Re: Would you call this a paradox?

by kunzmilan <kunzmilan@[EMAIL PROTECTED] > Jul 7, 2008 at 10:40 AM
On Jun 25, 1:36=A0pm, Frederick Williams <frederick.willia...@[EMAIL PROTECTED]
>
wrote:
> Doug Wedel wrote:
> > ineluctably to the conclusion that information is at its maximum in
ran=
dom
> > numbers.
>
> Let's suppose that the digits of pi are "random", i.e. that pi is
> normal. =A0Then with an appropriate coding of letters and punctuation
> marks by strings of digits, pi contains all the works of Shakespeare.
>
> --
> He is not here; but far away
> =A0 The noise of life begins again
> =A0 And ghastly thro' the drizzling rain
> On the bald street breaks the blank day.

Distribution of distances between consecutive numerals in the Ludolph
number (Pi)

100000 decimal digits of this number were obtaned on page
www.cecm.sfu.ca/projects.

The occurencies of numerals in the number are:
0		9999
1		10137
2		9908
3		10026
4		9971
5		10026
6		10029
7		10025
8		9978
9		9902


At first, the set 100000 decimal digits was split into five parts.
Distances between numerals in the parts were determined, and
evaluated by Statgraphic software. The best results of correlation
were obtained with the negative binomial distribution.

0

Part	Occurencies	Span
1 	     2002	     1-91	1/0.0963612
2	       1999			 1-70 1/0.100619
3        1999      1-64 1/0.09952
4        1996      1-92 1/0.096907
5        2003      1-74 1/0.09990

The test of consistency of parts gave this results

			2		  	3		   	4		  	5
1		0.1663  0.2988  0.8566  0.2489
2           0.7142  0.2135  0.8121
3                   0.3757  0.8993
4                           0.3150

1. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         196       192.9         .
049330
              1.000       3.794         336       331.9         .
051824
              3.794       6.588         415       387.2
1.993761
              6.588       9.382         280       285.7         .
114408
              9.382      12.176         186       210.8
2.923092
             12.176      14.971         105       108.9         .
137235
             14.971      17.765         135       127.0         .
500452
             17.765      20.559          93        93.7         .
005691
             20.559      23.353          69        69.2         .
000377
             23.353      26.147          39        51.0
2.837162
             26.147      28.941          31        26.4         .
819730
             28.941      31.735          32        30.7         .
050938
             31.735      34.529          14        22.7
3.327322
             34.529      37.324          13        16.7         .
836154
             37.324      40.118          12        12.4         .
010096
             40.118      42.912           3         6.4
1.789800
             42.912      45.706           9         7.4         .
325677
             45.706      48.500           9         5.5
2.240597
             48.500      54.088           5         7.0         .
592485
 above       54.088                      20         8.4
15.937193
-----------------------------------------------------------------------
Chisquare =3D 34.5433 with 18 d.f.  Sig. level =3D
0.0107838

2. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         192       201.1          .
41510
              1.000       3.235         348       343.6          .
05644
              3.235       5.471         290       277.9          .
52415
              5.471       7.706         227       224.8          .
02126
              7.706       9.941         160       181.8
2.62513
              9.941      12.176         227       209.7
1.42066
             12.176      14.412         119       107.0
1.34313
             14.412      16.647          87        86.6          .
00224
             16.647      18.882          58        70.0
2.06251
             18.882      21.118          66        80.8
2.69603
             21.118      23.353          50        41.2
1.87847
             23.353      25.588          25        33.3
2.08103
             25.588      27.824          29        27.0          .
15458
             27.824      30.059          38        31.1
1.53426
             30.059      32.294          18        15.9          .
28756
             32.294      34.529          17        12.8
1.35362
             34.529      36.765          11        10.4          .
03705
             36.765      39.000           8        12.0
1.31767
             39.000      41.235           2         6.1
2.76301
             41.235      45.706           7         8.9          .
41995
             45.706      50.176           6         7.0          .
13274
 above       50.176                      14        10.0
1.64456
-----------------------------------------------------------------------
Chisquare =3D 24.7712 with 20 d.f.  Sig. level =3D 0.210327

3. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         204       198.9           .
1285
              1.000       3.235         365       340.5
1.7686
              3.235       5.471         262       276.1           .
7168
              5.471       7.706         209       223.9           .
9854
              7.706       9.941         175       181.5           .
2337
              9.941      12.176         204       210.0           .
1702
             12.176      14.412         106       107.5           .
0200
             14.412      16.647          97        87.1
1.1157
             16.647      18.882          62        70.7
1.0610
             18.882      21.118          85        81.7           .
1301
             21.118      23.353          45        41.8           .
2396
             23.353      25.588          35        33.9           .
0343
             25.588      27.824          30        27.5           .
2262
             27.824      30.059          34        31.8           .
1495
             30.059      32.294          19        16.3           .
4527
             32.294      34.529          17        13.2
1.0908
             34.529      36.765           6        10.7
2.0695
             36.765      39.000           8        12.4
1.5534
             39.000      41.235           8         6.3           .
4350
             41.235      43.471           8         5.1
1.5909
             43.471      47.941           5         7.5           .
8600
             47.941      52.412           7         5.9           .
2007
 above       52.412                       8         8.6           .
0390
-----------------------------------------------------------------------
Chisquare =3D 15.2713 with 21 d.f.  Sig. level =3D 0.809099

4. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         197       193.4          .
06600
              1.000       4.206         484       474.9          .
17422
              4.206       7.412         352       349.8          .
01401
              7.412      10.618         244       257.6          .
72130
             10.618      13.824         185       189.8          .
11923
             13.824      17.029         181       177.6          .
06401
             17.029      20.235          72        93.0
4.72823
             20.235      23.441          84        68.5
3.52086
             23.441      26.647          60        50.4
1.81473
             26.647      29.853          40        37.1          .
21925
             29.853      33.059          30        34.8          .
65488
             33.059      36.265          18        18.2          .
00217
             36.265      39.471          10        13.4          .
86450
             39.471      42.676          13         9.9          .
99064
             42.676      45.882           6         7.3          .
22237
             45.882      49.088           6         6.8          .
09564
             49.088      55.500           4         6.2          .
77276
 above       55.500                      10         7.3          .
96770
-----------------------------------------------------------------------
Chisquare =3D 16.0125 with 16 d.f.  Sig. level =3D 0.452088

5. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         193       200.1         .
251931
              1.000       3.824         356       342.2         .
554290
              3.824       6.647         391       395.5         .
050931
              6.647       9.471         290       288.4         .
008802
              9.471      12.294         205       210.3         .
134491
             12.294      15.118         171       153.4
2.025814
             15.118      17.941          63        78.4
3.029327
             17.941      20.765         100        90.6         .
971887
             20.765      23.588          55        66.1
1.858062
             23.588      26.412          41        48.2
1.072442
             26.412      29.235          33        35.1         .
130486
             29.235      32.059          26        25.6         .
005441
             32.059      34.882          13        13.1         .
000788
             34.882      37.706          22        15.1
3.107594
             37.706      40.529          11        11.0         .
000154
             40.529      43.353           9         8.1         .
111685
             43.353      46.176          11         5.9
4.479151
             46.176      51.824           5         6.5         .
334374
 above       51.824                       8         9.3         .
193155
-----------------------------------------------------------------------
Chisquare =3D 18.3208 with 17 d.f.  Sig. level =3D 0.368878

1

Part	Occurencies	Span
1 	     2029	     1-77	1/0.0984187
2	       2035			 1-69 1/0.102005
3        2026      1-81 1/0.0988293
4        2030      1-87 1/0.102396
5        2017	     1-84	1/0.0985056

The test of consistency of parts gave this results

			2		  	3		   	4		  	5
1		0.2325  0.8914  0.1852  0.9763
2           0.2898  0.8958  0.2299
3                   0.2341  0.9118
4                           0.1814

1.part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         197       199.7         .
036278
              1.000       3.824         368       342.4
1.920664
              3.824       6.647         405       397.2         .
151588
              6.647       9.471         279       291.1         .
504347
              9.471      12.294         193       213.3
1.940133
             12.294      15.118         153       156.3         .
071766
             15.118      17.941          68        80.3
1.875306
             17.941      20.765         103        93.1
1.044502
             20.765      23.588          67        68.3         .
023086
             23.588      26.412          45        50.0         .
503966
             26.412      29.235          44        36.7
1.470600
             29.235      32.059          27        26.9         .
000682
             32.059      34.882          17        13.8         .
746111
             34.882      37.706          15        16.0         .
062879
             37.706      40.529          12        11.7         .
006314
             40.529      43.353           9         8.6         .
019106
             43.353      46.176           8         6.3         .
459545
             46.176      51.824           8         7.0         .
147245
 above       51.824                      11        10.3         .
048597
-----------------------------------------------------------------------
Chisquare =3D 11.0327 with 17 d.f.  Sig. level =3D 0.854858

2.part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         220       207.6         .
743096
              1.000       3.235         335       353.8         .
998732
              3.235       5.471         299       285.3         .
657809
              5.471       7.706         246       230.1
1.103708
              7.706       9.941         173       185.5         .
845350
              9.941      12.176         189       213.2
2.739894
             12.176      14.412         113       108.3         .
200897
             14.412      16.647          94        87.4         .
504588
             16.647      18.882          64        70.4         .
590033
             18.882      21.118          77        80.9         .
192191
             21.118      23.353          41        41.1         .
000457
             23.353      25.588          43        33.2
2.911292
             25.588      27.824          26        26.8         .
021045
             27.824      30.059          31        30.7         .
002263
             30.059      32.294          18        15.6         .
362432
             32.294      34.529          10        12.6         .
535175
             34.529      36.765          16        10.2
3.360298
             36.765      39.000          12        11.7         .
009262
             39.000      41.235           8         5.9         .
721359
             41.235      45.706           6         8.6         .
806776
             45.706      50.176           9         6.7         .
802387
 above       50.176                       5         9.4
2.046134
-----------------------------------------------------------------------
Chisquare =3D 20.1552 with 20 d.f.  Sig. level =3D 0.448261

3.part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         202       200.2          .
01568
              1.000       3.824         348       343.0          .
07152
              3.824       6.647         407       397.6          .
22248
              6.647       9.471         278       291.0          .
57895
              9.471      12.294         204       213.0          .
37638
             12.294      15.118         164       155.8          .
42629
             15.118      17.941          71        79.9          .
99545
             17.941      20.765          92        92.6          .
00425
             20.765      23.588          72        67.8          .
26155
             23.588      26.412          52        49.6          .
11499
             26.412      29.235          34        36.3          .
14672
             29.235      32.059          22        26.6          .
78667
             32.059      34.882          11        13.6          .
50612
             34.882      37.706          15        15.8          .
03980
            37.706      40.529          16        11.6
1.70720
             40.529      43.353           9         8.5          .
03464
             43.353      46.176          10         6.2
2.34434
             46.176      51.824           8         6.9          .
19172
 above       51.824                      11        10.0          .
09149
-----------------------------------------------------------------------
Chisquare =3D 8.91624 with 17 d.f.  Sig. level =3D 0.942853

4.part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         204       207.9           .
0718
              1.000       3.794         356       354.1           .
0107
              3.794       6.588         420       406.4           .
4568
              6.588       9.382         275       293.9
1.2139
              9.382      12.176         217       212.5           .
0937
             12.176      14.971          95       107.9
1.5412
             14.971      17.765         119       123.8           .
1891
             17.765      20.559         105        89.6
2.6618
             20.559      23.353          80        64.8
3.5816
             23.353      26.147          41        46.8           .
7283
             26.147      28.941          33        23.8
3.5760
             28.941      31.735          21        27.3
1.4509
             31.735      34.529          25        19.7
1.4029
             34.529      37.324          11        14.3           .
7511
             37.324      40.118           6        10.3
1.8104
             40.118      42.912           4         5.2           .
2937
             42.912      45.706           4         6.0           .
6750
             45.706      51.294           7         7.5           .
0328
 above       51.294                       7         8.2           .
1808
-----------------------------------------------------------------------
Chisquare =3D 20.7224 with 17 d.f.  Sig. level =3D 0.238955

5.part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         198       198.7          .
00237
              1.000       3.794         326       340.6          .
62454
              3.794       6.588         373       395.1
1.23504
              6.588       9.382         300       289.5          .
38398
              9.382      12.176         232       212.1
1.87351
             12.176      14.971         107       108.8          .
03136
             14.971      17.765         130       126.3          .
11038
             17.765      20.559         104        92.5
1.42769
             20.559      23.353          69        67.8          .
02215
             23.353      26.147          60        49.7
2.15560
             26.147      28.941          27        25.5          .
08995
             28.941      31.735          23        29.6
1.45761
             31.735      34.529          18        21.7          .
61848
             34.529      37.324          12        15.9          .
94330
             37.324      40.118          11        11.6          .
03373
             40.118      42.912           3         6.0
1.47557
             42.912      45.706           9         6.9          .
62357
             45.706      48.500           3         5.1          .
84617
             48.500      54.088           3         6.4
1.83582
 above       54.088                       9         7.5          .
31814
-----------------------------------------------------------------------
Chisquare =3D 16.109 with 18 d.f.  Sig. level =3D 0.584944

2

Part	Occurencies	Span
1 	     1980	     1-74	1/0.0980392
2	       1977      1-78 1/0.0932064
3        1988      1-82 1/0.0992809
4        1980      1-85 1/0.100431
5        1983      1-71 1/0.0979791

The test of consistency of parts gave this results

			2		  	3		    	4		  	5
1		0.0980  0.6765   0.4180   0.9836
2           *0.0406  *0.0143  0.2299
3                    0.7015   0.6622
4                             0.4069
The differences between the second part on one side and the third and
fourth part are significant.

1. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         215       194.1
2.2464
              1.000       3.909         317       333.0           .
7695
              3.909       6.818         399       386.8           .
3854
              6.818       9.727         262       283.8
1.6772
              9.727      12.636         210       208.3           .
0146
             12.636      15.545         128       152.8
4.0296
             15.545      18.455         119       112.1           .
4207
             18.455      21.364         102        82.3
4.7265
             21.364      24.273          56        60.4           .
3170
             24.273      27.182          46        44.3           .
0651
             27.182      30.091          39        32.5
1.2968
             30.091      33.000          26        23.9           .
1932
             33.000      35.909          10        12.3           .
4163
             35.909      38.818          12        14.2           .
3521

-----------------------------------------------------------------------
Chisquare =3D 21.6702 with 17 d.f.  Sig. level =3D 0.197737

2. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         174       184.3           .
5723
              1.000       3.909         311       318.6           .
1819
              3.909       6.818         395       375.0
1.0704
              6.818       9.727         303       279.6
1.9606
              9.727      12.636         195       208.5           .
8703
             12.636      15.545         157       155.4           .
0156
             15.545      18.455         110       115.9           .
3006
             18.455      21.364          82        86.4           .
2262
             21.364      24.273          69        64.4           .
3229
             24.273      27.182          47        48.0           .
0228
             27.182      30.091          25        35.8
3.2713
             30.091      33.000          23        26.7           .
5161
             33.000      35.909          11        13.9           .
6113
             35.909      38.818          11        16.4
1.7660
             38.818      41.727          19        12.2
3.7730
             41.727      44.636           8         9.1           .
1343
             44.636      47.545           9         6.8           .
7197
             47.545      50.455           6         5.1           .
1736
             50.455      56.273          10         6.6
1.7654
 above       56.273                      12         8.3
1.7040
-----------------------------------------------------------------------
Chisquare =3D 19.9782 with 18 d.f.  Sig. level =3D 0.334049

3.part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         175       197.4
2.535517
              1.000       3.879         349       337.9         .
364572
              3.879       6.758         395       391.1         .
037916
              6.758       9.636         310       285.8
2.043551
              9.636      12.515         213       208.9         .
081619
             12.515      15.394         139       152.6
1.217566
             15.394      18.273         115       111.5         .
107590
             18.273      21.152          76        81.5         .
371780
             21.152      24.030          53        59.6         .
722415
             24.030      26.909          29        30.5         .
074075
             26.909      29.788          35        35.3         .
002722
             29.788      32.667          23        25.8         .
304438
             32.667      35.545          20        18.9         .
069492
             35.545      38.424          17        13.8         .
753205
             38.424      41.303          10        10.1         .
000468
             41.303      44.182          11         7.4
1.803136
             44.182      47.061           3         5.4
1.050509
             47.061      52.818           5         5.9         .
149081
 above       52.818                      10         8.7         .
210375
-----------------------------------------------------------------------
Chisquare =3D 11.9 with 17 d.f.  Sig. level =3D 0.806153

4. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         197       198.9          .
01727
              1.000       3.879         315       339.8
1.80991
              3.879       6.758         404       392.1          .
36030
              6.758       9.636         278       285.4          .
19395
              9.636      12.515         230       207.8
2.37454
             12.515      15.394         157       151.3          .
21786
             15.394      18.273         124       110.1
1.75222
             18.273      21.152          68        80.2
1.84317
             21.152      24.030          53        58.3          .
49035
             24.030      26.909          30        29.8          .
00153
             26.909      29.788          37        34.4          .
20092
             29.788      32.667          23        25.0          .
16328
             32.667      35.545          14        18.2          .
97507
             35.545      38.424          18        13.3
1.69511
             38.424      41.303           9         9.7          .
04405
             41.303      44.182           6         7.0          .
14989
             44.182      47.061           3         5.1          .
87438
             47.061      52.818           7         5.6          .
33666
 above       52.818                       7         8.1          .
13997
-----------------------------------------------------------------------
Chisquare =3D 13.6404 with 17 d.f.  Sig. level =3D 0.69237

5. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         196       194.3        .
0150050
              1.000       3.303         338       333.3        .
0651322
              3.303       5.606         260       271.2        .
4641325
              5.606       7.909         229       220.7        .
3140107
              7.909      10.212         253       256.4        .
0440060
             10.212      12.515         139       131.8        .
3959833
             12.515      14.818          91       107.2
2.4533692
             14.818      17.121         133       124.6        .
5724535
             17.121      19.424          61        64.0        .
1429780
             19.424      21.727          48        52.1        .
3217267
             21.727      24.030          70        60.5
1.4858338
             24.030      26.333          25        31.1
1.1992381
             26.333      28.636          34        25.3
2.9831353
             28.636      30.939          17        20.6        .
6271463
             30.939      33.242          18        23.9
1.4667947
             33.242      35.545          13        12.3        .
0401225
             35.545      37.848           9        10.0        .
1011075
             37.848      40.152          12        11.6        .
0121790
             40.152      42.455          15         6.0
13.6320826
             42.455      47.061          11        10.5        .
0229345
             47.061      51.667           5         5.3        .
0133438
             51.667      58.576           1         5.3
3.4906813
 above       58.576                       5         5.0        .
0000222
-----------------------------------------------------------------------
Chisquare =3D 29.8634 with 21 d.f.  Sig. level =3D 0.0947671

3

Part	Occurencies	Span
1 	     1998	     1-71	1/0.0979268
2	       2001      1-80 1/0.0977337
3        2011      1-80 1/0.0993381
4        2005      1-99 1/0.0987733
5        2012      1-78 1/0.100832

The test of consistency of parts gave this results

			2		  	3		   	4		  	5
1		0.9468  0.6326  0.7750  0.3270
2           0.5911  0.7285  0.3015
3                   0.8533  0.6252
4                           0.5021

1.part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         183       195.7       .
81887146
              1.000       3.235         341       335.7       .
08331436
              3.235       5.471         292       273.2
1.29648918
              5.471       7.706         227       222.3       .
09950779
              7.706       9.941         154       180.9
3.99755239
              9.941      12.176         197       210.2       .
82537370
             12.176      14.412         110       108.1       .
03518418
             14.412      16.647          92        87.9       .
18892227
             16.647      18.882          79        71.5       .
77632561
             18.882      21.118          88        83.1       .
28551646
             21.118      23.353          55        42.7
3.51891129
             23.353      25.588          38        34.8       .
29880243
             25.588      27.824          25        28.3       .
38455308
             27.824      30.059          30        32.9       .
25216860
             30.059      32.294          14        16.9       .
49874456
             32.294      34.529          14        13.8       .
00436313
             34.529      36.765          18        11.2
4.13973244
             36.765      39.000          13        13.0       .
00000170
             39.000      41.235           2         6.7
3.28408753
             41.235      43.471           8         5.4
1.20414715
             43.471      47.941           7         8.0       .
13202551
             47.941      52.412           5         6.3       .
28226498
 above       52.412                       6         9.4
1.23030304
-----------------------------------------------------------------------
Chisquare =3D 23.6372 with 21 d.f.  Sig. level =3D 0.310969

2. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         187       195.6           .
3751
              1.000       3.824         343       335.7           .
1606
              3.824       6.647         395       390.2           .
0592
              6.647       9.471         282       286.6           .
0740
              9.471      12.294         213       210.5           .
0293
             12.294      15.118         145       154.6           .
5997
             15.118      17.941          92        79.5
1.9520
             17.941      20.765          88        92.5           .
2154
             20.765      23.588          57        67.9
1.7545
             23.588      26.412          62        49.9
2.9418
             26.412      29.235          35        36.6           .
0736
             29.235      32.059          23        26.9           .
5693
             32.059      34.882          24        13.8
7.4497
             34.882      37.706          20        16.1           .
9481
             37.706      40.529           8        11.8
1.2352
             40.529      43.353           4         8.7
2.5256
             43.353      46.176           5         6.4           .
2976
             46.176      51.824          10         7.1
1.1901
 above       51.824                       8        10.6           .
6170
-----------------------------------------------------------------------
Chisquare =3D 23.0679 with 17 d.f.  Sig. level =3D 0.147053

3. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         200       199.8        .
0002673
              1.000       3.824         364       342.0
1.4185033
              3.824       6.647         396       395.8        .
0000976
              6.647       9.471         289       289.2        .
0001093
              9.471      12.294         186       211.3
3.0239094
             12.294      15.118         158       154.4        .
0858202
             15.118      17.941          77        79.0        .
0527699
             17.941      20.765          90        91.5        .
0240692
             20.765      23.588          65        66.8        .
0505986
             23.588      26.412          47        48.8        .
0688201
             26.412      29.235          31        35.7        .
6133716
             29.235      32.059          28        26.1        .
1433871
             32.059      34.882          10        13.3        .
8396771
             34.882      37.706          16        15.4        .
0196655

-----------------------------------------------------------------------
Chisquare =3D 17.6115 with 17 d.f.  Sig. level =3D 0.413737

4. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         217       198.0
1.81510
              1.000       4.206         496       484.3          .
28303
              4.206       7.412         344       354.5          .
31069
              7.412      10.618         243       259.5
1.04726
             10.618      13.824         181       189.9          .
42069
             13.824      17.029         195       176.5
1.93066
             17.029      20.235          81        91.7
1.25239
             20.235      23.441          59        67.1          .
98594
             23.441      26.647          50        49.1          .
01496
             26.647      29.853          31        36.0          .
68710
             29.853      33.059          33        33.4          .
00562
             33.059      36.265          21        17.4          .
75865
             36.265      39.471          19        12.7
3.10728
             39.471      42.676          10         9.3          .
05163

-----------------------------------------------------------------------
Chisquare =3D 15.2389 with 16 d.f.  Sig. level =3D 0.507215

5. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         208       202.9          .
12952
              1.000       3.824         315       346.4
2.85358
              3.824       6.647         413       399.3          .
46713
              6.647       9.471         314       290.3
1.93256
              9.471      12.294         223       211.1          .
67637
             12.294      15.118         154       153.4          .
00211
             15.118      17.941          75        78.2          .
13379
             17.941      20.765          71        90.2
4.07981
             20.765      23.588          50        65.6
3.69302
             23.588      26.412          60        47.7
3.19455
             26.412      29.235          39        34.6          .
54651
             29.235      32.059          24        25.2          .
05610
             32.059      34.882          10        12.8          .
62969
             34.882      37.706          16        14.8          .
09644
             37.706      40.529           8        10.8          .
70930
             40.529      43.353           9         7.8          .
17660
             43.353      46.176           5         5.7          .
08327
             46.176      51.824           5         6.2          .
24778
 above       51.824                      13         8.9
1.88596
-----------------------------------------------------------------------
Chisquare =3D 21.5941 with 17 d.f.  Sig. level =3D 0.200836

4

Part	Occurencies	Span
1 	     2001	     1-79	1/0.101056
2	       1994      1-85 1/0.0974775
3        1991      1-95 1/0.0968856
4        1992      1-95 1/0.0974417
5        1994      1-74 1/0.0992385

The test of consistency of parts gave this results

			2		  	3		   	4		  	5
1		0.2348  0.1658  0.2279  0.5440
2           0.8425  0.9903  0.5532
3                   0.8513  0.4277
4                           0.5431

1.part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         186       202.2
1.29993
              1.000       3.824         356       345.2          .
33874
              3.824       6.647         411       397.7          .
44810
              6.647       9.471         283       288.9          .
11923
              9.471      12.294         209       209.8          .
00340
             12.294      15.118         158       152.4          .
20286
             15.118      17.941          81        77.7          .
14187
             17.941      20.765          83        89.5          .
47023
             20.765      23.588          71        65.0          .
55258
             23.588      26.412          37        47.2
2.21318
             26.412      29.235          33        34.3          .
04962
             29.235      32.059          21        24.9          .
61668
             32.059      34.882          15        12.7          .
41697
             34.882      37.706          16        14.6          .
12849
             37.706      40.529          12        10.6          .
17738
             40.529      43.353           8         7.7          .
01016
             43.353      46.176           4         5.6          .
46107
             46.176      51.824           7         6.1          .
11753
 above       51.824                      10         8.7          .
18102
-----------------------------------------------------------------------
Chisquare =3D 7.94905 with 17 d.f.  Sig. level =3D 0.967624

2. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         166       194.4
4.14089
              1.000       3.879         347       333.7          .
52627
              3.879       6.758         402       388.2          .
48742
              6.758       9.636         294       285.4          .
25816
              9.636      12.515         226       209.8
1.24726
             12.515      15.394         145       154.3          .
55476
             15.394      18.273         112       113.4          .
01721
             18.273      21.152          78        83.4          .
34506
             21.152      24.030          61        61.3          .
00132
             24.030      26.909          28        31.5          .
39872
             26.909      29.788          34        36.7          .
19832
             29.788      32.667          22        27.0          .
91862
             32.667      35.545          23        19.8          .
50573
             35.545      38.424          10        14.6
1.43878
             38.424      41.303          11        10.7          .
00739
             41.303      44.182           7         7.9          .
09821
             44.182      47.061           9         5.8
1.77576
             47.061      52.818           8         6.5          .
37215
 above       52.818                      11         9.6          .
19546
-----------------------------------------------------------------------
Chisquare =3D 13.4875 with 17 d.f.  Sig. level =3D 0.70299

3. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         218       192.9
3.266206
              1.000       4.303         474       473.6         .
000289
              4.303       7.606         337       348.9         .
404082
              7.606      10.909         245       257.0         .
558307
             10.909      14.212         238       240.6         .
027520
             14.212      17.515         121       125.9         .
192250
             17.515      20.818          92        92.8         .
006098
             20.818      24.121          84        86.8         .
092299
             24.121      27.424          48        45.4         .
143201
             27.424      30.727          40        33.5
1.270851
             30.727      34.030          39        31.3
1.872096
             34.030      37.333          12        16.4
1.182362
             37.333      40.636           8        12.1
1.379763
             40.636      43.939          11         8.9         .
495319
             43.939      47.242           6         8.3         .
652775
             47.242      53.848           6         7.6         .
326971
 above       53.848                      12         9.0
1.013011
-----------------------------------------------------------------------
Chisquare =3D 12.8834 with 15 d.f.  Sig. level =3D 0.611304

4. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         196       194.1          .
01852
              1.000       4.303         464       476.0          .
30357
              4.303       7.606         367       350.0          .
82700
              7.606      10.909         256       257.3          .
00680
             10.909      14.212         251       240.4          .
46869
             14.212      17.515         115       125.5          .
88596
             17.515      20.818          74        92.3
3.63046
             20.818      24.121         100        86.2
2.19873
             24.121      27.424          42        45.0          .
20463
             27.424      30.727          36        33.1          .
25192
             30.727      34.030          36        30.9          .
83021
             34.030      37.333          14        16.2          .
28749
             37.333      40.636           7        11.9
2.00314
             40.636      43.939           7         8.7          .
34389
             43.939      47.242          10         8.2          .
41583
             47.242      53.848           7         7.4          .
02094
 above       53.848                      10         8.7          .
19452
-----------------------------------------------------------------------
Chisquare =3D 12.8923 with 15 d.f.  Sig. level =3D 0.610617

5. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         195       197.9          .
04196
              1.000       3.909         335       338.8          .
04261
              3.909       6.818         391       392.2          .
00389
              6.818       9.727         290       286.7          .
03879
              9.727      12.636         211       209.5          .
01060
             12.636      15.545         146       153.1          .
33115
             15.545      18.455         123       111.9
1.09928
             18.455      21.364          85        81.8          .
12609
             21.364      24.273          61        59.8          .
02509
             24.273      27.182          53        43.7
1.98532
             27.182      30.091          28        31.9          .
48341
             30.091      33.000          16        23.3
2.30573
             33.000      35.909           9        12.0          .
72930
             35.909      38.818           8        13.8
2.46266
             38.818      41.727          11        10.1          .
07776
             41.727      44.636           9         7.4          .
35015
             44.636      47.545           7         5.4          .
47277
             47.545      53.364           9         6.8          .
68693
 above       53.364                       7         7.8          .
08901
-----------------------------------------------------------------------
Chisquare =3D 11.3625 with 17 d.f.  Sig. level =3D 0.837111


5

Part	Occurencies	Span
1 	     2016	     1-64	1/0.102847
2	       2005      1-89 1/0.0963248
3        2006      1-70 1/0.101482
4        1996      1-76 1/0.0965885
5        2004      1-81 1/0.097737

The test of consistency of parts gave this results

			2		  	3		   	4		  	5
1		*0.0305  0.6521  *0.0365  0.0926
2           0.0832  0.9284  0.6352
3                   0.0978  0.2119
4                           0.6978

The first part differs significantly from the second and fourth ones.
These parts are wery similar.

1. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         193       207.3          .
99172
              1.000       3.235         370       352.9          .
82864
              3.235       5.471         278       284.0          .
12856
              5.471       7.706         247       228.6
1.47742
              7.706       9.941         182       184.0          .
02204
              9.941      12.176         204       210.9          .
22874
             12.176      14.412         103       107.0          .
14592
             14.412      16.647          83        86.1          .
11039
             16.647      18.882          69        69.3          .
00118
             18.882      21.118          78        79.4          .
02565
             21.118      23.353          47        40.3
1.12474
             23.353      25.588          30        32.4          .
17958
             25.588      27.824          20        26.1
1.42088
             27.824      30.059          32        29.9          .
14651
             30.059      32.294          12        15.2          .
65973
             32.294      34.529          16        12.2
1.18051
             34.529      36.765          13         9.8
1.02749
             36.765      39.000          11        11.3          .
00604
             39.000      41.235           4         5.7          .
51172
             41.235      45.706           6         8.3          .
63446
             45.706      50.176           9         6.4
1.06635
 above       50.176                       9         8.9          .
00197
-----------------------------------------------------------------------
Chisquare =3D 11.9203 with 20 d.f.  Sig. level =3D 0.918793

2. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         201       193.1           .
3206
              1.000       3.794         318       332.2           .
6107
              3.794       6.588         407       387.7           .
9597
              6.588       9.382         298       286.1           .
4935
              9.382      12.176         188       211.1
2.5371
             12.176      14.971         102       109.0           .
4548
             14.971      17.765         132       127.2           .
1776
             17.765      20.559          95        93.9           .
0128
             20.559      23.353          72        69.3           .
1054
             23.353      26.147          52        51.1           .
0145
             26.147      28.941          27        26.4           .
0132
             28.941      31.735          27        30.8           .
4732
             31.735      34.529          13        22.7
4.1741
             34.529      37.324          23        16.8
2.3023
             37.324      40.118           9        12.4           .
9256
             40.118      42.912           4         6.4           .
8978
             42.912      45.706          14         7.5
5.7226
             45.706      48.500           5         5.5           .
0469
             48.500      54.088           8         7.1           .
1238
 above       54.088                      10         8.4           .
2849
-----------------------------------------------------------------------
Chisquare =3D 20.6512 with 18 d.f.  Sig. level =3D 0.297377

3. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         202       203.6       .
01215284
              1.000       3.235         350       347.3       .
02153492
              3.235       5.471         267       280.4       .
63658182
              5.471       7.706         215       226.3       .
56852217
              7.706       9.941         197       182.7
1.11355369
              9.941      12.176         226       210.3
1.17765582
             12.176      14.412         107       107.0       .
00000296
             14.412      16.647          89        86.4       .
07829097
             16.647      18.882          64        69.8       .
47449586
             18.882      21.118          73        80.3       .
65693406
             21.118      23.353          44        40.9       .
24282521
             23.353      25.588          32        33.0       .
02912065
             25.588      27.824          30        26.6       .
42757575
             27.824      30.059          23        30.6
1.90373295
             30.059      32.294          17        15.6       .
12690040
             32.294      34.529          16        12.6       .
92420529
             34.529      36.765          10        10.2       .
00263168
             36.765      39.000          18        11.7
3.39958953
             39.000      41.235           5         6.0       .
15233429
             41.235      45.706           8         8.7       .
05403147
             45.706      50.176           8         6.7       .
23714077
 above       50.176                       5         9.5
2.14657537
-----------------------------------------------------------------------
Chisquare =3D 14.3864 with 20 d.f.  Sig. level =3D 0.810377

4. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         210       192.8
1.536221
              1.000       3.824         334       331.5         .
018619
              3.824       6.647         370       386.6         .
711279
              6.647       9.471         275       285.0         .
353321
              9.471      12.294         213       210.2         .
038303
             12.294      15.118         175       155.0
2.592319
             15.118      17.941          65        80.0
2.800817
             17.941      20.765          93        93.2         .
000661
             20.765      23.588          70        68.8         .
022580
             23.588      26.412          43        50.7
1.167695
             26.412      29.235          42        37.4         .
571627
             29.235      32.059          25        27.6         .
237679
             32.059      34.882          16        14.2         .
222292
             34.882      37.706          15        16.6         .
151350
             37.706      40.529          15        12.2         .
628408
             40.529      43.353           7         9.0         .
450761
             43.353      46.176           7         6.6         .
018676
             46.176      51.824          11         7.4
1.714320
             51.824      57.471           2         5.1
1.904887
 above       57.471                       8         6.1         .
588638
-----------------------------------------------------------------------
Chisquare =3D 15.7305 with 18 d.f.  Sig. level =3D 0.611353

5. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         191       195.9          .
12084
              1.000       3.824         326       336.2          .
30774
              3.824       6.647         414       390.8
1.37882
              6.647       9.471         285       287.0          .
01448
              9.471      12.294         240       210.8
4.03489
             12.294      15.118         146       154.9          .
50689
             15.118      17.941          80        79.7          .
00148
             17.941      20.765          66        92.6
7.64037
             20.765      23.588          60        68.0          .
94448
             23.588      26.412          43        50.0          .
96904
             26.412      29.235          40        36.7          .
29773
             29.235      32.059          31        27.0          .
60775
             32.059      34.882          12        13.9          .
25061
             34.882      37.706          18        16.1          .
22014
             37.706      40.529          13        11.8          .
11412
             40.529      43.353          11         8.7          .
61107
             43.353      46.176           4         6.4          .
89182
             46.176      51.824           7         7.1          .
00152
 above       51.824                      17        10.6
3.91875
-----------------------------------------------------------------------
Chisquare =3D 22.8325 with 17 d.f.  Sig. level =3D 0.154782

6

Part	Occurencies	Span
1 	     2005	     1-65	1/0.0995383
2	       2009      1-83 1/0.099068
3        2005      1-72 1/0.0965846
4        2006      1-61 1/0.100667
5        2004      1-82 1/0.0988117

The test of consistency of parts gave this results

			2		  	3		   	4		  	5
1		0.8733  0.3061  0.6958  0.8022
2           0.4047  0.5929  0.9319
3                   0.1631  0.4479
4                           0.5282


1. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         182       199.6
1.547573
              1.000       3.235         313       341.5
2.383291
              3.235       5.471         303       276.9
2.455539
              5.471       7.706         229       224.5         .
088667
              7.706       9.941         183       182.1         .
004828
              9.941      12.176         227       210.6
1.276337
             12.176      14.412         114       107.8         .
358707
             14.412      16.647          77        87.4
1.235985
             16.647      18.882          78        70.9         .
719217
             18.882      21.118          83        82.0         .
012940
             21.118      23.353          52        42.0
2.407589
             23.353      25.588          33        34.0         .
030259
             25.588      27.824          23        27.6         .
760577
             27.824      30.059          23        31.9
2.484906
             30.059      32.294          18        16.3         .
171311
             32.294      34.529          14        13.2         .
043757
             34.529      36.765          15        10.7
1.694949
             36.765      39.000          13        12.4         .
027337
             39.000      41.235           5         6.4         .
288870
             41.235      43.471           2         5.2
1.929032
             43.471      47.941           5         7.6         .
870069
             47.941      52.412           6         5.9         .
000968
 above       52.412                       7         8.6         .
296397
-----------------------------------------------------------------------
Chisquare =3D 21.0891 with 21 d.f.  Sig. level =3D 0.453514

2. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         201       199.0          .
01955
              1.000       3.794         350       340.9          .
24526
              3.794       6.588         413       394.8          .
83904
              6.588       9.382         263       288.7
2.28849
              9.382      12.176         213       211.1          .
01675
             12.176      14.971         107       108.2          .
01307
             14.971      17.765         116       125.3          .
69183
             17.765      20.559          88        91.6          .
14425
             20.559      23.353          74        67.0          .
72910
             23.353      26.147          54        49.0          .
50970
             26.147      28.941          28        25.1          .
33226
             28.941      31.735          20        29.1
2.83808
             31.735      34.529          24        21.3          .
35059
             34.529      37.324          13        15.6          .
41923
             37.324      40.118           9        11.4          .
49543
             40.118      42.912           6         5.8          .
00504
             42.912      45.706           5         6.8          .
45414
             45.706      51.294          10         8.5          .
24707
 above       51.294                      15         9.8
2.72757
-----------------------------------------------------------------------
Chisquare =3D 13.3664 with 17 d.f.  Sig. level =3D 0.711331

3. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         193       193.7          .
00220
              1.000       3.235         328       333.0          .
07505
              3.235       5.471         287       271.8          .
85228
              5.471       7.706         209       221.8          .
74050
              7.706       9.941         193       181.0          .
79047
              9.941      12.176         210       211.1          .
00585
             12.176      14.412         108       108.9          .
00819
             14.412      16.647          80        88.9          .
89408
             16.647      18.882          67        72.6          .
42748
             18.882      21.118          82        84.6          .
08142
             21.118      23.353          47        43.7          .
25377
             23.353      25.588          55        35.6
10.51310
             25.588      27.824          25        29.1          .
57504
             27.824      30.059          37        33.9          .
27923
             30.059      32.294          15        17.5          .
35867
             32.294      34.529           8        14.3
2.76692
             34.529      36.765           7        11.7
1.86295
             36.765      39.000           8        13.6
2.30453
             39.000      41.235          10         7.0
1.26783
             41.235      43.471           5         5.7          .
09234
             43.471      47.941          12         8.5
1.45183
             47.941      52.412           8         6.7          .
23371
             52.412      59.118           5         5.2          .
00669
 above       59.118                       6         5.0          .
19744
-----------------------------------------------------------------------
Chisquare =3D 26.0416 with 22 d.f.  Sig. level =3D 0.249902

4. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         181       201.9
2.170963
              1.000       3.265         362       344.9         .
844062
              3.265       5.529         303       279.0
2.067220
              5.529       7.794         192       225.6
5.016109
              7.794      10.059         257       260.2         .
039713
             10.059      12.324         135       132.7         .
038241
             12.324      14.588         112       107.4         .
200034
             14.588      16.853          89        86.8         .
053860
             16.853      19.118         102       100.1         .
034471
             19.118      21.382          51        51.1         .
000148
             21.382      23.647          48        41.3
1.080256
             23.647      25.912          41        33.4
1.719809
             25.912      28.176          39        38.5         .
005513
             28.176      30.441          17        19.7         .
360018
             30.441      32.706          12        15.9         .
957202
             32.706      34.971          11        12.9         .
269300
             34.971      37.235          15        14.8         .
001914
             37.235      39.500           8         7.6         .
024870
             39.500      41.765          11         6.1
3.892235
             41.765      44.029           3         7.1
2.332457
             44.029      48.559           9         6.5         .
950594
             48.559      53.088           2         5.1
1.859781
 above       53.088                       6         7.2         .
214367
-----------------------------------------------------------------------
Chisquare =3D 24.1331 with 21 d.f.  Sig. level =3D 0.286653

5. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         182       198.0
1.295823
              1.000       3.794         362       339.3
1.522696
              3.794       6.588         370       393.2
1.373189
              6.588       9.382         292       287.8         .
061079
              9.382      12.176         202       210.6         .
354688
             12.176      14.971         120       108.0
1.327856
             14.971      17.765         149       125.2
4.521667
             17.765      20.559          99        91.6         .
591548
             20.559      23.353          58        67.1
1.226205
             23.353      26.147          49        49.1         .
000154
             26.147      28.941          19        25.2
1.513772
             28.941      31.735          30        29.2         .
023203
             31.735      34.529          17        21.4         .
887965
             34.529      37.324          11        15.6
1.371124
             37.324      40.118           8        11.4
1.033835
             40.118      42.912           9         5.9
1.674187
             42.912      45.706           9         6.8         .
712324
             45.706      51.294           7         8.6         .
303924
 above       51.294                      11         9.9         .
112504
-----------------------------------------------------------------------
Chisquare =3D 19.9077 with 17 d.f.  Sig. level =3D 0.278975

7

Part	Occurencies	Span
1 	     1998	     1-65	1/0.0965731
2	       2002      1-80 1/0.0999102
3        2009      1-68 1/0.0991169
4        2005      1-69 1/0.100479
5        2011      1-81 1/0.0984819

The test of consistency of parts gave this results

			2		  	3		   	4		  	5
1		0.2549  0.3892  0.1896  0.5140
2           0.7917  0.8516  0.6311
3                   0.6558  0.8323
4                           0.509

1. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         193       193.0        .
0000114
              1.000       3.235         342       331.8        .
3133480
              3.235       5.471         287       270.8        .
9677266
              5.471       7.706         203       221.0
1.4708920
              7.706       9.941         173       180.4        .
3036295
              9.941      12.176         214       210.4        .
0624486
             12.176      14.412          93       108.6
2.2325065
             14.412      16.647          90        88.6        .
0217570
             16.647      18.882          73        72.3        .
0063382
             18.882      21.118          94        84.3
1.1064903
             21.118      23.353          27        43.5
6.2741460
             23.353      25.588          45        35.5
2.5274484
             25.588      27.824          19        29.0
3.4450488
             27.824      30.059          42        33.8
1.9828930
             30.059      32.294          20        17.4        .
3728509
             32.294      34.529          19        14.2
1.5897311
             34.529      36.765          14        11.6        .
4857275
             36.765      39.000          12        13.6        .
1784330
             39.000      41.235           9         7.0        .
5744060
             41.235      43.471           8         5.7        .
9188434
             43.471      47.941           5         8.5
1.4173170
             47.941      52.412           8         6.7        .
2420065
 above       52.412                       8        10.2        .
4604464
-----------------------------------------------------------------------
Chisquare =3D 26.9544 with 21 d.f.  Sig. level =3D 0.172366

2. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         195       200.0         .
126000
              1.000       3.824         337       342.1         .
075583
              3.824       6.647         405       395.3         .
237380
              6.647       9.471         279       288.3         .
298060
              9.471      12.294         230       210.2
1.862853
             12.294      15.118         133       153.3
2.685633
             15.118      17.941          92        78.4
2.371480
             17.941      20.765         101        90.6
1.203228
             20.765      23.588          55        66.0
1.845257
             23.588      26.412          44        48.2         .
358810
             26.412      29.235          35        35.1         .
000389
             29.235      32.059          24        25.6         .
100951
             32.059      34.882          16        13.1         .
646091
             34.882      37.706          15        15.1         .
001095
             37.706      40.529          14        11.0         .
798415
             40.529      43.353           7         8.0         .
135699
             43.353      46.176           5         5.9         .
127968
             46.176      51.824           7         6.5         .
044283
 above       51.824                       8         9.3         .
190506
-----------------------------------------------------------------------
Chisquare =3D 13.1097 with 17 d.f.  Sig. level =3D 0.728813

3. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         213       199.1        .
9666850
              1.000       3.235         327       341.0        .
5745981
              3.235       5.471         287       276.8        .
3795937
              5.471       7.706         229       224.6        .
0858807
              7.706       9.941         188       182.3        .
1788773
              9.941      12.176         211       211.1        .
0000575
             12.176      14.412          91       108.2
2.7252405
             14.412      16.647          82        87.8        .
3817681
             16.647      18.882          60        71.2
1.7759926
             18.882      21.118          91        82.5        .
8728329
             21.118      23.353          38        42.3        .
4329892
             23.353      25.588          35        34.3        .
0137597
             25.588      27.824          38        27.8
3.7009134
             27.824      30.059          28        32.3        .
5602842
             30.059      32.294          19        16.5        .
3707522
             32.294      34.529          14        13.4        .
0258352
             34.529      36.765           9        10.9        .
3262871
             36.765      39.000          10        12.6        .
5385118
             39.000      41.235           4         6.5        .
9360438
             41.235      43.471           5         5.2        .
0111634
             43.471      47.941           7         7.7        .
0648584
             47.941      52.412          12         6.0
5.8591598
 above       52.412                      11         8.8        .
5357771
-----------------------------------------------------------------------
Chisquare =3D 21.3179 with 21 d.f.  Sig. level =3D 0.439685

4. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         198       201.5           .
0592
              1.000       3.235         372       344.2
2.2422
              3.235       5.471         282       278.5           .
0434
              5.471       7.706         219       225.4           .
1797
              7.706       9.941         158       182.4
3.2521
              9.941      12.176         219       210.4           .
3515
             12.176      14.412          99       107.4           .
6559
             14.412      16.647          82        86.9           .
2759
             16.647      18.882          74        70.3           .
1935
             18.882      21.118          84        81.1           .
1018
             21.118      23.353          40        41.4           .
0479
             23.353      25.588          35        33.5           .
0667
             25.588      27.824          25        27.1           .
1643
             27.824      30.059          34        31.3           .
2364
             30.059      32.294          11        16.0
1.5448
             32.294      34.529          16        12.9           .
7348
             34.529      36.765           9        10.5           .
2021
             36.765      39.000          11        12.1           .
0934
             39.000      41.235           3         6.2
1.6182
             41.235      45.706          13         9.0
1.7649
             45.706      50.176           5         7.0           .
5834
 above       50.176                      16        10.1
3.5019
-----------------------------------------------------------------------
Chisquare =3D 17.9137 with 20 d.f.  Sig. level =3D 0.59309

5. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         198       198.0        .
0000112
              1.000       3.824         334       339.5        .
0891927
              3.824       6.647         389       393.9        .
0599760
              6.647       9.471         327       288.6
5.1151680
              9.471      12.294         199       211.4        .
7319987
             12.294      15.118         130       154.9
4.0090612
             15.118      17.941          80        79.5        .
0028767
             17.941      20.765          94        92.3        .
0330508
             20.765      23.588          79        67.6
1.9246986
             23.588      26.412          48        49.5        .
0470049
             26.412      29.235          29        36.3
1.4634487
             29.235      32.059          30        26.6        .
4379873
             32.059      34.882          19        13.6
2.0992821
             34.882      37.706          14        15.8        .
2121040
            37.706      40.529           9        11.6        .
5829234
             40.529      43.353           9         8.5        .
0294641
             43.353      46.176           4         6.2        .
7968036
             46.176      51.824           9         6.9        .
6355673
 above       51.824                      10        10.2        .
0026796
-----------------------------------------------------------------------
Chisquare =3D 18.2733 with 17 d.f.  Sig. level =3D 0.371799

8

Part	Occurencies	Span
1 	     1989	     1-65	1/0.09653
2	       2003      1-83 1/0.102728
3        1990      1-73 1/0.0973867
4        1991      1-78 1/0.096136
5        2005      1-77 1/0.099563

The test of consistency of parts gave this results

			2		  	3		    	4		    	5
1		*0.0381  0.7677   0.9045   0.3115
2            0.0767  *0.0294   0.3101
3                     0.6798   0.4720
4                              0.2616

The difference between the first and the second parts is significant,
similarly as between the second and the fourth parts.

1. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         179       192.0         .
879969
              1.000       3.303         346       330.2         .
757533
              3.303       5.606         283       269.5         .
674624
              5.606       7.909         204       220.0
1.162864
              7.909      10.212         240       256.6
1.071085
             10.212      12.515         125       132.4         .
416665
             12.515      14.818         138       108.1
8.272992
             14.818      17.121         127       126.1         .
006847
             17.121      19.424          67        65.1         .
057282
             19.424      21.727          53        53.1         .
000242
             21.727      24.030          56        61.9         .
570679
             24.030      26.333          29        32.0         .
276305
             26.333      28.636          24        26.1         .
168592
             28.636      30.939          16        21.3
1.319808
             30.939      33.242          23        24.8         .
136975
             33.242      35.545          14        12.8         .
107996
             35.545      37.848           9        10.5         .
205618
             37.848      40.152          18        12.2
2.748426
             40.152      42.455          13         6.3
7.122938
             42.455      44.758           4         5.1         .
254041
             44.758      47.061           4         6.0         .
665713
             47.061      51.667           9         5.6
2.028158
             51.667      58.576           6         5.7         .
014710
 above       58.576                       2         5.5
2.241243
-----------------------------------------------------------------------
Chisquare =3D 31.1613 with 22 d.f.  Sig. level =3D 0.0928617

2. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         228       205.8
2.40290
              1.000       3.794         352       350.3          .
00838
              3.794       6.588         384       401.7          .
77871
              6.588       9.382         277       290.2          .
59814
              9.382      12.176         214       209.6          .
09155
             12.176      14.971         107       106.3          .
00443
             14.971      17.765         120       121.9          .
03004
             17.765      20.559          95        88.1          .
54542
             20.559      23.353          69        63.6          .
45488
             23.353      26.147          38        46.0
1.37826
             26.147      28.941          21        23.3          .
22876
             28.941      31.735          21        26.7
1.22810
             31.735      34.529          20        19.3          .
02472
             34.529      37.324          18        13.9
1.17666
             37.324      40.118          13        10.1          .
84824
             40.118      42.912           2         5.1
1.89321
             42.912      45.706           9         5.9
1.68198
             45.706      51.294           8         7.3          .
06879
 above       51.294                       7         8.0          .
11535
-----------------------------------------------------------------------
Chisquare =3D 13.5585 with 17 d.f.  Sig. level =3D 0.698068

3. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         201       193.8          .
26753
              1.000       3.303         319       332.8          .
57358
              3.303       5.606         285       271.1          .
70752
              5.606       7.909         213       220.9          .
28310
              7.909      10.212         255       257.0          .
01624
             10.212      12.515         129       132.3          .
08474
             12.515      14.818         120       107.8
1.37447
             14.818      17.121         117       125.5          .
57097
             17.121      19.424          68        64.6          .
17895
             19.424      21.727          60        52.6
1.03195
             21.727      24.030          56        61.2          .
44825
             24.030      26.333          34        31.5          .
19325
             26.333      28.636          15        25.7
4.44765
             28.636      30.939          20        20.9          .
04125
             30.939      33.242          21        24.4          .
46156
             33.242      35.545          19        12.5
3.32927
             35.545      37.848          15        10.2
2.24074
             37.848      40.152          11        11.9          .
06613
             40.152      42.455           4         6.1          .
73455
             42.455      47.061          12        10.8          .
13612
             47.061      51.667           6         5.4          .
06181
             51.667      58.576           5         5.5          .
04171
 above       58.576                       5         5.2          .
00955
-----------------------------------------------------------------------
Chisquare =3D 17.3009 with 21 d.f.  Sig. level =3D 0.692713

4. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         200       191.5           .
3771
              1.000       3.909         324       329.5           .
0924
              3.909       6.818         378       384.7           .
1158
              6.818       9.727         292       284.0           .
2248
              9.727      12.636         208       209.7           .
0136
             12.636      15.545         150       154.8           .
1498
             15.545      18.455         111       114.3           .
0954
             18.455      21.364          95        84.4
1.3336
             21.364      24.273          64        62.3           .
0460
             24.273      27.182          37        46.0
1.7616
             27.182      30.091          27        34.0
1.4279
             30.091      33.000          30        25.1           .
9669
             33.000      35.909          16        13.0           .
7156
             35.909      38.818          10        15.1
1.7359
             38.818      41.727           9        11.2           .
4202
             41.727      44.636          14         8.2
4.0187
             44.636      47.545           9         6.1
1.3944
             47.545      53.364           9         7.8           .
1807
 above       53.364                       8         9.4           .
1979
-----------------------------------------------------------------------
Chisquare =3D 15.2684 with 17 d.f.  Sig. level =3D 0.576159

5. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         204       199.6          .
09594
              1.000       3.824         354       341.6          .
45004
              3.824       6.647         394       395.1          .
00322
              6.647       9.471         293       288.5          .
07120
              9.471      12.294         197       210.6          .
87821
             12.294      15.118         146       153.8          .
39074
             15.118      17.941          82        78.7          .
14007
             17.941      20.765          94        91.0          .
09830
             20.765      23.588          63        66.4          .
17834
             23.588      26.412          50        48.5          .
04595
             26.412      29.235          32        35.4          .
32896
             29.235      32.059          18        25.9
2.38581
             32.059      34.882          16        13.2          .
57978
             34.882      37.706          14        15.3          .
11103
             37.706      40.529           7        11.2
1.55828
             40.529      43.353           9         8.2          .
08720
             43.353      46.176          10         6.0
2.74788
             46.176      51.824           8         6.6          .
31021
 above       51.824                      14         9.5
2.09304
-----------------------------------------------------------------------
Chisquare =3D 12.5542 with 17 d.f.  Sig. level =3D 0.765481

9

Part  	Occurencies	Span
1 	     1989	     1-77	1/0.0995894
2	       1976      1-119 1/0.0973159
3        1979      1-61 1/0.0987969
4        1986      1-65 1/0.0979483
5        1972      1-72 1/0.0948168

The test of consistency of parts gave this results

			2		  	3		   	4		  	5
1		0.4550  0.7905  0.5891  0.1056
2           0.6163  0.8335  0.3920
3                   0.7737  0.1646
4                           0.2828

1. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         194       198.1          .
08417
              1.000       3.909         355       339.0          .
75998
              3.909       6.818         409       392.0          .
73428
              6.818       9.727         281       286.2          .
09390
              9.727      12.636         190       208.9
1.71232
             12.636      15.545         153       152.5          .
00160
             15.545      18.455         114       111.3          .
06406
             18.455      21.364          68        81.3
2.16687
             21.364      24.273          47        59.3
2.56139
             24.273      27.182          37        43.3          .
91899
             27.182      30.091          40        31.6
2.22370
             30.091      33.000          31        23.1
2.71848
             33.000      35.909          17        11.8
2.28122
             35.909      38.818          12        13.7          .
20152
             38.818      41.727          11        10.0          .
10616
             41.727      44.636           7         7.3          .
01069
             44.636      47.545           6         5.3          .
08867
             47.545      53.364           9         6.7          .
78113
 above       53.364                       8         7.7          .
01548
-----------------------------------------------------------------------
Chisquare =3D 17.5246 with 17 d.f.  Sig. level =3D 0.419407

2. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         189       192.3          .
05650
              1.000       5.212         623       599.4          .
92981
              5.212       9.424         379       398.0          .
90459
              9.424      13.636         260       264.2          .
06802
             13.636      17.848         192       175.4
1.56215
             17.848      22.061         128       138.9          .
85347
             22.061      26.273          69        69.8          .
00957
             26.273      30.485          47        46.4          .
00895
             30.485      34.697          30        30.8          .
01970
             34.697      38.909          17        20.4          .
57766
             38.909      43.121          17        16.2          .
04181
             43.121      47.333           6         8.1          .
55910
             47.333      51.545           6         5.4          .
06677
 above       51.545                      13        10.7          .
50942
-----------------------------------------------------------------------
Chisquare =3D 6.1675 with 12 d.f.  Sig. level =3D 0.907404

3. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         184       195.5     .
6786492187
              1.000       3.333         335       335.0     .
0000000360
              3.333       5.667         265       272.1     .
1838814450
              5.667       8.000         328       315.4     .
5063334464
              8.000      10.333         164       161.7     .
0317721839
             10.333      12.667         134       131.4     .
0532876757
             12.667      15.000         148       152.3     .
1188876157
             15.000      17.333          78        78.1     .
0000887198
             17.333      19.667          75        63.4
2.1157629325
             19.667      22.000          76        73.5     .
0845467590
             22.000      24.333          32        37.7     .
8612012838
             24.333      26.667          27        30.6     .
4272895323
             26.667      29.000          31        35.5     .
5676967785
             29.000      31.333          21        18.2     .
4307154983
             31.333      33.667          20        14.8
1.8422936119
             33.667      36.000          16        17.1     .
0749909255
             36.000      38.333          10         8.8     .
1674879847
             38.333      40.667           6         7.1     .
1809610804
             40.667      43.000          11         8.3     .
8997370805
             43.000      47.667           6         7.7     .
3704671662
             47.667      52.333           8         6.0     .
6347480039
 above       52.333                       4         8.9
2.6624800291
-----------------------------------------------------------------------
Chisquare =3D 12.8933 with 20 d.f.  Sig. level =3D 0.881916

4. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         208       194.5        .
9333844
              1.000       3.303         314       333.8
1.1694875
              3.303       5.606         281       271.6        .
3269634
              5.606       7.909         238       221.0
1.3106747
              7.909      10.212         268       256.7        .
4942479
             10.212      12.515         128       132.0        .
1201049
             12.515      14.818          92       107.4
2.2063069
             14.818      17.121         111       124.8
1.5194362
             17.121      19.424          70        64.1        .
5352777
             19.424      21.727          42        52.2
1.9899310
             21.727      24.030          58        60.6        .
1145371
             24.030      26.333          26        31.2        .
8578687
             26.333      28.636          26        25.4        .
0159539
             28.636      30.939          27        20.6
1.9608225
             30.939      33.242          24        24.0        .
0000206
             33.242      35.545           8        12.3
1.5184977
             35.545      37.848          10        10.0        .
0000894
             37.848      40.152          17        11.7
2.4537558
             40.152      42.455          10         6.0
2.6837806
             42.455      47.061          11        10.5        .
0203087
             47.061      51.667           4         5.3        .
3103368
             51.667      58.576           8         5.3
1.3524092
 above       58.576                       5         5.0        .
0001568
-----------------------------------------------------------------------
Chisquare =3D 21.8944 with 21 d.f.  Sig. level =3D 0.40562

5. part
Chisquare
Test
-----------------------------------------------------------------------
              Lower       Upper      Observed
Expected
              Limit       Limit      Frequency   Frequency
Chisquare
-----------------------------------------------------------------------
        at or below       1.000         177       187.0          .
53255
              1.000       3.303         311       322.5          .
40674
              3.303       5.606         276       264.2          .
52671
              5.606       7.909         229       216.5          .
72447
              7.909      10.212         253       253.7          .
00168
             10.212      12.515         119       131.6
1.19744
             12.515      14.818         111       107.8          .
09577
             14.818      17.121         133       126.3          .
35565
             17.121      19.424          63        65.5          .
09551
             19.424      21.727          52        53.7          .
05189
             21.727      24.030          69        62.9          .
59450
             24.030      26.333          41        32.6
2.15626
             26.333      28.636          25        26.7          .
11103
             28.636      30.939          12        21.9
4.47204
             30.939      33.242          29        25.7          .
43600
             33.242      35.545          15        13.3          .
21579
             35.545      37.848           8        10.9          .
77248
             37.848      40.152          13        12.8          .
00399
             40.152      42.455           4         6.6
1.04012
             42.455      44.758           5         5.4          .
03379
             44.758      47.061          11         6.4
3.38418
             47.061      51.667           4         6.0          .
66751
             51.667      58.576           6         6.2          .
00392
 above       58.576                       6         6.1          .
00178
-----------------------------------------------------------------------
Chisquare =3D 17.8818 with 22 d.f.  Sig. level =3D 0.712973

The results can be compared with the another irrational number, the
number e. Chisquare test values (3) of the first parts can be
compared
with the results on this page:

Digit			 0 		1		2		3		4		5		6		7		8		9
Ludolph	 736	650	818	831	417	156	116	972	793	895
e-number 010	854	197	310	967	918	453	172	092	419
The digits in both irrational numbers have different distributions.
kunzmilan