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 = 34.5433 with 18 d.f. Sig. level = 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 = 24.7712 with 20 d.f. Sig. level = 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 = 15.2713 with 21 d.f. Sig. level = 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 = 16.0125 with 16 d.f. Sig. level = 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 = 18.3208 with 17 d.f. Sig. level = 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 = 11.0327 with 17 d.f. Sig. level = 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 = 20.1552 with 20 d.f. Sig. level = 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 = 8.91624 with 17 d.f. Sig. level = 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 = 20.7224 with 17 d.f. Sig. level = 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 = 16.109 with 18 d.f. Sig. level = 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 = 21.6702 with 17 d.f. Sig. level = 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 = 19.9782 with 18 d.f. Sig. level = 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 = 11.9 with 17 d.f. Sig. level = 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 = 13.6404 with 17 d.f. Sig. level = 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 = 29.8634 with 21 d.f. Sig. level = 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 = 23.6372 with 21 d.f. Sig. level = 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 = 23.0679 with 17 d.f. Sig. level = 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 = 17.6115 with 17 d.f. Sig. level = 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 = 15.2389 with 16 d.f. Sig. level = 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 = 21.5941 with 17 d.f. Sig. level = 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 = 7.94905 with 17 d.f. Sig. level = 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 = 13.4875 with 17 d.f. Sig. level = 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 = 12.8834 with 15 d.f. Sig. level = 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 = 12.8923 with 15 d.f. Sig. level = 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 = 11.3625 with 17 d.f. Sig. level = 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 = 11.9203 with 20 d.f. Sig. level = 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 = 20.6512 with 18 d.f. Sig. level = 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 = 14.3864 with 20 d.f. Sig. level = 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 = 15.7305 with 18 d.f. Sig. level = 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 = 22.8325 with 17 d.f. Sig. level = 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 = 21.0891 with 21 d.f. Sig. level = 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 = 13.3664 with 17 d.f. Sig. level = 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 = 26.0416 with 22 d.f. Sig. level = 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 = 24.1331 with 21 d.f. Sig. level = 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 = 19.9077 with 17 d.f. Sig. level = 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 = 26.9544 with 21 d.f. Sig. level = 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 = 13.1097 with 17 d.f. Sig. level = 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 = 21.3179 with 21 d.f. Sig. level = 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 = 17.9137 with 20 d.f. Sig. level = 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 = 18.2733 with 17 d.f. Sig. level = 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 = 31.1613 with 22 d.f. Sig. level = 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 = 13.5585 with 17 d.f. Sig. level = 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 = 17.3009 with 21 d.f. Sig. level = 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 = 15.2684 with 17 d.f. Sig. level = 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 = 12.5542 with 17 d.f. Sig. level = 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 = 17.5246 with 17 d.f. Sig. level = 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 = 6.1675 with 12 d.f. Sig. level = 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 = 12.8933 with 20 d.f. Sig. level = 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 = 21.8944 with 21 d.f. Sig. level = 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 = 17.8818 with 22 d.f. Sig. level = 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.