010.020.030.040.050.060.070.080.090.10

0.200.180.160.140.12

(b)

0.35

0.30

0.25

0.20

0.15

0.10

0.05

0.000.20

0.40

0.180.160.140.12

(a)

0.350.30

0.25

0.20

0.15

0.10

0.05

0.00

0.20

0.40

0.180.160.140.120.1

0.68

0.200.180.160.140.120.1

Fig. 2.1 (a) Relative frequency and (b) cumulative relative frequency.

Characterizing the frequency function


5/19

1.0

Limiting Case

Limiting Case

Frequency distribution for a largenumber of classes


6/19

0.14 0.16 0.16

1

0

Characterizing continuous distribution


7/19

Histogram for (a) porosity and (b) permeability data for Well 34-29.

0.200

0.150

0.100

0.050

0.000

0.300

0.250

0.2000.1000.000

Porosity, fraction

Frequency

(a)

0.500

0.400

0.300

0.200

0.100

0.000

0.600

600200 4000 800

Freq

uency

Permeability, md(b)


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0.500

0.400

0.300

0.200

0.100

0.000

0

0.600

200 400 600 800

Permeability, md

Fre

quency

(a)

0.200

0.100

0.000

-5.0

0.300

-3.0 -1.0 1.0 3.0

In k, In md

Frequency

(b)

Effect of log transform on permeability histogram: (a) permeabilitydata and (b) log kdata for Well 34-29


9/19

0.300

0.200

0.100

0.000

0.100 0.200 0.3000.000

Porosity, fraction

Frequency

(a)

0.300

0.200

0.100

0.000

0.100 0.200 0.3000.000

Porosity, fraction

Frequency

(b)

Porosity histogram for Wells (a) 31-23 and (b) 36-16.


10/19

Univariate

MEAN = ARITHEMTIC AVERAGE

MODE = VALUE OCCURRING WITH GREATEST FREQUENCY

MEDIAN = VALUE MIDWAY IN THE FREQUENCY DISTRIBUTION

n

i

xn

x1

1

1

2/1~ nxx

2

~ 12/2/ nn xxx


11/19

22 1

1

n

i

i

x x

sn

2 2

1

2 1

1

n

i

x nx

sn

2s sStandard Deviation

Coefficient of Variation vs

Cx

Variance


12/19

0.2500.200

0.150

0.100

0.050

0.000

0.000

0.300

0.100 0.150 0.200 0.250 0.300

Porosity: Well 34-29

Poro

sity:Well31-w23

(a)

0.050

0.250

0.200

0.150

0.100

0.050

0.000

0.000

0.300

0.200 0.250 0.300

Porosity: Well 34-29

P

orosity:Well36-16

(b)0.100 0.1500.050

Percentile plot (Q-Qplot) comparisons of porosities of two wells:(a) Well 34-29 vs. Well 31-w23 and (b) Well 34-29 vs. Well 36-16.


13/19

Correlation of two variables

n

i

i

n

i

i

n

i

ii yn

xn

yxn

yxc111

111,

2 21

2 1

n

ix

x nx

sn

yx ss

yxcyxr

,,

Covariance

Variance2 2

1

2 1

n

iy

y ny

sn


14/19

y = mx + b

3.00

1.50

2.00

2.50

30

3.50

2826242220

Y

, %

log

k

Relationship between log kand forNumerical Example 2.5.

2

,

xs

yxcm

xmyb


15/19

Propability

6

111 XpP 6

165432 PPPPP

.16

1

6

1

6

1

6

1

6

1

6

16

1

i

ixP

.1

dxxf f (x)

a b x

Probability of value falling within an interval.

dxxfbXapb

a


16/19

Cumulative-Distribution

Function

.4.050

20

50

15030

50

30

dxxp

0.8

0.6

0.4

0.2

0

6

1

543210

Cumulative distribution function forrolling-a-die experiment


17/19

xXpxF

bXapaXpbXp

aFbFaXpbXpbXap

ax

i

i

xPaF

f (x)

a b x

,dxxfaFa


18/19

Numerical Example

.3

1

6

1

6

12

6

11

2

1

1

1

i

i

i

i

xPF

xPF

aFbFbXap

2

1

3

1

6

52552 FFXp


19/19

Summary 16 Feb 2012

1. membahas statistik dasar, memahami konsep

probability, rdf, cdf, mean, mode, median,

koef korelasi, variansi, st. deviasi.

2. Mahasiswa diharapkan prinsip dasar

probability, kecenderungan, dan beberapa

aplikasi untuk analisa error.

3. Makalah yang sudah didapatkan dianjurkan

mulai sedikit sedikit dipelajari.

3. principles of statistics 16 feb 2012

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