Le Système SAS

La procédure UNIVARIATE
Variable : varz

Moments
N 350 Somme poids 350
Moyenne 39.6186083 Somme obs. 13866.5129
Écart-type 2.12273783 Variance 4.50601589
Skewness 0.00333226 Kurtosis -0.4233906
SS non corrigée 550944.542 SS corrigée 1572.59954
Coeff Variation 5.35793134 Moy. erreur std 0.11346511

Mesures statistiques de base
Position Variabilité
Moyenne 39.61861 Écart-type 2.12274
Médiane 39.58670 Variance 4.50602
Mode 40.41850 Étendue 10.96360
    Intervalle interquartile 3.12950

Modes
Mode Effectif
40.4185 2

Intervalles de confiance sous hypothèse de normalité
Paramètre Estimation 95% Limites de confiance
Moyenne 39.61861 39.39545 39.84177
Écart-type 2.12274 1.97627 2.29284
Variance 4.50602 3.90563 5.25711

Tests de position : Mu0=0
Test Statistique p Value
t de Student t 349.17 Pr > |t| <.0001
Signe M 175 Pr >= |M| <.0001
Rangs signés S 30712.5 Pr >= |S| <.0001

Position : Mu0=0.00
Effectif Valeur
Num Obs > Mu0 350
Num Obs ^= Mu0 350
Num Obs < Mu0 0

Tests de normalité
Test Statistique p Value
Shapiro-Wilk W 0.99462 Pr < W 0.2589
Kolmogorov-Smirnov D 0.032911 Pr > D >0.1500
Cramer-von Mises W-Sq 0.077971 Pr > W-Sq 0.2260
Anderson-Darling A-Sq 0.487879 Pr > A-Sq 0.2292

Moyennes tronquées
Pourcent.
tronqué
en queue
Nombre
tronqué
en queue
Moyenne
tronquée
Erreur Std
Moyenne
tronquée
95% Limites de confiance DF t pour H0:
Mu0=0.00
Pr > |t|
25.14 88 39.62846 0.131631 39.36866 39.88827 173 301.0581 <.0001

Winsorized Means
Percent
Winsorized
in Tail
Number
Winsorized
in Tail
Winsorized
Mean
Std Error
Winsorized
Mean
95% Limites de confiance DF t for H0:
Mu0=0.00
Pr > |t|
25.14 88 39.61169 0.131822 39.35150 39.87187 173 300.4943 <.0001

Mesures d'échelle robustes
Mesure Valeur Estimation
de Sigma
Intervalle interquartile 3.129500 2.319901
Écart à la moyenne de Gini 2.418313 2.143174
MAD 1.543050 2.287726
Sn 2.126644 2.126644
Qn 2.191460 2.167923

Quantiles (Définition 5)
Quantile Estimation   Statistiques d'ordre
95% Intervalle de confiance
sous hypothèse de normalité
95% Intervalle de confiance;Distribution libre Rang LCL Rang UCL Coverage
100% Max 44.9798              
99% 44.3637 44.15470 45.01576 43.7829 44.9798 343 350 94.43
95% 43.0982 42.78778 43.47351 42.8491 43.6759 325 341 95.18
90% 42.3533 42.05362 42.65670 42.0634 42.8506 304 326 95.02
75% Q3 41.1804 40.81177 41.30650 40.8006 41.5189 247 279 95.20
50% Médiane 39.5867 39.39545 39.84177 39.3921 39.7774 157 194 95.22
25% Q1 38.0509 37.93072 38.42544 37.7321 38.5490 72 104 95.20
10% 36.8099 36.58051 37.18359 36.4417 37.0669 25 47 95.02
5% 36.0358 35.76371 36.44944 35.6057 36.4595 10 26 95.18
1% 35.3258 34.22146 35.08252 34.0162 35.5024 1 8 94.43
0% Min 34.0162              

Observations extrêmes
Inférieures Supérieures
Valeur Obs. Valeur Obs.
34.0162 316 44.2364 349
34.5225 141 44.3637 35
34.7523 106 44.7942 210
35.3258 281 44.7954 350
35.3490 317 44.9798 105

Valeurs extrêmes
Inférieures Supérieures
Ordre Valeur Fréq Ordre Valeur Fréq
1 34.0162 1 345 44.2364 1
2 34.5225 1 346 44.3637 1
3 34.7523 1 347 44.7942 1
4 35.3258 1 348 44.7954 1
5 35.3490 1 349 44.9798 1

Nombres d'occurrences
Valeur Effectif Pourcentages
Cellule Cum.
34.0162 1 0.3 0.3
34.5225 1 0.3 0.6
34.7523 1 0.3 0.9
35.3258 1 0.3 1.1
35.3490 1 0.3 1.4
35.4636 1 0.3 1.7
35.4859 1 0.3 2.0
35.5024 1 0.3 2.3
35.5628 1 0.3 2.6
35.6057 1 0.3 2.9
35.6207 1 0.3 3.1
35.7306 1 0.3 3.4
35.7643 1 0.3 3.7
35.8541 1 0.3 4.0
35.8933 1 0.3 4.3
35.9865 1 0.3 4.6
36.0078 1 0.3 4.9
36.0358 1 0.3 5.1
36.1065 1 0.3 5.4
36.1454 1 0.3 5.7
36.2623 1 0.3 6.0
36.3617 1 0.3 6.3
36.3757 1 0.3 6.6
36.3990 1 0.3 6.9
36.4417 1 0.3 7.1
36.4595 1 0.3 7.4
36.6201 1 0.3 7.7
36.6301 1 0.3 8.0
36.6792 1 0.3 8.3
36.6896 1 0.3 8.6
36.6973 1 0.3 8.9
36.7148 1 0.3 9.1
36.7528 1 0.3 9.4
36.8067 1 0.3 9.7
36.8087 1 0.3 10.0
36.8110 1 0.3 10.3
36.8508 1 0.3 10.6
36.8782 1 0.3 10.9
36.8944 1 0.3 11.1
36.9409 1 0.3 11.4
36.9515 1 0.3 11.7
36.9779 1 0.3 12.0
37.0036 1 0.3 12.3
37.0156 1 0.3 12.6
37.0230 1 0.3 12.9
37.0481 1 0.3 13.1
37.0669 1 0.3 13.4
37.0713 1 0.3 13.7
37.0800 1 0.3 14.0
37.1052 1 0.3 14.3
37.1107 1 0.3 14.6
37.1417 1 0.3 14.9
37.1998 1 0.3 15.1
37.2403 1 0.3 15.4
37.2481 1 0.3 15.7
37.2534 1 0.3 16.0
37.2904 1 0.3 16.3
37.3100 1 0.3 16.6
37.3210 1 0.3 16.9
37.3394 1 0.3 17.1
37.3485 1 0.3 17.4
37.3742 1 0.3 17.7
37.4134 1 0.3 18.0
37.4401 1 0.3 18.3
37.4439 1 0.3 18.6
37.4871 1 0.3 18.9
37.5407 1 0.3 19.1
37.5535 1 0.3 19.4
37.5790 1 0.3 19.7
37.6360 1 0.3 20.0
37.7281 1 0.3 20.3
37.7321 1 0.3 20.6
37.8216 1 0.3 20.9
37.8278 1 0.3 21.1
37.8501 1 0.3 21.4
37.8554 1 0.3 21.7
37.8778 1 0.3 22.0
37.8890 1 0.3 22.3
37.9367 1 0.3 22.6
37.9587 1 0.3 22.9
37.9894 1 0.3 23.1
37.9975 1 0.3 23.4
38.0080 1 0.3 23.7
38.0101 1 0.3 24.0
38.0180 1 0.3 24.3
38.0222 1 0.3 24.6
38.0470 1 0.3 24.9
38.0509 1 0.3 25.1
38.0571 1 0.3 25.4
38.0865 1 0.3 25.7
38.1230 1 0.3 26.0
38.1258 1 0.3 26.3
38.1759 1 0.3 26.6
38.1871 1 0.3 26.9
38.2456 1 0.3 27.1
38.2795 1 0.3 27.4
38.3130 1 0.3 27.7
38.3682 1 0.3 28.0
38.3961 1 0.3 28.3
38.4146 1 0.3 28.6
38.4267 1 0.3 28.9
38.4388 1 0.3 29.1
38.5335 1 0.3 29.4
38.5490 1 0.3 29.7
38.6214 1 0.3 30.0
38.6317 1 0.3 30.3
38.6372 1 0.3 30.6
38.6671 1 0.3 30.9
38.7102 1 0.3 31.1
38.7199 1 0.3 31.4
38.7413 1 0.3 31.7
38.7592 1 0.3 32.0
38.7597 1 0.3 32.3
38.7807 1 0.3 32.6
38.7880 1 0.3 32.9
38.8074 1 0.3 33.1
38.8256 1 0.3 33.4
38.8272 1 0.3 33.7
38.8551 1 0.3 34.0
38.8637 1 0.3 34.3
38.8806 1 0.3 34.6
38.8970 1 0.3 34.9
38.9167 1 0.3 35.1
38.9202 1 0.3 35.4
38.9280 1 0.3 35.7
38.9452 1 0.3 36.0
38.9466 1 0.3 36.3
38.9540 1 0.3 36.6
38.9794 1 0.3 36.9
39.0616 1 0.3 37.1
39.0625 1 0.3 37.4
39.0820 1 0.3 37.7
39.0862 1 0.3 38.0
39.0907 1 0.3 38.3
39.1362 1 0.3 38.6
39.1508 1 0.3 38.9
39.1606 1 0.3 39.1
39.1677 1 0.3 39.4
39.1847 1 0.3 39.7
39.1909 1 0.3 40.0
39.1939 1 0.3 40.3
39.2154 1 0.3 40.6
39.2349 1 0.3 40.9
39.2386 1 0.3 41.1
39.2409 1 0.3 41.4
39.2511 1 0.3 41.7
39.2681 1 0.3 42.0
39.2689 1 0.3 42.3
39.3053 1 0.3 42.6
39.3201 1 0.3 42.9
39.3217 1 0.3 43.1
39.3226 1 0.3 43.4
39.3281 1 0.3 43.7
39.3433 1 0.3 44.0
39.3458 1 0.3 44.3
39.3696 1 0.3 44.6
39.3921 1 0.3 44.9
39.4004 1 0.3 45.1
39.4162 1 0.3 45.4
39.4212 1 0.3 45.7
39.4576 1 0.3 46.0
39.4591 1 0.3 46.3
39.4665 1 0.3 46.6
39.4666 1 0.3 46.9
39.4757 1 0.3 47.1
39.4909 1 0.3 47.4
39.5085 1 0.3 47.7
39.5130 1 0.3 48.0
39.5233 1 0.3 48.3
39.5331 1 0.3 48.6
39.5426 1 0.3 48.9
39.5479 1 0.3 49.1
39.5734 1 0.3 49.4
39.5853 1 0.3 49.7
39.5854 1 0.3 50.0
39.5880 1 0.3 50.3
39.5890 1 0.3 50.6
39.5954 1 0.3 50.9
39.6072 1 0.3 51.1
39.6107 1 0.3 51.4
39.6136 1 0.3 51.7
39.6538 1 0.3 52.0
39.6664 1 0.3 52.3
39.6688 1 0.3 52.6
39.6805 1 0.3 52.9
39.6809 1 0.3 53.1
39.7160 1 0.3 53.4
39.7176 1 0.3 53.7
39.7281 1 0.3 54.0
39.7387 1 0.3 54.3
39.7612 1 0.3 54.6
39.7699 1 0.3 54.9
39.7753 1 0.3 55.1
39.7774 1 0.3 55.4
39.7775 1 0.3 55.7
39.8012 1 0.3 56.0
39.8016 1 0.3 56.3
39.8436 1 0.3 56.6
39.8824 1 0.3 56.9
39.8879 1 0.3 57.1
39.9009 1 0.3 57.4
39.9060 1 0.3 57.7
39.9127 1 0.3 58.0
39.9345 1 0.3 58.3
39.9447 1 0.3 58.6
39.9510 1 0.3 58.9
40.0266 1 0.3 59.1
40.0576 1 0.3 59.4
40.0639 1 0.3 59.7
40.0749 1 0.3 60.0
40.0780 1 0.3 60.3
40.0920 1 0.3 60.6
40.1041 1 0.3 60.9
40.1265 1 0.3 61.1
40.1462 1 0.3 61.4
40.1723 1 0.3 61.7
40.1770 1 0.3 62.0
40.2026 1 0.3 62.3
40.2411 1 0.3 62.6
40.2421 1 0.3 62.9
40.2483 1 0.3 63.1
40.2859 1 0.3 63.4
40.3184 1 0.3 63.7
40.3296 1 0.3 64.0
40.3323 1 0.3 64.3
40.3332 1 0.3 64.6
40.3387 1 0.3 64.9
40.4101 1 0.3 65.1
40.4121 1 0.3 65.4
40.4185 2 0.6 66.0
40.4189 1 0.3 66.3
40.4324 1 0.3 66.6
40.4741 1 0.3 66.9
40.5005 1 0.3 67.1
40.5033 1 0.3 67.4
40.5395 1 0.3 67.7
40.6096 1 0.3 68.0
40.6238 1 0.3 68.3
40.6306 1 0.3 68.6
40.6490 1 0.3 68.9
40.6672 1 0.3 69.1
40.7276 1 0.3 69.4
40.7483 1 0.3 69.7
40.7859 1 0.3 70.0
40.7968 1 0.3 70.3
40.8006 1 0.3 70.6
40.8602 1 0.3 70.9
40.8846 1 0.3 71.1
40.9096 1 0.3 71.4
40.9163 1 0.3 71.7
40.9471 1 0.3 72.0
40.9668 1 0.3 72.3
40.9687 1 0.3 72.6
40.9843 1 0.3 72.9
41.0143 1 0.3 73.1
41.0532 1 0.3 73.4
41.0549 1 0.3 73.7
41.0596 1 0.3 74.0
41.0845 1 0.3 74.3
41.0901 1 0.3 74.6
41.1331 1 0.3 74.9
41.1804 1 0.3 75.1
41.2328 1 0.3 75.4
41.2458 1 0.3 75.7
41.2556 1 0.3 76.0
41.2679 1 0.3 76.3
41.2764 1 0.3 76.6
41.3162 1 0.3 76.9
41.3316 1 0.3 77.1
41.3345 1 0.3 77.4
41.4093 1 0.3 77.7
41.4415 1 0.3 78.0
41.4461 1 0.3 78.3
41.4531 1 0.3 78.6
41.4554 1 0.3 78.9
41.4611 1 0.3 79.1
41.4910 1 0.3 79.4
41.5189 1 0.3 79.7
41.5219 1 0.3 80.0
41.5253 1 0.3 80.3
41.5414 1 0.3 80.6
41.5947 1 0.3 80.9
41.6032 1 0.3 81.1
41.6538 1 0.3 81.4
41.6827 1 0.3 81.7
41.7053 1 0.3 82.0
41.7270 1 0.3 82.3
41.7602 1 0.3 82.6
41.7670 1 0.3 82.9
41.7849 1 0.3 83.1
41.8026 1 0.3 83.4
41.8096 1 0.3 83.7
41.8239 1 0.3 84.0
41.8240 1 0.3 84.3
41.8312 1 0.3 84.6
41.8666 1 0.3 84.9
41.8988 1 0.3 85.1
41.9062 1 0.3 85.4
41.9416 1 0.3 85.7
41.9448 1 0.3 86.0
41.9925 1 0.3 86.3
42.0226 1 0.3 86.6
42.0634 1 0.3 86.9
42.1264 1 0.3 87.1
42.1484 1 0.3 87.4
42.1647 1 0.3 87.7
42.1750 1 0.3 88.0
42.1764 1 0.3 88.3
42.1984 1 0.3 88.6
42.2005 1 0.3 88.9
42.2646 1 0.3 89.1
42.3396 1 0.3 89.4
42.3423 1 0.3 89.7
42.3505 1 0.3 90.0
42.3560 1 0.3 90.3
42.4650 1 0.3 90.6
42.4788 1 0.3 90.9
42.5292 1 0.3 91.1
42.6217 1 0.3 91.4
42.6517 1 0.3 91.7
42.6636 1 0.3 92.0
42.6859 1 0.3 92.3
42.8392 1 0.3 92.6
42.8491 1 0.3 92.9
42.8506 1 0.3 93.1
42.8790 1 0.3 93.4
42.8999 1 0.3 93.7
42.9026 1 0.3 94.0
42.9181 1 0.3 94.3
42.9545 1 0.3 94.6
42.9828 1 0.3 94.9
43.0982 1 0.3 95.1
43.1701 1 0.3 95.4
43.1870 1 0.3 95.7
43.2455 1 0.3 96.0
43.3478 1 0.3 96.3
43.3932 1 0.3 96.6
43.4467 1 0.3 96.9
43.4677 1 0.3 97.1
43.6759 1 0.3 97.4
43.7229 1 0.3 97.7
43.7829 1 0.3 98.0
43.8318 1 0.3 98.3
43.8531 1 0.3 98.6
44.2364 1 0.3 98.9
44.3637 1 0.3 99.1
44.7942 1 0.3 99.4
44.7954 1 0.3 99.7
44.9798 1 0.3 100.0



Le Système SAS

La procédure UNIVARIATE
Variable : varz

              Stem Leaf                                              #               Boîte            
                45 0                                                 1                |               
                44 88                                                2                |               
                44 24                                                2                |               
                43 577889                                            6                |               
                43 001222344                                         9                |               
                42 55567778899999                                   14                |               
                42 001112222233344                                  15                |               
                41 555555556677778888888899999                      27                |               
                41 0000111111222333333444                           22             +-----+            
                40 5555666677788899999                              19             |     |            
                40 0011111111222222333333444444                     28             |     |            
                39 555555555555666666666777777777888888889999999    45             *--+--*            
                39 001111112222222222333333333344444                33             |     |            
                38 5566677778888888999999999                        25             |     |            
                38 00000000111112223344444                          23             +-----+            
                37 55666778899999                                   14                |               
                37 0000001111112223333334444                        25                |               
                36 566777788889999                                  15                |               
                36 0001134444                                       10                |               
                35 5556667899                                       10                |               
                35 33                                                2                |               
                34 58                                                2                |               
                34 0                                                 1                |               
                   ----+----+----+----+----+----+----+----+----+                                      
                                                                                                      
                                                                                                      
                                         Courbe de probabilité normale                                
                        45.25+                                                                        
                             |                                                +**                     
                             |                                              +**                       
                             |                                            ***                         
                             |                                         ****                           
                             |                                      ****                              
                             |                                    ***                                 
                             |                                 ****                                   
                             |                               ***                                      
                             |                             ***                                        
                             |                           ***                                          
                        39.75+                        ****                                            
                             |                      ***                                               
                             |                    ***                                                 
                             |                  **                                                    
                             |                ***                                                     
                             |             ****                                                       
                             |           ***                                                          
                             |        ***                                                             
                             |     ****                                                               
                             |  ***+                                                                  
                             |**++                                                                    
                        34.25+*                                                                       
                              +----+----+----+----+----+----+----+----+----+----+                     
                                  -2        -1         0        +1        +2                          
                                                                                                      
                                                                                                      



La procédure UNIVARIATE
Variable : varz

Histogram for varz



Le Système SAS

La procédure UNIVARIATE
Fitted Distribution for varz

Parameters for Normal Distribution
Paramètre Symbole Estimation
Mean Mu 39.61861
Std Dev Sigma 2.122738

Goodness-of-Fit Tests for Normal Distribution
Test Statistique p Value
Kolmogorov-Smirnov D 0.03291063 Pr > D >0.150
Cramer-von Mises W-Sq 0.07797141 Pr > W-Sq 0.226
Anderson-Darling A-Sq 0.48787876 Pr > A-Sq 0.229

Quantiles for Normal Distribution
Pourcentage Quantile
Observé Estimé
1.0 35.3258 34.6804
5.0 36.0358 36.1270
10.0 36.8099 36.8982
25.0 38.0509 38.1868
50.0 39.5867 39.6186
75.0 41.1804 41.0504
90.0 42.3533 42.3390
95.0 43.0982 43.1102
99.0 44.3637 44.5568



Q-Q plot for varz



Probability plot for varz