PROIECT STATISTICA

STOC MATERII PRIME LA LUNA IUNIE 2009

Nr.crt Tip bustean(materie prima) Cantitate (Buc) Volum(mc) Specie1 Bustean rotund Φ19x4 m 10 1.130 B2 Bustean rotund Φ30x4 m 5 1.415 B3 Bustean rotund Φ40x4 m 3 1.509 B4 Bustean rotund Φ43x4 m 6 3.486 B5 Bustean rotund Φ45x4 m 5 3.180 F6 Bustean rotund Φ25x6 m 3 0.885 B7 Bustean rotund Φ30x6 m 7 2.968 F8 Bustean rotund Φ37x6 m 8 5.160 F9 Bustean rotund Φ42x6 m 10 8.310 B

10 Bustean rotund Φ48x6m 12 13.032 B11 Bustean rotund Φ17x8 m 4 0.644 F12 Bustean rotund Φ20x8 m 5 1.255 F13 Bustean rotund Φ24x8 m 7 2.534 B14 Bustean rotund Φ29x8 m 1 0.528 F15 Bustean rotund Φ35x8 m 2 1.452 F16 Bustean rotund Φ40x8 m 15 15.075 B17 Bustean rotund Φ42x8 m 12 13.296 B18 Bustean rotund Φ44x8 m 2 2.432 F19 Bustean rotund Φ45x8 m 4 5.088 F20 Bile manele Φ15x12 m 11 2.332 B21 Bile manele Φ18x12 m 19 5.795 B22 Bile manele Φ24x12 m 12 6.516 B23 Bile manele Φ32x12 m 7 6.755 B24 Bile manele Φ34x12 m 3 3.270 B25 Bile manele Φ36x12 m 11 13.431 B26 Bile manele Φ38x12 m 3 4.083 B27 Bile manele Φ39x12 m 7 10.038 B28 Bile manele Φ41x12 m 8 12.672 B29 Bile manele Φ43x12 m 3 5.229 B30 Bile manele Φ52x12 m 1 2.548 B

206 156.048

LEGENDAB BradF FagΦ Diametrul

TABEL DE CUBAJ

Lungime 4m Diametrul(1/2 cm) Volum(mc)19 0.11330 0.28340 0.50343 0.58145 0.636

Lungime 6m 25 0.29530 0.42437 0.64542 0.83148 1.086

Lungime 8m 17 0.18220 0.25124 0.36229 0.52835 0.7740 1.00542 1.10844 1.21645 1.272

Lungime 12m 15 0.21218 0.30524 0.54332 0.96534 1.0936 1.22137 1.2939 1.43441 1.58448 2.17152 2.584

1) Eliminati datele aberante (daca este cazul) din sirul datelor de mai sus stiind ca pentrun=40 si a=0.05, Z= 2.904

Trebuie sa precizam ca pentru n=30, Z=2.792

Mai intai calculam media artimetica a celor doua valori numerice, cantitate si volum

Cantitate (buc) Volum(mc)10 9.80 1.130 16.56

5 3.50 1.415 14.333 14.98 1.509 13.626 0.76 3.486 2.945 3.50 3.180 4.083 14.98 0.885 18.627 0.02 2.968 4.988 1.28 5.160 0.00

10 9.80 8.310 9.6712 26.32 13.032 61.34

4 8.24 0.644 20.765 3.50 1.255 15.567 0.02 2.534 7.111 34.46 0.528 21.832 23.72 1.452 14.05

15 66.10 15.075 97.5212 26.32 13.296 65.55

2 23.72 2.432 7.664 8.24 5.088 0.01

11 17.06 2.332 8.2319 147.14 5.795 0.3512 26.32 6.516 1.73

7 0.02 6.755 2.423 14.98 3.270 3.72

11 17.06 13.431 67.753 14.98 4.083 1.257 0.02 10.038 23.418 1.28 12.672 55.833 14.98 5.229 0.001 34.46 2.548 7.03

6.87 567.47 5.20 567.91media aritmetica media aritmetica

18.92 18.939.46 9.47

Apoi calculam abaterea medie patratica in functie de cantitate si volum, folosindu-ne de urmatoarea formula pentru date nesistematizate:

Pentru calculul valorilor aberante vom folosi urmatoarea formula: Zn=|xn-x|¤d

(xi-6,87)2 (xi-5,20)2

d2= d2=d= d=

Apoi trecem sa calculam efectiv :

i) eliminarea datelor aberante din valoarea numerica denumita cantitate:

Cantitate (buc)10 3.13 3.13 0.331

5 -1.87 1.87 0.1983 -3.87 3.87 0.4096 -0.87 0.87 0.0925 -1.87 1.87 0.1983 -3.87 3.87 0.4097 0.13 0.13 0.0148 1.13 1.13 0.119

10 3.13 3.13 0.33112 5.13 5.13 0.542

4 -2.87 2.87 0.3035 -1.87 1.87 0.1987 0.13 0.13 0.0141 -5.87 5.87 0.6212 -4.87 4.83 0.511

15 8.13 8.17 0.86412 5.13 5.17 0.547

2 -4.87 4.87 0.5154 -2.87 2.87 0.303

10 3.13 3.13 0.33119 12.13 12.13 1.28212 5.13 5.13 0.542

7 0.13 0.13 0.0143 -3.87 3.87 0.409

11 4.13 4.13 0.4373 -3.87 3.87 0.4097 0.13 0.13 0.0148 1.13 1.13 0.1193 -3.87 3.87 0.4091 -5.87 5.87 0.621

Volum(mc)1.390 -3.81 3.81 0.4022.830 -2.37 2.37 0.2501.509 -3.69 3.69 0.3903.168 -2.03 2.03 0.2143.180 -2.02 2.02 0.213

d ={[ å(xi-x)^2]/n}^1/2

Zn=|xn-x|¤d

xn-6,87 úxn-6,87ú úxn-6,87ú/d

xn-5,20 úxn-5,20ú úxn-5,20ú/d

0.885 -4.32 4.32 0.4562.968 -2.23 2.23 0.2355.160 -0.04 0.04 0.0048.310 3.11 3.11 0.328

13.032 7.83 7.83 0.8270.728 -4.47 4.47 0.4721.255 -3.95 3.95 0.4172.534 -2.67 2.67 0.2820.528 -4.67 4.67 0.4931.540 -3.66 3.66 0.386

15.075 9.88 9.88 1.04313.296 8.10 8.1 0.855

2.434 -2.77 2.77 0.2935.088 -0.11 0.11 0.0122.332 -2.87 2.87 0.3035.795 0.59 0.6 0.0634.887 -0.31 0.31 0.0334.824 -0.38 0.38 0.0402.724 -2.48 2.48 0.262

11.198 6.00 6 0.6343.402 -1.80 1.8 0.1908.365 3.17 3.17 0.335

10.560 5.36 5.36 0.5664.356 -0.84 0.84 0.0892.124 -3.08 3.08 0.325

2) Sistematizati datele prin grupare folosind tipurile de scale cunoscute:a) scala nominala (pentru sistematizare dupa "specie")b) scala interval (pentru sistematizare dupa caracteristicile

numerice, folosind intervale egale si neegale)

Nr.crt Tip bustean(materie prima) Cantitate (Buc) Volum(mc) Specie1 Bustean rotund Φ19x4 m 10 1.130 B2 Bustean rotund Φ30x4 m 5 1.415 B3 Bustean rotund Φ40x4 m 3 1.509 B4 Bustean rotund Φ43x4 m 6 3.486 B5 Bustean rotund Φ45x4 m 5 3.180 F6 Bustean rotund Φ25x6 m 3 0.885 B7 Bustean rotund Φ30x6 m 7 2.968 F8 Bustean rotund Φ37x6 m 8 5.160 F9 Bustean rotund Φ42x6 m 10 8.310 B

10 Bustean rotund Φ48x6m 12 13.032 B11 Bustean rotund Φ17x8 m 4 0.644 F12 Bustean rotund Φ20x8 m 5 1.255 F13 Bustean rotund Φ24x8 m 7 2.534 B14 Bustean rotund Φ29x8 m 1 0.528 F15 Bustean rotund Φ35x8 m 2 1.452 F16 Bustean rotund Φ40x8 m 15 15.075 B17 Bustean rotund Φ42x8 m 12 13.296 B18 Bustean rotund Φ44x8 m 2 2.432 F19 Bustean rotund Φ45x8 m 4 5.088 F20 Bile manele Φ15x12 m 11 2.332 B21 Bile manele Φ18x12 m 19 5.795 B22 Bile manele Φ24x12 m 12 6.516 B23 Bile manele Φ32x12 m 7 6.755 B24 Bile manele Φ34x12 m 3 3.270 B25 Bile manele Φ36x12 m 11 13.431 B26 Bile manele Φ38x12 m 3 4.083 B27 Bile manele Φ39x12 m 7 10.038 B28 Bile manele Φ41x12 m 8 12.672 B29 Bile manele Φ43x12 m 3 5.229 B30 Bile manele Φ52x12 m 1 2.548 B

a)dupa specie, materiile prime se sistematizeaza astfel:

Nr.crt Tip bustean(materie prima) Cantitate (Buc) Volum(mc) Specie1 Bustean rotund Φ19x4 m 10 1.130 B2 Bustean rotund Φ30x4 m 5 1.415 B3 Bustean rotund Φ40x4 m 3 1.509 B4 Bustean rotund Φ43x4 m 6 3.486 B6 Bustean rotund Φ45x4 m 3 0.885 B9 Bustean rotund Φ25x6 m 10 8.310 B

10 Bustean rotund Φ30x6 m 12 13.032 B13 Bustean rotund Φ37x6 m 7 2.534 B16 Bustean rotund Φ42x6 m 15 15.075 B17 Bustean rotund Φ48x6m 12 13.296 B20 Bustean rotund Φ17x8 m 11 2.332 B21 Bustean rotund Φ20x8 m 19 5.795 B22 Bustean rotund Φ24x8 m 12 6.516 B23 Bustean rotund Φ29x8 m 7 6.755 B24 Bustean rotund Φ35x8 m 3 3.270 B25 Bustean rotund Φ40x8 m 11 13.431 B26 Bustean rotund Φ42x8 m 3 4.083 B27 Bustean rotund Φ44x8 m 7 10.038 B28 Bustean rotund Φ45x8 m 8 12.672 B29 Bile manele Φ15x12 m 3 5.229 B30 Bile manele Φ18x12 m 1 2.548 B

5 Bile manele Φ24x12 m 5 3.180 F7 Bile manele Φ32x12 m 7 2.968 F8 Bile manele Φ34x12 m 8 5.160 F

11 Bile manele Φ36x12 m 4 0.644 F12 Bile manele Φ38x12 m 5 1.255 F14 Bile manele Φ39x12 m 1 0.528 F15 Bile manele Φ41x12 m 2 1.452 F18 Bile manele Φ43x12 m 2 2.432 F19 Bile manele Φ52x12 m 4 5.088 F

Nr.materii prime CantitateMaterii prime B(brad) 21 168.00Materii prime F(fag) 9 38.00

Total 30 206.00

b) scala interval dupa valoarea numerica denumita "cantitate"

Nr.crt Tip bustean(materie prima) Cantitate (Buc) Cantitate (Buc)1 Bustean rotund Φ19x4 m 10 12 Bustean rotund Φ30x4 m 5 13 Bustean rotund Φ40x4 m 3 24 Bustean rotund Φ43x4 m 6 25 Bustean rotund Φ45x4 m 5 36 Bustean rotund Φ25x6 m 3 37 Bustean rotund Φ30x6 m 7 38 Bustean rotund Φ37x6 m 8 39 Bustean rotund Φ42x6 m 10 3

10 Bustean rotund Φ48x6m 12 411 Bustean rotund Φ17x8 m 4 412 Bustean rotund Φ20x8 m 5 513 Bustean rotund Φ24x8 m 7 514 Bustean rotund Φ29x8 m 1 515 Bustean rotund Φ35x8 m 2 616 Bustean rotund Φ40x8 m 15 717 Bustean rotund Φ42x8 m 12 718 Bustean rotund Φ44x8 m 2 719 Bustean rotund Φ45x8 m 4 720 Bile manele Φ15x12 m 11 821 Bile manele Φ18x12 m 19 822 Bile manele Φ24x12 m 12 1023 Bile manele Φ32x12 m 7 1024 Bile manele Φ34x12 m 3 1125 Bile manele Φ36x12 m 11 1126 Bile manele Φ38x12 m 3 1227 Bile manele Φ39x12 m 7 1228 Bile manele Φ41x12 m 8 1229 Bile manele Φ43x12 m 3 1530 Bile manele Φ52x12 m 1 19

Limita inferioara = 1.00Limita superioara= 19.00

Amplitudinea= limita superioara-limita inferioara= 19-1=18

n=30;

Calculam h = 19/1+3,322*1,4771 si obtinem h=3,05

Marimea intervalului de grupare este h = A/(1+3,322*logn)

logn=log30=1,4771

Distributia statistica pe intervale egale a materiilor prime dupa cantitate este urmatoarea:

0-3 43-6 106-9 7

9-12 412-15 315-18 118-21 1Total 30

sau

0-3 43-6 106-9 7

9-12 512 si peste 4 interval deschis

Total Err:522

Distributia statistica pe intervale neegale a materiilor prime dupa cantitate este urmatoarea:

cantitate mica 14cantitate medie 11cantitate mare 5

Total 30

Grupe de materii primedupa cantitate

Numar de materii prime





c) scala interval dupa valoarea numerica volum

Nr.crt Tip bustean(materie prima) Volum(mc)1 Bustean rotund Φ19x4 m 1.1302 Bustean rotund Φ30x4 m 1.4153 Bustean rotund Φ40x4 m 1.5094 Bustean rotund Φ43x4 m 3.4865 Bustean rotund Φ45x4 m 3.1806 Bustean rotund Φ25x6 m 0.8857 Bustean rotund Φ30x6 m 2.9688 Bustean rotund Φ37x6 m 5.1609 Bustean rotund Φ42x6 m 8.310

10 Bustean rotund Φ48x6m 13.03211 Bustean rotund Φ17x8 m 0.64412 Bustean rotund Φ20x8 m 1.25513 Bustean rotund Φ24x8 m 2.53414 Bustean rotund Φ29x8 m 0.52815 Bustean rotund Φ35x8 m 1.45216 Bustean rotund Φ40x8 m 15.07517 Bustean rotund Φ42x8 m 13.29618 Bustean rotund Φ44x8 m 2.43219 Bustean rotund Φ45x8 m 5.08820 Bile manele Φ15x12 m 2.33221 Bile manele Φ18x12 m 5.79522 Bile manele Φ24x12 m 6.51623 Bile manele Φ32x12 m 6.75524 Bile manele Φ34x12 m 3.27025 Bile manele Φ36x12 m 13.43126 Bile manele Φ38x12 m 4.08327 Bile manele Φ39x12 m 10.03828 Bile manele Φ41x12 m 12.67229 Bile manele Φ43x12 m 5.22930 Bile manele Φ52x12 m 2.548

Limita inferioara = 0.53Limita superioara= 15.08

Amplitudinea= limita superioara-limita inferioaraAmplitudinea= 15,08-0,53=14,55

n=30;

Calculam h = 14,55/1+3,322*1,4771 si obtinem h=2,46

Marimea intervalului de grupare este h = A/(1+3,322*logn)

logn=log30=1,4771

Distributia statistica pe intervale egale a materiilor prime dupa volum este urmatoarea:

0-2,5 102,5-5 75-7,5 6

7,5-10 110-12,5 112,5-15 415-17,5 1Total 30

Distributia statistica pe intervale neegale a materiilor prime dupa volum este urmatoarea:

volum mic 23volum mediu 2volum mare 5

Total 30

Grupe de materii primedupa volum




Volum(mc)0.5280.6440.8851.1301.2551.4151.4521.5092.3322.432

Distributia statistica pe intervale neegale a materiilor prime dupa volum este urmatoarea: 2.5342.548

2.9683.1803.2703.4864.0835.0885.1605.2295.7956.5166.7558.310

10.03812.67213.03213.29613.43115.075

3) Reprezentati grafic distributiile obtinute prin histograme, poligoane ale frecventelorsi diagrame de structura

Materii prime B(brad)

Materii prime F(fag)

Total0

5

10

15

20

25

30

35

21

9

30

Distributia de materii prime dupa specia de bustean

Nr.materii prime

Tip materie prima

Nr.

mat

rie

pri

ma

0-3 3-6 3-6 3-6 3-6 15-18 18-21 Total0

5

10

15

20

25

30

35

4

107

4 31 1

30

Distributia materiilor prime dupa cantitate

Grupe materii prime

Nr.

ma

teri

i pri

me

0-3 3-6 3-6 3-6 12 si peste Total0123456789

10

4

10

7

54


Grupe de materii prime

Nr de materii prime

0

1

2

3

4

5

6

7

8

9

10



Nr. de materii prime

0-2,5 2,5-5 5-7,5 7,5-10 10-12,5 12,5-15 15-17,5 Total0

5

10

15

20

25

30

35

Distributia materiilor prime dupa volum(mc)

distributia materiilor prime dupa volum(mc)

Nr.

de

mat

erii

pri

me

0123456789

10


Grupe materii prime dupa volum

Nr

de

mat

erii

pri

me

0123456789

10



Numar de ma-terii prime

0123456789

10



Numar de ma-terii prime

Materii prime B(brad) Materii prime F(fag)0

5

10

15

20

25

Poligonul frecventelor al materiilor prime in functie de specia de bustean

Tip materie prima

Nr.

ma

teri

e p

rim

a

0-3 3-6 3-6 3-6 3-6 15-18 18-210

2

4

6

8

10

12

Poligonul frecventelor dupa cantitatea materiilor prime


Nr.

de

mat

erii

pri

me

0-3 3-6 3-6 3-6 12 si peste0

2

4

6

8

10

12

Poligonul frecventelor dup cantitatea materiilor prime


Nr.

de

mat

erii

pri

me

0-3 3-6 3-6 3-6 12 si peste0

2

4

6

8

10

12

Poligonul frecventelor dup cantitatea materiilor prime


Nr.

de

mat

erii

pri

me

cantitate mica cantitate medie cantitate mare0

2

4

6

8

10

12

14

16

Poligonul frecventelor al materiilor prime in functie de canti-tate


Nr.

de

mat

erii

pri

me

0-2,5 2,5-5 5-7,5 7,5-10 10-12,5 12,5-15 15-17,50

2

4

6

8

10

12

Poligonul frecventeloral materiilor prime in functie de volum(mc)


Nu

ma

r d

e m

ate

rii

pri

me

volum mic volum mediu volum mare0

5

10

15

20

25

poligonul frecventelor al materiilor prime in functie de volum(mc)


Nu

mar

de

mat

erii

pri

me

volum mic volum mediu volum mare0

5

10

15

20

25

poligonul frecventelor al materiilor prime in functie de volum(mc)


Nu

mar

de

mat

erii

pri

me

Diagrama materiilor prime in functie de tipul busteanului

Materii prime B(brad)Materii prime F(fag)

Diagrama materiilor prime dupa cantitate

0-33-63-63-63-615-1818-21


0-33-63-63-63-615-1818-21

Diagrama materiilor primematerii prime dupa cantitate

0-33-63-63-612 si peste


cantitate micacantitate mediecantitate mare


cantitate micacantitate mediecantitate mare

Diagrama materiilor prime dupa volum(mc)

0-2,52,5-55-7,57,5-1010-12,512,5-1515-17,5

Diagrama materiilor prime dupa volum(mc)materii prime

volum micvolum mediuvolum mare

Diagrama materiilor prime dupa volum(mc)materii prime

volum micvolum mediuvolum mare

4)Pe baza distributiilor de la punctul 2) construiti tabelul centralizator si calculati sianalizati situatia prin coeficienti (marimi relative de structura).

0-3 4 13.33 6 2.7033-6 10 33.33 45 20.2706-9 7 23.33 52.5 23.649

9-12 4 13.33 42 18.91912-15 3 10.00 40.5 18.24315-18 1 3.33 16.5 7.43218-21 1 3.33 19.5 8.784Total 30 100.00 222 100.000

0-3 1.53-6 4.56-9 7.5

9-12 10.512-15 13.515-18 16.518-21 19.5

0-2,5 10 33.33 12.5 7.4632,5-5 7 23.33 26.25 15.6725-7,5 6 20.00 37.5 22.388

7,5-10 1 3.33 8.75 5.22410-12,5 1 3.33 11.25 6.71612,5-15 4 13.33 55 32.83615-17,5 1 3.33 16.25 9.701Total 30 100.00 167.5 100.000

0-2,5 1.252,5-5 3.755-7,5 6.25

7,5-10 8.7510-12,5 11.2512,5-15 13.7515-17,5 16.25


dupa cantitate


Numar de materii prime %

Valori centralizate

dupa cantitate

Valori centralizate

dupa cantitate %


dupa cantitate

Centrul intervalului


dupa volum


Numar de materii prime %

Valori centralizate

dupa volum

Valori centralizate

dupa volum %


dupa volum


5) Analizati gradul de concentrare (dupa caracteristicile numerice)

2.703 0.02703 0.0007320.270 0.2027 0.0410923.649 0.23649 0.0559318.919 0.18919 0.0357918.243 0.18243 0.033287.432 0.07432 0.005528.784 0.08784 0.00772

100.00 1.0000 0.18006

0.42 sau 42%

0.207000

0.21 sau 21%

7.463 0.07463 0.0055715.672 0.15672 0.0245622.388 0.22388 0.050125.224 0.05224 0.002736.716 0.06716 0.00451

32.836 0.32836 0.107829.701 0.09701 0.00941

100.000 1.00000 0.20472

0.45 sau 45%

[(1,433 - 1)/6]^1/2 =0,072^1/2

0.27 sau 27%

Valori centralizate

dupa cantitate %

pi pi2

KGINI= 0,18006^(1/2)

KGINI =

KSTRUCK=[(7*0,18006 - 1)/6]^1/2

KSTRUCK =

KSTRUCK =

Valori centralizate

dupa volum %

pi pi2

KGINI= 0,20472^(1/2)

KGINI =

KSTRUCK=[(7*0,20472 - 1)/6]^1/2

KSTRUCK =

KSTRUCK =

6) Calculati nivelul mediu al variabilelor numerice

Pentru date nesistematizate

Nr.crt Tip bustean(materie prima) Cantitate (Buc) Volum(mc)1 Bustean rotund Φ19x4 m 10 1.1302 Bustean rotund Φ30x4 m 5 1.4153 Bustean rotund Φ40x4 m 3 1.5094 Bustean rotund Φ43x4 m 6 3.4865 Bustean rotund Φ45x4 m 5 3.1806 Bustean rotund Φ25x6 m 3 0.8857 Bustean rotund Φ30x6 m 7 2.9688 Bustean rotund Φ37x6 m 8 5.1609 Bustean rotund Φ42x6 m 10 8.310

10 Bustean rotund Φ48x6m 12 13.03211 Bustean rotund Φ17x8 m 4 0.64412 Bustean rotund Φ20x8 m 5 1.25513 Bustean rotund Φ24x8 m 7 2.53414 Bustean rotund Φ29x8 m 1 0.52815 Bustean rotund Φ35x8 m 2 1.45216 Bustean rotund Φ40x8 m 15 15.07517 Bustean rotund Φ42x8 m 12 13.29618 Bustean rotund Φ44x8 m 2 2.43219 Bustean rotund Φ45x8 m 4 5.08820 Bile manele Φ15x12 m 11 2.33221 Bile manele Φ18x12 m 19 5.79522 Bile manele Φ24x12 m 12 6.51623 Bile manele Φ32x12 m 7 6.75524 Bile manele Φ34x12 m 3 3.27025 Bile manele Φ36x12 m 11 13.43126 Bile manele Φ38x12 m 3 4.08327 Bile manele Φ39x12 m 7 10.03828 Bile manele Φ41x12 m 8 12.67229 Bile manele Φ43x12 m 3 5.229

30 Bile manele Φ52x12 m 1 2.548

Xg Xh

6.87 33.033 5.4236 3.9969

5.2016 22.9935 3.5322 2.2936

Me Mo

6.5 3

3.378 x

Xa XP

Date nesistematizatevariabila cantitate

Date nesistematizatevariabila pret

Date nesistematizatevariabila cantitate

Date nesistematizatevariabila volum

Ordonam in mod ascendent materiile prime dupa cantitate, pentru a afla mediana.

Nr.crt Tip bustean(materie prima) Cantitate (Buc)14 Bustean rotund Φ29x8 m 1 1.0030 Bile manele Φ52x12 m 1 1.0015 Bustean rotund Φ35x8 m 2 4.0018 Bustean rotund Φ44x8 m 2 4.00

3 Bustean rotund Φ40x4 m 3 9.006 Bustean rotund Φ25x6 m 3 9.00

24 Bile manele Φ34x12 m 3 9.0026 Bile manele Φ38x12 m 3 9.0029 Bile manele Φ43x12 m 3 9.0011 Bustean rotund Φ17x8 m 4 16.0019 Bustean rotund Φ45x8 m 4 16.00


12 Bustean rotund Φ20x8 m 5 25.004 Bustean rotund Φ43x4 m 6 36.007 Bustean rotund Φ30x6 m 7 49.00

13 Bustean rotund Φ24x8 m 7 49.0023 Bile manele Φ32x12 m 7 49.0027 Bile manele Φ39x12 m 7 49.00

8 Bustean rotund Φ37x6 m 8 64.0028 Bile manele Φ41x12 m 8 64.00


20 Bile manele Φ15x12 m 11 121.0025 Bile manele Φ36x12 m 11 121.0010 Bustean rotund Φ48x6m 12 144.0017 Bustean rotund Φ42x8 m 12 144.00

Cantitate2

22 Bile manele Φ24x12 m 12 144.0016 Bustean rotund Φ40x8 m 15 225.0021 Bile manele Θ18x12 m 19 361.00

1982.00 TOTAL

Mo=3Ordonam in mod ascendent materiile prime dupa volum pentru a afla mediana

Nr.crt Tip bustean(materie prima) Volum(mc)14 Bustean rotund Φ29x8 m 0.528 0.27878411 Bustean rotund Φ17x8 m 0.644 0.414736

6 Bustean rotund Φ25x6 m 0.885 0.7832251 Bustean rotund Φ19x4 m 1.130 1.2769



20 Bile manele Φ15x12 m 2.332 5.438218 Bustean rotund Φ44x8 m 2.432 5.914613 Bustean rotund Φ24x8 m 2.534 6.42115630 Bile manele Φ52x12 m 2.548 6.492304


24 Bile manele Φ34x12 m 3.270 10.69294 Bustean rotund Φ43x4 m 3.486 12.152196

26 Bile manele Φ38x12 m 4.083 16.67088919 Bustean rotund Φ45x8 m 5.088 25.887744

8 Bustean rotund Φ37x6 m 5.160 26.625629 Bile manele Φ43x12 m 5.229 27.342421 Bile manele Φ18x12 m 5.795 33.582022 Bile manele Φ24x12 m 6.516 42.45825623 Bile manele Φ32x12 m 6.755 45.630025

9 Bustean rotund Φ42x6 m 8.310 69.056127 Bile manele Φ39x12 m 10.038 100.761444

Me=(6+7)/2=6,5

Volum(mc)2

28 Bile manele Φ41x12 m 12.672 160.579610 Bustean rotund Φ48x6m 13.032 169.83302417 Bustean rotund Φ42x8 m 13.296 176.78361625 Bile manele Φ36x12 m 13.431 180.391816 Bustean rotund Φ40x8 m 15.075 227.255625

1379.607242

Mo=

Pentru date nesistematizate dupa caracteristica numerica cantitate

0-3 43-6 10 intervalul modal, deoarece are frecventa 6-9 7 cea mai mare

9-12 412-15 315-18 118-21 1Total 30

Mo=3+3 *(10-4)/[(10-4)+(10-7)]=3+3*6/9=3+2=5

0-3 4 43-6 10 146-9 7 21 >15-interval median

Me=(3,270+3,486)/2=3,378





Frecventecumulate

9-12 4 2512-15 3 2815-18 1 3018-21 1 31

Me=6+3(15,5-14)/7=6,63

Me Mo

6.63 5

4.475 x

0-2,5 10 intervalul modal, deoarece are frecventa 2,5-5 7 cea mai mare

Me=Xme+h*(åfi +1/2-fCMe)/fCMe

(åfi)/2=30/2=15

Date sistematizatevariabila cantitate

Date sistematizatevariabila volum



5-7,5 67,5-10 1

10-12,5 112,5-15 415-17,5 1Total 30

Mo=0+2,5(10-7)=2,5*3= cum se calculeaza modulul in aceasta situatie?

0-2,5 10 102,5-5 7 17 >15-interval median5-7,5 6 23

7,5-10 1 2410-12,5 1 2512,5-15 4 2915-17,5 1 30Total 30

Me=2,5+2,5(15,5-10)/7=4,475



Frecventecumulate

Me=Xme+h*(åfi+1/2-fCMe)/fCMe

(åfi)/2=30/2=15

0-3 4 1.5 63-6 10 4.5 45.006-9 7 7.5 52.5

9-12 4 10.5 42.0012-15 3 13.5 40.515-18 1 16.5 16.5018-21 1 19.5 19.5Total 30 325.5

Media aritmetica=325,5/30Media aritmetica= 10.85

0-2,5 10 1.5 152,5-5 7 4.5 31.505-7,5 6 7.5 45

7,5-10 1 10.5 10.5010-12,5 1 13.5 13.512,5-15 4 16.5 66.0015-17,5 1 19.5 19.5Total 30 304.5

Media aritmetica=304/30Media aritmetica= 10.15


Numar de materii prime (fi)

Centrul intervalului (xi)

xi*fi




xi*fi

0-3 4 1.5 2.25 9.003-6 10 4.5 20.25 202.506-9 7 7.5 56.25 393.75

9-12 4 10.5 110.25 441.0012-15 3 13.5 182.25 546.7515-18 1 16.5 272.25 272.2518-21 1 19.5 380.25 380.25Total 30 2245.50

Media patratica este=(2245,5/30)^1/2=Media patratica= 37.425

0-2,5 10 1.5 2.25 22.502,5-5 7 4.5 20.25 141.755-7,5 6 7.5 56.25 337.50

7,5-10 1 10.5 110.25 110.2510-12,5 1 13.5 182.25 182.2512,5-15 4 16.5 272.25 1089.0015-17,5 1 19.5 380.25 380.25Total 30 2263.50

media patratica=(2263,50/30)^1/2




xi2 xi

2f




xi2 xi

2f

media patratica= 37.725

0-3 4 1.5 5.0633-6 10 4.5 3405062.8926-9 7 7.5 1334838.8671875

9-12 4 10.5 12155.062512-15 3 13.5 2460.37515-18 1 16.5 16.50018-21 1 19.5 19.5Total 30 2.21409410210315E+023

Media geometrica=2,21409E+23^1/30nu se poate calcula exact

0-2,5 10 1.5 57.6652,5-5 7 4.5 37366.9455-7,5 6 7.5 177978.515625

7,5-10 1 10.5 10.510-12,5 1 13.5 13.50012,5-15 4 16.5 74120.06315-17,5 1 19.5 19.5




xifi




xifi

Total 30 7.85708086852817E+019

0-3 4 1.5 2.6673-6 10 4.5 2.2226-9 7 7.5 0.933

9-12 4 10.5 0.38112-15 3 13.5 0.22215-18 1 16.5 0.06118-21 1 19.5 0.051Total 30 6.537

Media armonica este 30/6,537= 4.5891

0-2,5 10 1.5 6.6672,5-5 7 4.5 1.5565-7,5 6 7.5 0.800

7,5-10 1 10.5 0.095

De asemenea media geometrica nu se poate calcula exact




1/Xi*fi

Media armonica este åfi/å(1/xi)*fi




1/Xi*fi

10-12,5 1 13.5 0.07412,5-15 4 16.5 0.24215-17,5 1 19.5 0.051Total 30 9.485

Media armonica este 30/9,485= 3.1628Media armonica este åfi/å(1/xi)*fi

7) Analizati, prin masurarea variatiei (abatere medie patratica si coeficient de variatie),daca mediile calculate anterior sunt reprezentative sau nu. Explicati.

0-3 4 1.5 87.4225 349.69003-6 10 4.5 40.3225 403.22506-9 7 7.5 11.2225 78.5575

9-12 4 10.5 0.1225 0.490012-15 3 13.5 7.0225 21.067515-18 1 16.5 31.9225 31.922518-21 1 19.5 74.8225 74.8225Total 30 959.7750

unde X este media aritmeticaMedia aritmetica este 10,85

959,7750/30)^1/215.9963

v= 1.4743

0-2,5 10 1.5 44.4889 444.88902,5-5 7 4.5 13.4689 94.28235-7,5 6 7.5 0.4489 2.6934

7,5-10 1 10.5 5.4289 5.428910-12,5 1 13.5 28.4089 28.408912,5-15 4 16.5 69.3889 277.555615-17,5 1 19.5 128.3689 128.3689Total 30 981.6270

unde X este media aritmeticaMedia aritmetica este 10,15

(981,6270/30)^1/216.3605

v= 1.6119

Abaterea medie patratica pentru date sistematizate este egala cu d=[å(xi-x)2*fi/åfi]^1/2


dupa cantitate


(fi)


(xi)(Xi-X)2 (Xi-X)2*fi

d=d=

Coeficientul de variatie este v=d/x, unde x-media aritmetica


dupa volumNumar de

materii prime


(xi)(Xi-X)2 (Xi-X)2*fi

d=d=

Coeficientul de variatie este v=d/x, unde x-media aritmetica

Cantitate (Buc) Volum(mc)1 0.5281 2.5482 1.4522 2.4323 1.5093 0.8853 3.2703 4.0833 5.2294 0.6444 5.0885 1.4155 3.1805 1.2556 3.4867 2.9687 2.5347 6.7557 10.0388 5.1608 12.672

10 1.13010 8.31011 2.33211 13.43112 13.03212 13.29612 6.51615 15.07519 5.795

Cantitate Specie Volum(mc)Specie1 F 0.528 F1 B 0.644 F2 F 0.885 B2 F 1.130 B3 B 1.255 F3 B 1.415 B3 B 1.452 F3 B 1.509 B3 B 2.332 B4 F 2.432 F4 F 2.534 B5 B 2.548 B5 F 2.968 F5 F 3.180 F6 B 3.270 B7 F 3.486 B7 B 4.083 B7 B 5.088 F7 B 5.160 F8 F 5.229 B

8 B 5.795 B10 B 6.516 B10 B 6.755 B11 B 8.310 B11 B 10.038 B12 B 12.672 B12 B 13.032 B12 B 13.296 B15 B 13.431 B19 B 15.075 B

8)Pe baza distributiilor de la punctul 2) construiti tabelele de contingenta (cu dubla intrare)si tabele de asociere.Conform tabelului de mai sus, combinati

Cantitate - volumCantitate - tip specievolum - tip specie

0-3 3-6 6-9 9-12 12-15 15-18 18-21

total

0-2,5 3 5 0 2 0 0 0 10

2,5-5 1 3 3 0 0 0 0 7

5-7,5 0 2 2 0 1 0 1 6

7,5-10 0 0 0 1 0 0 0 1

10-12,5 0 0 1 0 0 0 0 1

12,5-15 0 0 1 1 2 0 0 4

15-17,5 0 0 0 0 0 1 0 1

total 4 10 7 4 3 1 1 30

total

B 7 9 5 21

F 7 2 0 9

total 14 11 5 30

Grupare dupa

cantitate

Grupare dupavolum

Grupare dupa

cantitateCantitate mica

0-6Cantitate medie

6-12Cantitate mare

12-21

Grupare dupatip specie

total

B 14 2 5 21

F 9 0 0 9

total 23 2 5 30

Grupare dupa

volumvolum mic

0-7,5volum mediu

7,5-12,5volum mare

12,5-17,5

Grupare dupatip specie

0 2 4 6 8 10 12 14 16 18 200.000

2.000

4.000

6.000

8.000

10.000

12.000

14.000

16.000

Norul de puncte

Cantitate Volum(mc)10 1.130

5 1.4153 1.5096 3.4865 3.1803 0.8857 2.9688 5.160

10 8.31012 13.032

4 0.6445 1.2557 2.5341 0.5282 1.452

15 15.07512 13.296

2 2.4324 5.088

11 2.33219 5.79512 6.516

7 6.7553 3.270

11 13.4313 4.0837 10.0388 12.6723 5.2291 2.548

Cantitate (Buc) Volum(mc)1 0.5284 0.6443 0.885

10 1.1305 1.2555 1.4152 1.4523 1.509

11 2.3322 2.4327 2.5341 2.5487 2.9685 3.1803 3.2706 3.4863 4.0834 5.0888 5.1603 5.229

19 5.79512 6.516

7 6.75510 8.310

7 10.0388 12.672

12 13.03212 13.29611 13.43115 15.075

9) Analizati intensitatea legaturii dintre variabilele numerice (Kendall, Spearmann,coeficientul de asociere, Corell) si elaborati functii de regresie care exprima legatura.

Nr.crt Tip bustean(materie prima) Cantitate (Buc) Volum(mc) Nr.crt Volum(mc)1 Bustean rotund Φ19x4 m 10 1.130 16 15.075 12 Bustean rotund Φ30x4 m 5 1.415 25 13.431 23 Bustean rotund Φ40x4 m 3 1.509 17 13.296 34 Bustean rotund Φ43x4 m 6 3.486 10 13.032 45 Bustean rotund Φ45x4 m 5 3.180 28 12.672 56 Bustean rotund Φ25x6 m 3 0.885 27 10.038 67 Bustean rotund Φ30x6 m 7 2.968 9 8.310 78 Bustean rotund Φ37x6 m 8 5.160 23 6.755 89 Bustean rotund Φ42x6 m 10 8.310 22 6.516 9

10 Bustean rotund Φ48x6m 12 13.032 21 5.795 1011 Bustean rotund Φ17x8 m 4 0.644 29 5.229 1112 Bustean rotund Φ20x8 m 5 1.255 8 5.160 1213 Bustean rotund Φ24x8 m 7 2.534 19 5.088 1314 Bustean rotund Φ29x8 m 1 0.528 26 4.083 1415 Bustean rotund Φ35x8 m 2 1.452 4 3.486 1516 Bustean rotund Φ40x8 m 15 15.075 24 3.270 1617 Bustean rotund Φ42x8 m 12 13.296 5 3.180 1718 Bustean rotund Φ44x8 m 2 2.432 7 2.968 1819 Bustean rotund Φ45x8 m 4 5.088 30 2.548 1920 Bile manele Φ15x12 m 11 2.332 13 2.534 2021 Bile manele Φ18x12 m 19 5.795 18 2.432 2122 Bile manele Φ24x12 m 12 6.516 20 2.332 2223 Bile manele Φ32x12 m 7 6.755 3 1.509 2324 Bile manele Φ34x12 m 3 3.270 15 1.452 2425 Bile manele Φ36x12 m 11 13.431 2 1.415 2526 Bile manele Φ38x12 m 3 4.083 12 1.255 2627 Bile manele Φ39x12 m 7 10.038 1 1.130 2728 Bile manele Φ41x12 m 8 12.672 6 0.885 2829 Bile manele Φ43x12 m 3 5.229 11 0.644 2930 Bile manele Φ52x12 m 1 2.548 14 0.528 30

Nr.crt Tip bustean(materie prima) Cantitate (Buc) X Y d d^2 P Q P-Q21 Bile maneleΦ 18x12 m 19 1 10 -9 81 20 9 1116 Bustean rotundΦ40x8 m 15 2 1 1 1 28 0 2810 Bustean rotundΦ48x6m 12 3 4 -1 1 25 2 2317 Bustean rotund Φ42x8 m 12 4 3 1 1 25 1 2422 Bile maneleΦ24x12 m 12 5 9 -4 16 20 5 1520 Bile manele Φ15x12 m 11 6 22 -16 256 7 13 -625 Bile manele Φ36x12 m 11 7 2 5 25 23 0 23

1 Bustean rotundΦ19x4 m 10 8 27 -19 361 3 19 -169 Bustean rotund Φ42x6 m 10 9 7 2 4 19 2 178 Bustean rotund Φ37x6 m 8 10 12 -2 4 16 4 12

28 Bile manele Φ41x12 m 8 11 5 6 36 19 0 197 Bustean rotundΦ30x6 m 7 12 18 -6 36 10 8 2

13 Bustean rotund Φ24x8 m 7 13 20 -7 49 8 9 -123 Bile manele Φ32x12 m 7 14 8 6 36 15 1 1427 Bile manele Φ39x12 m 7 15 6 9 81 15 0 15

4 Bustean rotund Φ43x4 m 6 16 15 1 1 11 3 82 Bustean rotund Φ30x4 m 5 17 25 -8 64 4 8 -45 Bustean rotund Φ45x4 m 5 18 17 1 1 8 4 4

12 Bustean rotund Φ20x8 m 5 19 26 -7 49 3 7 -411 Bustean rotundΦ17x8 m 4 20 29 -9 81 1 9 -819 Bustean rotund Φ45x8 m 4 21 13 8 64 8 1 7

3 Bustean rotund Φ40x4 m 3 22 23 -1 1 3 5 -26 Bustean rotund Φ25x6 m 3 23 28 -5 25 1 6 -5

24 Bile manele Φ34x12 m 3 24 16 8 64 4 2 226 Bile maneleΦ38x12 m 3 25 14 11 121 4 1 329 Bile manele Φ43x12 m 3 26 11 15 225 4 0 415 Bustean rotundΦ35x8 m 2 27 24 3 9 1 2 -118 Bustean rotundΦ44x8 m 2 28 21 7 49 1 1 014 Bustean rotund Φ29x8 m 1 29 30 -1 1 0 1 -130 Bile manele Φ52x12 m 1 30 19 11 121 0 0 0

TOTAL 0 1864 306 123 183

Coeficientul Kendall:

42%

Coeficientul Spearman:

59%

Grupare dupa volum sub 5,202 peste 5,202Grupare dupa cantitate TOTAL

sub 6,87 14 1 15

peste 6,87 5 10 15

TOTAL 19 11 30

Coeficientul de asociere: q=(ad-bc)/(ad+bc)

a=14 q=(14*10 - 1*5)/(14*10 + 1*5)

kk=2(P-Q)/n(n-1)

kk= 2*183/30(30-1)

kk= 0,42

ks=1-[6åd2/n(n2-1)]

ks=1-[(6*1864)/30*(900-1)]

ks=0,59

b=1 q= 0,93c=5 q= 93%d=10

Nr.crt Cantitate (Buc) Volum(mc) Cant. (Buc) Volum(mc)1 10 1.130 10 1.1302 5 1.415 5 1.4153 3 1.509 3 1.5094 6 3.486 6 3.4865 5 3.180 5 3.1806 3 0.885 3 0.8857 7 2.968 7 2.9688 8 5.160 8 5.1609 10 8.310 10 8.310

10 12 13.032 12 13.03211 4 0.644 4 0.64412 5 1.255 5 1.25513 7 2.534 7 2.53414 1 0.528 1 0.52815 2 1.452 2 1.45216 15 15.075 15 15.07517 12 13.296 12 13.29618 2 2.432 2 2.43219 4 5.088 4 5.08820 11 2.332 11 2.33221 19 5.795 19 5.79522 12 6.516 12 6.51623 7 6.755 7 6.75524 3 3.270 3 3.27025 11 13.431 11 13.43126 3 4.083 3 4.083

27 7 10.038 7 10.03828 8 12.672 8 12.67229 3 5.229 3 5.22930 1 2.548 1 2.548

6.87 5.202

CORELL= 0.62394987 media aritmetica media aritmetica

10) Realizati un studiu de dinamica folosind date din firma, institutia, compania,…, in care lucrati, dupa modelul din suportul de curs, capitolul "Serii cronologice".

Firma S.C.PINU IMP-EXP S.R.L. a inregistrat in ultimul an calendaristic urmatoarea evolutie a vanzarilor de produse finite pentru export

Luna Vanzari (mii euro)iulie 16.66

august 16.75septembrie 11.45octombrie 11.00noiembrie 6.00decembrie 5.50

ianuarie 5.66februarie 5.40

martie 10.20aprilie 16.35

mai 14.00iunie 6.50

125.47

I) Indicatorii absoluti:

Nivelul absolut: 16,66; 16,75; 11,45; 11,00; 6,00; 5,50; 5,66; 5,40; 10,20; 16,35; 14; 6,5

Volumul absolut este: 125.47

Sporul absolut- Vanzari (mii euro)16.66

16.75 0.0911.45 -5.2111.00 -5.666.00 -10.665.50 -11.165.66 -11.005.40 -11.26

10.20 -6.4616.35 -0.3114.00 -2.666.50 -10.16

Vanzari (mii euro)16.6616.75 0.0911.45 -5.3011.00 -0.456.00 -5.005.50 -0.505.66 0.165.40 -0.26

10.20 4.8016.35 6.1514.00 -2.35

∆n/1=yn-y1

cu baza fixa: ∆n/1=yn-y1

cu baza mobila: ∆n/n-1=yn-yn-1 ∆n/n-1=yn-yn-1

6.50 -7.50

II) Indicatori relativi:

Indicele de dinamica:

Vanzari (mii euro)

16.66 100%16.75 100.5411.45 68.7311.00 66.036.00 36.015.50 33.015.66 33.975.40 32.41

10.20 61.2216.35 98.1414.00 84.036.50 39.02

Vanzari(mii euro)16.6616.75 100.5411.45 68.3611.00 96.076.00 54.555.50 91.675.66 102.915.40 95.41

10.20 188.8916.35 160.2914.00 85.636.50 46.43

Ritmul de dinamica:

Vanzari(mii euro)16.66 100% 016.75 100.54 0.54%11.45 68.73 -31.27%11.00 66.03 -33.976.00 36.01 -63.99%5.50 33.01 -66.99%5.66 33.97 -66.03%5.40 32.41 -67.53

10.20 61.22 -38.78%16.35 98.14 -1.86%14.00 84.03 -15.97%6.50 39.02 -60.98%

In/1=yn/y1*100 %

cu baza fixa: In/1=yn/y1*100

cu baza mobila: In/n-1=yn/yn-1*100 In/n-1=yn/yn-1*100 %

cu baza fixa: Rn/1=In/1-100%

In/1=yn/y1*100 % Rn/1=In/1-100%

PROIECT STATISTICA

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