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The Pamphlet Collection of Sir Robert Stout: Volume 80a

Ages Over Seventy-Five

Ages Over Seventy-Five.

As the numbers living over 75 were few, it I was not thought desirable to adhere strictly to the data after that, age, and finding that the probabilities! according to the healthy districts, closely approximated those of this colony, a junction was effected between 76 and 80, and the calculations completed by the probabilities of that table, with this difference, that the table of males was brought to a close at age 100, and that of females at age 103.

It will he seen from the comparisons made, and the tables appended hereto, that the rates of mortality which have prevailed in this colony are very favourable—so favourable, indeed, as to be remarkable—and a full description of the materials and processes employed has been given so that any one so inclined may test the correctness of the results.

Tables of monetary values, calculated on a 4 per cent basis, are attached, and by means of them a large number of questions relating to annuities, assurances, endowments to children, old age pensions, and superannuation to the members of Friendly Societies, can be answered

Much has been said and written of the natural resources of this colony—of the fertility of its soil, of its mineral treasures, of the variety and grandeur of its scenery, of its many striking natural phenomena—and the results of this inquiry, while not making any claim to a discovery of a new source of wealth, will, it is hoped (from the length of time over which the observations extend, and the care exercised in dealing with the data and deducing the various results), assist in confirming the judgments passed by others on its climate, and afford fresh proof that New Zealand can still be regarded as the healthiest country in the world. The uses of inch tables as we have deduced are manifold, They will be of use to the physician, to the political economist, and to the social and sanitary reformer. And here it may be said that one of the main objects in entering upon this inquiry originally, was to determine, from the actual mortality experience of the colony, the monetary value of certain benefits connected with our friendly societies, and some of the schemes of old age pensions.

For this reason tables of the values of annuities, and the single and annual premiums for the assurance of a unit (say £1), accompany the tables of mortality, and will, it is hoped, be found worthy of some attention. Whether the tables now submitted will ever be adopted to any great extent for the valuation of interests dependant on human life, will depend on the estimate formed by those more immediately interested, of how far the past experience is likely to be repeated in the future.

Meantime it behoves the people of this colony to strive to maintain the position here exhibited, and to improve upon it in every direction that science and experience dictates.

Comparison of Various Mortality Tables-Showing out of 10,000 Born Alive the Number Entering on Each of the Ages Specified.
Males
Ages New Zeal' nd Victoria. Healthy Districts, England. Peerage.
0 10,000 10,000 10,000 10,000
5 8,733 8,120 8,141 8,907
10 8,593 7,966 7,857 8,753
15 8,493 7,865 7,713 8,605
20 8,336 7,713 7,510 8,288
25 8,118 7,488 7,240 7,857
30 7,900 7,221 6,957 7,4S0
35 7,655 6,926 6,671 7,162
40 7,374 6,585 6,380 6,847
45 7,040 6,185 6,071 6,486
50 6,629 5,706 6,728 6,061
55 6,142 5,129 6,320 5,578
60 5,504 4,447 4,851 5,034
65 4,706 3,67l 4,195 4,382
70 3,747 2,759 3,354 3,528
75 2,703 1,828 2,383 2,409
80 1,606 992 1,413 1,352
85 730 407 642 576
90 228 115 196 95
95 43 20 37 -
Famales
0 10,000 10,000 10,000 10,000
5 8,900 8,204 8,356 9,093
10 8,785 8,147 8,052 8,870
15 3,687 8,054 7,864 8,612
20 8,536 7,902 7,614 8,294
25 3,330 7,686 7,314 7,961
30 8,086 7,416 7,004 7,629
35 7,810 7,116 6,690 7,281
40 7,512 6,775 6,373 6,900
45 7,207 6,399 6,050 6,510
50 6,881 5,988 5,714 6,106
55 6,485 5,530 5,354 5,646
60 6,980 4,983 4,923 5,078
65 5,305 4,333 4,300 4,386
70 4,429 3,429 3,506 3,549
75 3,375 2,437 2, 566 2,666
80 2,118 1,401 1,586 1,799
85 1,015 686 760 1,048
90 330 230 254 480
95 69 50 52 134
Table E. Mortality Table.—New Zealand, 1880-1892, Males.
Age,x lx dx px qx °ex Age,x.
0 100,000 9,402 .90503 .09492 54.444 0
1 90,508 1,620 .98209 .01791 59.102 1
2 88,888 685 .90229 .00771 59.169 2
3 88,203 450 .99490 .00510 53.626 3
4 87,753 372 .99577 .00423 57.924 4
5 37,381 349 .99600 .00400 57.167 5
6 87,032 326 .99625 .00375 56.396 6
7 86,706 293 .99662 .00338 55.606 7
8 46,413 260 .99699 .06301 54.791 8
9 36,153 221 .99742 .00258 53.956 9
10 85,932 193 .99777 .09223 53.094 10
11 85,739 171 .99800 .00200 52.212 11
12 85,563 183 .99772 .00214 51.316 12
13 85,385 191 .99772 .00223 50.425 13
14 85,191 216 .99747 .00253 49.539 14
15 84,075 246 .99710 .00290 48.663 15
16 84,729 283 .99644 .00356 47.303 16
17 84,446 323 .99616 .00384 46.960 17
18 84,123 363 .99570 .00430 46.139 18
19 83,760 397 .99524 .00476 45.336 19
20 83,363 423 .99492 .00508 44.551 20
21 83,940 438 .99472 .00528 43.775 21
22 82,502 445 .99463 .00537 43.005 22
23 82,057 444 .99458 .00542 42.235 23
24 81,613 438 .99463 .00537 41.463 24
25 81,175 433 .99467 .00533 40.684 25
26 80,742 429 .99470 .00530 39.899 26
27 30,313 432 .99460 .00540 39.108 27
28 79,881 437 .99453 .00547 38.319 28
29 79,444 448 .99437 .00563 37.526 29
30 78,996 461 .99415 .00585 36.736 30
31 78,535 476 .99394 .00606 35.949 31
32 78,059 491 .99371 .00629 35.165 32
33 77,568 503 .99353 .00647 34.384 33
34 77,065 517 .99328 .00672 33.605 34
35 76,548 530 .99309 .00691 32.829 35
36 76,018 543 .99284 .00716 32.054 36
37 75,475 559 .99259 .00741 31.282 37
38 74,916 577 .99232 .00768 30.511 38
39 74,339 597 .99195 .00805 29.744 39
40 73,742 613 .99163 .00837 28.979 40
41 73,124 641 .99124 .00876 28.220 41
42 72,483 666 .99081 .00919 27.465 42
43 71,817 692 .99035 .00965 26.715 43
44 71,125 721 .98987 .01013 25.971 44
45 70,404 754 .98928 .01072 25.231 45
46 69,650 787 .98871 .01129 34.499 46
47 68,863 824 .98803 .01197 23.773 47
48 68,039 857 .98739 .01261 23.055 48
49 67,182 889 .98678 .01322 22.344 49
50 66,293 916 .98619 .01381 21.636 50
61 65,377 939 .98562 .01438 20.932 51
52 64,438 967 .98501 .01499 20.231 52
53 63,471 1,002 .98419 .01581 19.530 53
54 62,469 1,053 .98316 .01685 18.836 54
55 61,416 1,120 .98177 .01823 18.150 55
56 60,296 1,198 .98012 .01988 17.478 56
57 50,098 1,281 .97834 .02166 16.822 57
58 67,817 1,356 .97664 .02346 16.183 58
59 66,461 1,421 .97483 .02517 16.560 59
60 55,040 1,477 .97315 .02685 14.949 60
61 53,503 1,527 .97149 .02851 14.348 61
62 52,036 l,584 .96957 .03043 13.754 62
63 60,452 1,654 .96721 .03279 13.170 63
64 48,798 1,738 .96438 .03662 12.600 64
65 47,000 1,823 .96126 .03874 12.046 65
66 45,237 1,899 .95803 .04197 11.512 66
67 43,338 1,942 .95519 .04481 10.004 67
68 41,396 1,963 .95282 .04718 10.436 68
69 39,443 1,976 .94990 .05010 9.981 69
70 37,407 2,000 .94661 .05339 9.481 70
71 36,467 2,033 .94269 .06731 8.988 71
72 33,434 2,081 .93776 .06224 8.504 72
73 31,353 2,137 .93184 .06816 8.035 73
74 29,216 2,189 .92508 .07492 7.588 74
75 27,627 2,227 .91759 .08241 7.160 75
76 24,800 2,240 .90968 .09032 6.758 76
77 52,560 2,223 .90147 .09853 6.379 77
78 20,337 2,176 .89304 .10696 6.022 78
79 18,162 2,102 .88428 .11572 5.683 79
80 16,060 2,006 .87508 .12492 5.362 80
81 14,054 1,893 .86631 .13469 5.054 81
82 12,161 1,766 .86477 .14523 4.765 82
83 10,896 1,626 .84359 .16641 4.489 83
84 8,769 1,473 .83201 .16799 4.229 84
85 7,296 1,315 .81977 .18023 3.082 85
86 6,981 1,156 .80673 .19327 8.747 86
87 4,626 997 .79336 .20644 3.525 87
88 3,828 846 .77926 .22074 3.313 88
89 2,983 703 .76433 .23567 3.110 89
90 2,280 572 .74913 .25087 2.914 90
91 1,706 453 .73477 .26623 2.723 91
92 1,265 355 .71713 .23287 2.525 92
93 900 269 .70112 .29888 2.323 93
94 631 200 .068305 .31695 2.101 94
95. 431 149 .65429 .34571 1.843 95
96 282 112 .60284 .39716 1.553 96
97 170 83 .51176 .48824 1.247 97
98 87 53 .39080 .60920 .960 98
99 34 28 .17647 .82353 .677 90
100 6 6 .. 1.0000 .500 100
Table F.
Females.
Age x lx. dx. px qx ex ax=Value of £1 per annum far life, 4 per cent. interest x Age
0 100,000 8,027 .91973 .08027 57.260 19.595 0
1 91,973 1,498 .98372 .01623 61.214 21.156 1
2 90,475 635 .99298 .00702 61.220 11.303 2
3 89,840 425 .99527 .00473 60.647 21.379 3
4 89,415 391 .99641 .00359 59.934 21.340 4
5 89,094 295 .99669 .00331 59.148 21.276 5
6 88,790 271 .99694 .00306 58.343 21.199 6
7 88,528 248 .99719 .00281 57.520 21.113 7
8 88,280 226 .99745 .00255 55.680 21.020 8
9 88,054 205 .99768 .00232 55.825 20.910 9
10 87,849 186 .99788 .00212 54.953 20.804 10
11 87,663 180 .99793 .00207 54.069 20.681 11
12 87,483 189 .99784 .00210 53.180 20.664 12
13 87,294 203 .99762 .00232 52.294 20.423 13
14 87,091 225 .99742 .00258 51.415 20.289 14
15 86,866 250 .99713 .00287 50.545 20.155 15
16 86,616 275 .99683 .00317 49.690 20.022 16
17 84,341 202 .99651 .00349 48.847 19.889 17
18 86,039 328 .99619 .00381 43.010 19.757 18
19 85,711 352 .99589 .00411 47.193 19.626 19
20 85,359 374 .99561 .00430 46.393 19.496 20
21 84,985 394 .99536 .00464 45.593 19.365 21
22 84,591 413 .99533 .00487 44.803 19.233 22
23 84,178 431 .99488 .00512 44.021 19.100 23
24 83,747 447 .99467 .00633 43.244 18.966 24
25 83,300 462 .99444 .00556 42.474 18.831 25
26 82,838 476 .99426 .00574 41.708 18.093 26
27 82,302 488 .99103 .00592 40.940 18.588 27
28 81,874 500 .99389 .00611 40.187 18.410 28
29 81,374 513 .99309 .00631 39.431 18.205 29
30 80,861 526 099348 .00052 38.678 18.115 30
31 80,335 640 .99330 .00070 37.928 17.904 31
32 79,795 553 .99307 .00693 37.181 17.809 32
33 79,242 564 .99234 .00714 30.433 17.650 33
34 78,678 576 .99268 .00732. 35.095 17.488 34
35 78,102 580 .99250 .00750 34.954 17.322 35
36 77,510 593 .99236 .00764 34.215 17.161 36page 8
37 76,923 599 .99220 .00780 33.475 16.974 37
38 76,324 602 .99211 .00789 32.734 16.792 38
39 76,722 604 .99202 .00798 31.990 16.602 39
40 76,118 605 .99195 .00805 21.243 16.405 40
41 74,613 606 .99188 .00812 30.493 16.200 41
42 73,907 608 .99177 .00823 29.789 16.986 42
43 73,299 612 .99165 .00835 23.981 15.763 43
44 72,687 617 .99149 .00856 28.221 15.532 44
45 72,070 624 .99136 .00864 27.458 16.292 45
46 71,446 634 .99113 .00887 26.694 15.042 46
47 70,812 648 .99083 .00917 25.927 14.784 47
48 70,164 667 .99051 .00949 25.163 14.517 48
49 69,497 691 .99006 .00994 24.399 14.242 49
50 68,806 721 .98951 .01049 23.640 13.961 50
51 68,085 758 .98894 .01106 22.885 13.676 51
52 67,332 789 .98828 .01172 22.135 13.380 52
53 66,543 828 .98765 .01245 21.392 13.079 53
54 66,715 868 .98680 .01320 20.065 12.774 54
55 64,847 911 .98596 .01404 19.926 12.463 55
56 68,986 955 .98505 .01495 19.202 12.146 56
57 62,981 1,004 .98406 .01594 18.485 11.823 57
58 61,977 1,057 .98295 .01705 17.776 11.496 58
59 60,920 1,116 .98168 .01332 17.077 11.163 59
60 59,804 1,178 .98030 .01970 16.386 10.320 60
61 68,626 1,255 .97859 .02141 15.705 10.485 61
62 57,371 1,343 .97661 .02339 15.037 10.143 62
63 56,028 1,439 .97432 .02568 14.386 9.801 63
64 54,589 1,535 .97187 .02813 13.752 9.462 64
65 53,054 1,623 .96942 .03068 13.135 9.126 65
66 51,431 1,697 .96699 .03301 12.534 8.790 66
67 49,734 1,763 .96456 .03544 11.946 8.454 67
68 47,971 1,815 .96217 .03783 11.365 8.115 68
69 46,166 1,871 .95947 .04053 10.792 7.771 69
70 44,285 1,938 .95622 .04378 10.227 7.424 70
71 42,347 2,014 .96245 .04755 9.073 7.074 71
72 40,333 2,098 .94798 .05202 9.130 6.724 72
73 38,235 2,183 .94291 .05709 8.604 6.377 73
74 36,052 2,307 .93601 .06399 3.095 6.034 74
75 33,745 2,420 .92828 .07172 7.614 5.704 75
76 31,325 2,503 .92009 .07991 7.164 5.391 70
77 28,822 2,552 .91147 .08853 6.742 5.093 77
78 26,270 2,565 .90236 .09704 6.346 4.812 78
79 23,705 2,530 .89326 .10674 6.982 4.545 79
80 21,176 2,462 .88373 .11627 5.636 4.292 80
81 13,713 2,355 .87416 .12584 5.312 4.051 81
82 10,358 2,226 .86397 .13603 5.005 3.819 82
83 14,183 2,075 .85320 .14680 4.714 3.598 83
84 12,068 1,908 .84170 .14824 4.430 3.365 84
85 10,150 1,729 .82964 .17036 4.180 3.183 86
86 8,421 1,541 .81701 .18299 3.935 2.989 86
87 6,880 1,350 .80379 .19621 3.705 2.805 87
88 6,580 1,163 .78968 .21032 8.487 2.630 88
89 4,367 981 .77537 .22463 3.283 2.463 89
90 3,386 812 .76019 .23981 3.089 2.304 90
91 2,574 658 .74437 .25563 2.731 2.152 91
92 1,916 621 .72806 .27194 2.731 2.067 92
93 1,305 402 .71184 .28816 2.564 1.866 93
94 993 304 .69386 .30614 2.400 1.727 94
95 689 225 .67344 .32656 2.238 1.588 95
96 464 162 .65086 .34914 2.082 1.452 96
97 302 112 .62913 .37087 1.931 1.321 97
98 190 75 .60527 .39473 1.774 1.133 98
98 115 49 .57391 .42609 1.600 1.032 99
100 66 30 .54546 .45454 1.424 0.871 100
101 36 18 .50000 .50004 1.195 0.661 101
102 18 11 .38889 .61111 0.889 0.374 102
103 7 7 .. 1.00000 .500 .. 103

lx. Number dying at each age out of 100,000 children born.

dx. Number dying at each age out of 100,000 children born.

px. Probability of living a year.

qx. Probability of dying in a year.

°ex Complete expectation of life.

Table G. New Zealand Mortality, 1880-1892. Values of Annuities and Single and Annual Premiums for Assurance of £1;4 per cent. interest.
x Age ax. Ax. Px.
0 19.074 .22792 .011354
1 20.918 .15702 .007164
2 21.151 .14805 .006684
3 21.168 .14740 .006649
4 21.127 .14895 .006732
5 21.066 .15132 .006858
6 20.997 .16399 .007001
7 20.918 .15690 .007162
8 20.828 .16044 .007350
9 20.727 .16434 .007564
10 20.612 .16378 .007810
11 20.485 .17368 .008084
12 20.346 .17899 .008385
13 20.205 .18440 .008696
14 20.062 .18994 .009018
15 19.917 .19549 .009346
16 19.774 .20100 .009675
17 19.634 .20639 .010003
18 19.498 .21163 .010325
19 19.365 .21671 .010641
20 19.236 .22170 .019955
21 19.108 .22604 .011271
22 18.977 .23164 .011595
23 13.343 .23679 .011959
24 18.704 .24215 .012290
25 18.557 .24782 .012672
26 16.403 .2537 5 .013078
27 18.241 .25996 .013511
28 18.073 .26642 .013968
29 17.900 .27310 .014450
30 37.721 .27996 .014954
31 17.538 .28700 .015482
32 17.351 .29420 .016032
33 17.159 .30157 .016607
34 16.962 .30915 .017212
35 16.760 .31695 .017846
36 16.552 .32494 .018514
37 16.337 .33318 .019217
38 16.118 .34164 .019058
39 15.892 .35029 .020737
40 15.662 .35915 .021556
41 15.426 .36823 .022417
42 15.185 .37749 .023324
43 14.939 .38696 .024278
44 14.638 .39664 .025284
45 14.431 .40647 .026340
46 14.171 .41649 .027453
47 13.907 .42668 .028623
43 13.638 .43700 .029854
49 13.364 .44752 .031165
50 13.085 .46826 .032535
51 12.799 .46925 .034006
52 12.505 .48055 .035582
53 12.204 .49216 .037276
54 11.895 .50403 .039036
55 11.583 .51602 .041009
56 11.270 .52806 .043035
57 10.959 .54005 .045159
58 10.660 .55192 .045159
59 10.342 .56379 .049710
60 10.033 .57565 .052176
61 9.722 .58761 .054804
62 9.408 .59972 .057023
63 9.091 .61187 .060035
64 8.775 .62402 .063837
65 8.464 .63603 .067209
66 8.157 .64784 .670751
67 7.855 .65943 .074473
68 7.552 .67109 .078471
69 7.243 .66295 .082851
70 6.930 .69498 .087642
71 6.614 .70716 .092832
72 6.296 .71935 .098592
73 5.983 .73141 .10474
74 5.677 .74317 .11130
75 5.383 .75452 .11822
76 5.101 .76535 .12546
77 4.831 .77571 .13303
73 4.574 .78562 .14095
79 4.326 .79513 .14929
80 4.088 .80430 .15303
81 3.858 .81313 .16736
82 3.687 .82154 .17718
83 3.426 .32981 .18750
84 3.223 .83759 .19833
85 0.029 .84505 .20974
86 2.843 .85220 .22177
87 2.665 .85903 .23441
88 2.498 .86569 .24773
89 2.327 .87203 .26208
90 2.167 .87321 .27733
91 2.008 .88428 .29397
92 1.842 .89072 .31340
93 1.671 .89728 .33539
94 1.479 .90463 .36489
95 1.252 .91338 .40555
96 .990 .92344 .46396
97 .708 .93429 .54689
98 .440 .94463 .65619
99 .170 .95497 .81647
100 .. .96154 .96164

ax. The present value of an annuity of £1, payable at the end of each year through which x shall live.

Ax. The present value of an assurance of £1, payable at the end of the year in which x shall die

Px. The annual premium for an assurance of £1 on the life aged x.