# Transactions and Proceedings of the New Zealand Institute/Volume 29/Article 2

Art. II.—An Investigation into the Rates of Mortality in New Zealand during the Period 1881–91.
By C. E. Adams, B.Sc., A.I.A., F.S.S., Lecturer on Applied Mathematics, Lincoln College.
[Read before the Philosophical Institute of Canterbury, 6th May, 1896.]
Plates I.–IV.
The following tables, showing the rates of mortality in New Zealand during the period 1881–91, are deduced from the censuses for 1881, 1886, and 1891, and from the deaths for each year during the period.
Generally it may be said that the final tables show a comparison of the numbers living at each age with the deaths occurring at that age. It would have been possible to have computed the tables from one census and the deaths in that census year, but it was considered preferable to use average results, and for this purpose the average population as given by the three censuses has been employed, and the average number of deaths has also been used. In adopting this method there is a greater chance of the final results exhibiting correctly the general mortality of the colony than there would have been had the figures relating to one year only been employed.
The census has never been taken in the middle of a calendar year in New Zealand. In 1881 it was taken on the 3rd April, in 1886 on the 28th March, and in 1891 on the 5th April. This necessitates an assumption being made as to the population living on the 1st July in each year, for the numbers living in the middle of the year have to be compared with the deaths during the year. It was assumed that the population on the 1st July was the mean of the populations on the 1st January and the 31st December. The numbers living in each age-group, as given by the census, were increased in the same proportion as the whole population had increased from the date of the census to the 1st July. This adjustment was made for each of the three censuses, and the total for each agegroup found. One-third of these totals gives the average number of persons living in each of the age-groups, as shown in Table A.
No adjustments were necessary for the deaths. One-eleventh of the total number of deaths in each age-period for the eleven years 1881-91 was taken for the average number of deaths, and the results are given in Table A.
​It will be observed that the average deaths and average population in Table A are given in groups of five years. The next step in the construction of the final tables is to ascertain the population and deaths at each year of age. The method now generally adopted is that known as Milne's Graphic Method. After a very careful consideration of this method it was decided not to adopt it, but to use instead a mathematical process of distribution based on the method employed by G. W. Berridge ("Journal of the Institute of Actuaries," xiii., 220, and xiv., 244; "Text-book of the Institute of Actuaries," Part ii., p. 465). The results of the distribution are given in Table B. As a test of the smoothness of the distribution, the results were drawn to scale on large diagrams, of which Plates I. and II. are reduced copies.
The population and deaths from 5 to 75 were treated in this way, the figures relating to the first five years of life requiring special treatment.
From Table B the ratio of deaths to population at each age ($m_{x}$) is at once obtained, and these ratios are given in Table C.
The probability of living a year at each age ($p_{x}$) is derived immediately from $m_{x}$ by means of the relation $p_{x}={\frac {2-m_{x}}{2+m_{x}}}$. The columns headed $p_{x}$ in Table E, from 5 to 75, were calculated by means of this formula.
The ages 0 to 5 now require consideration. Table D gives the annual births and deaths of children under five years of age for each of the years 1880–92. From these figures, by means of a modification of the method used by Dr. Farr ("Journal of the Institute of Actuaries," ix., p. 134), the probabilities of living a year at each age were determined. The results, after a slight adjustment to make them join smoothly on to the rest of the table, are given in column $p_{x}$, ages 0–5, in Table E.
The probability of dying in the year at each age ($q_{x}$) is obtained from $p_{x}$ by subtracting $p_{x}$ from unity: thus, ${q_{x}}={1-p_{x}}$.
The next column in the order of formation is the $l_{x}$ column. Starting with an assumed 10,000 births ($l_{0}$), the number surviving the year ($l_{1}$) is obtained from the relation $l_{1}=l_{0}\times p_{0}$. Similarly the number who reach the age of two alive, out of 10,000 born alive, is $l_{2}=l_{1}\times p_{1}$ or generally for any year x, $l_{x}=l_{x-1}\times p_{x-1}$.
The difference between the number born, $l_{0}$, and the number surviving the first year, $l_{1}$, gives the number who die in the first year, $d_{0}$, or $d_{0}=l_{0}-l_{1}$. Similarly for the number who die in the second year, $d_{1}$, $d_{1}=l_{1}-l_{2}$, and generally for the number dying in the xth year $d_{x-1}=l_{x-1}-l_{x}$. In this manner the column $d_{x}$ was formed.
​It is not intended in the present investigation to carry these results past age 75, as the available data are insufficient to warrant satisfactory results. It must also be borne in mind that the colony dates from 1840, and the above tables terminate at 1891, consequently all results past age 51 cannot relate to native-born New-Zealanders.
General Explanation of Table E.
Column $l_{x}$: This column shows how many out of 10,000 born alive reach each year of age up to 75. Thus, $l_{25}$ (males) = 8,112, and $l_{25}$ (females) = 8,316, or, out of 10,000 males born alive, 8,112 reach the age of 25, and out of 10,000 females born alive 8,316 reach the age of 25.
The two columns $l_{x}$ for males and females are not strictly comparable, for they do not represent the actual numbers born, but only numbers proportional to them. As is well known, the number of male births exceeds the number of female births. The columns show for each sex how, out of 10,000 born, the numbers gradually diminish.
Column $d_{x}$: This colunm shows the deaths each year out of 10,000 born alive. Thus, $d_{25}$ (males) = 43, and $d_{25}$ (females) = 45, or 43 males die between the ages 25 and 26, and 45 females die between the ages 25 and 26.
Column $p_{x}$: This column gives the probability of living a year at each age. Thus, $p_{25}$ (males) = .9947, and $p_{25}$ (females) = .9946, or 9,947 males out of 10,000 alive at age 25 survive the year; and 9,946 out of 10,000 females alive at age 25 reach age 26.
Column $q_{x}$: This column gives the probability of dying in a year at each age. Thus, $q_{25}$ (males) = .0053, and $q_{25}$ (females) = .0054, or 53 males out of 10,000 alive at age 25 die in the year; and 54 out of the same number of females alive at 25 die in the year.
Plates III. and IV. show the results of the life tables graphically. From the column $l_{x}$ it will be observed that the males are reduced to half the number born between the ages 63 and 64, while it is not till between the ages 66 and 67 that the females are similarly reduced.
The whole of the calculation was done in duplicate, and every care has been exercised to insure accuracy. Some of the results have been checked graphically, results true to four significant figures being easily obtained by this process.
In conclusion, I have to express my thanks to my friend, Mr. Morris Fox, A.I.A., Actuary to the Government Life Insurance Department, for his ever-ready and valuable assistance in the preparation of this paper.
Table A.—Average Population and Average Deaths, 1881–91, in Five-year Periods.
| Ages. | Males. | Males. | Females. | Females. |
| Ages. | Population. | Deaths. | Population. | Deaths. |
| 0–5 | 42,832 | 1234.20 | 41,766 | 1025.50 |
| 5–10 | 40,348 | 137.18 | 39,551 | 113.09 |
| 10–15 | 34,771 | 77.09 | 34,323 | 74.45 |
| 15–20 | 27,783 | 103.36 | 28,167 | 102.82 |
| 20–25 | 25,172 | 134.64 | 24,674 | 119.36 |
| 25–30 | 24,171 | 129.64 | 19,778 | 113.73 |
| 30–35 | 21,736 | 136.91 | 16,227 | 109.45 |
| 35–40 | 20,258 | 149.09 | 14,302 | 116.00 |
| 40–45 | 19,165 | 176.64 | 12,601 | 104.27 |
| 45–50 | 16,433 | 200.55 | 9,897 | 90.64 |
| 50–55 | 13,365 | 205.73 | 7,491 | 91.78 |
| 55–60 | 7,938 | 175.00 | 4,533 | 74.91 |
| 60–65 | 5,520 | 168.09 | 3,409 | 77.55 |
| 65–70 | 2,968 | 147.73 | 2,026 | 74.45 |
| 70–75 | 1,761 | 108.82 | 1,350 | 72.09 |
Table B.—Population and Deaths for each Year from 5 to 75.
| Ages. | Males. | Males. | Females. | Females. |
| Ages. | Population. | Deaths. | Population. | Deaths. |
| 5 | 8,356.2 | 40.16 | 8,210.6 | 33.32 |
| 6 | 8,240.9 | 32.06 | 8,082.3 | 26.17 |
| 7 | 8,098.3 | 25.81 | 7,935.6 | 20.96 |
| 8 | 7,926.6 | 21.19 | 7,763.4 | 17.42 |
| 9 | 7,726.0 | 17.98 | 7,568.1 | 15.22 |
| 10 | 7,497.9 | 15.96 | 7,352.2 | 14.15 |
| 11 | 7,244.4 | 14.95 | 7,119.4 | 13.94 |
| 12 | 6,969.8 | 14.77 | 6,873.4 | 14.42 |
| 13 | 6,679.2 | 15.23 | 6,618.5 | 15.35 |
| 14 | 6,379.7 | 16.19 | 6,359.5 | 16.59 |
| 15 | 5,995.8 | 17.50 | 6,043.7 | 17.97 |
| 16 | 5,729.0 | 19.03 | 5,810.5 | 19.38 |
| 17 | 5,502.9 | 20.68 | 5,605.2 | 20.72 |
| 18 | 5,820.9 | 22.32 | 5,423.6 | 21.90 |
| 19 | 5,184.4 | 23.87 | 5,279.0 | 22.85 |
| 20 | 5,147.3 | 25.56 | 5,243.7 | 23.33 |
| 21 | 5,076.0 | 26.60 | 5,105.6 | 23.81 |
| 22 | 5,021.9 | 27.29 | 4,952.1 | 24.08 |
| 23 | 4,980.3 | 27.59 | 4,780.7 | 24.14 |
| 24 | 4,946.5 | 27.56 | 4,591.9 | 24.00 |
| 25 | 4,951.2 | 26.25 | 4,828.2 | 23.40 |
| 26 | 4,908.4 | 25.96 | 4,130.2 | 23.06 |
| 27 | 4,850.5 | 25.76 | 3,942.7 | 22.73 |
| 28 | 4,775.8 | 25.74 | 3,768.1 | 22.40 |
| 29 | 4,685.1 | 25.89 | 3,608.8 | 22.14 |
| 30 | 4,527.1 | 26.62 | 3,470.8 | 21.78 |
| 31 | 4,427.7 | 26.97 | 3,343.2 | 21.71 |
| 32 | 4,336.8 | 27.34 | 3,230.9 | 21.78 |
| 33 | 4,256.6 | 27.76 | 3,133.2 | 21.95 |
| 34 | 4,187.8 | 28.21 | 3,048.9 | 22.23 |
| 35 | 4,140.1 | 28.32 | 2,988.1 | 23.14 |
| 36 | 4,090.5 | 28.92 | 2,921.6 | 23.35 |
| 37 | 4,047.2 | 29.68 | 2,858.7 | 23.38 |
| 38 | 4,008.4 | 30.57 | 2,797.6 | 23.24 |
| 39 | 3,971.8 | 31.61 | 2,736.0 | 22.89 |
| 40 | 3,904.9 | 33.01 | 2,686.6 | 22.10 |
| 41 | 3,914.6 | 34.19 | 2,613.7 | 21.52 |
| 42 | 3,849.0 | 35.36 | 2,530.5 | 20.87 |
| 43 | 3,707.3 | 36.49 | 2,437.0 | 20.22 |
| 44 | 3,669.2 | 37.55 | 2,333.2 | 19.56 |
| 45 | 3,613.4 | 38.64 | 2,191.2 | 18.67 |
| 46 | 3,399.5 | 39.53 | 2,081.4 | 18.23 |
| 47 | 3,286.3 | 40.28 | 1,975.1 | 17.97 |
| 48 | 3,173.5 | 40.87 | 1,873.4 | 17.86 |
| 49 | 3,060.3 | 41.28 | 1,775.9 | 17.91 |
| 50 | 3,011.6 | 41.76 | 1,716.7 | 18.79 |
| 51 | 2,868.8 | 41.70 | 1,615.2 | 18.77 |
| 52 | 2,698.6 | 41.39 | 1,505.5 | 18.56 |
| 53 | 2,502.2 | 40.81 | 1,388.3 | 18.12 |
| 54 | 2,283.8 | 40.04 | 1,205.3 | 17.49 |
| 55 | 1,948.8 | 36.94 | 1,090.4 | 15.85 |
| 56 | 1,737.9 | 35.70 | 980.1 | 15.20 |
| 57 | 1,555 9 | 34.73 | 887.8 | 14.77 |
| 58 | 1,406.3 | 34.02 | 814.7 | 14.54 |
| 59 | 1,289.1 | 33.61 | 760.0 | 14.55 |
| 60 | 1,286.0 | 34.32 | 769.1 | 15.31 |
| 61 | 1,199.4 | 34.10 | 729.6 | 15.47 |
| 62 | 1,109.3 | 33.76 | 686.5 | 15.57 |
| 63 | 1,013.6 | 33.29 | 638.5 | 15.62 |
| 64 | 911.7 | 32.63 | 585.3 | 15.58 |
| 65 | 760.2 | 31.93 | 496.5 | 15.42 |
| 66 | 664.1 | 30.93 | 443.8 | 15.19 |
| 67 | 580.6 | 29.73 | 397.9 | 14.90 |
| 68 | 510.1 | 28.33 | 359.2 | 14.61 |
| 69 | 453.0 | 26.78 | 328.6 | 14.33 |
| 70 | 430.4 | 25.14 | 320.0 | 14.10 |
| 71 | 389.3 | 23.42 | 295.7 | 14.01 |
| 72 | 350.5 | 21.68 | 270.8 | 14.14 |
| 73 | 313.5 | 20.03 | 245.2 | 14.53 |
| 74 | 277.3 | 18.53 | 218.3 | 15.31 |
Table C.—Ratio of Deaths to Population at each Age ($m_{x}$).
| Ages. | Males. | Females. | Ages. | Males. | Females. |
| 5 | .0048 | .0042 | 40 | .0083 | .0082 |
| 6 | .0039 | .0033 | 41 | .0087 | .0082 |
| 7 | .0032 | .0026 | 42 | .0092 | .0082 |
| 8 | .0027 | .0022 | 43 | .0097 | .0083 |
| 9 | .0023 | .0020 | 44 | .0102 | .0084 |
| 10 | .0021 | .0019 | 45 | .0110 | .0085 |
| 11 | .0021 | .0020 | 46 | .0116 | .0088 |
| 12 | .0021 | .0021 | 47 | .0123 | .0091 |
| 13 | .0023 | .0023 | 48 | .0129 | .0095 |
| 14 | .0025 | .0026 | 49 | .0135 | .0101 |
| 15 | .0029 | .0030 | 50 | .0139 | .0109 |
| 16 | .0033 | .0033 | 51 | .0145 | .0116 |
| 17 | .0038 | .0037 | 52 | .0153 | .0123 |
| 18 | .0042 | .0040 | 53 | .0163 | .0131 |
| 19 | .0046 | .0043 | 54 | .0175 | .0138 |
| 20 | .0050 | .0044 | 55 | .0190 | .0145 |
| 21 | .0052 | .0047 | 56 | .0205 | .0155 |
| 22 | .0054 | .0049 | 57 | .0223 | .0166 |
| 23 | .0055 | .0050 | 58 | .0242 | .0178 |
| 24 | .0056 | .0052 | 59 | .0261 | .0191 |
| 25 | .0053 | .0054 | 60 | .0267 | .0199 |
| 26 | .0053 | .0056 | 61 | .0284 | .0212 |
| 27 | .0053 | .0058 | 62 | .0305 | .0227 |
| 28 | .0054 | .0059 | 63 | .0328 | .0245 |
| 29 | .0055 | .0061 | 64 | .0358 | .0266 |
| 30 | .0059 | .0063 | 65 | .0420 | .0311 |
| 31 | .0061 | .0065 | 66 | .0466 | .0342 |
| 32 | .0063 | .0067 | 67 | .0512 | .0374 |
| 33 | .0065 | .0070 | 68 | .0556 | .0407 |
| 34 | .0067 | .0073 | 69 | .0591 | .0430 |
| 35 | .0068 | .0077 | 70 | .0585 | .0441 |
| 36 | .0071 | .0080 | 71 | .0602 | .0474 |
| 37 | .0073 | .0082 | 72 | .0618 | .0522 |
| 38 | .0076 | .0083 | 73 | .0638 | .0593 |
| 39 | .0080 | .0084 | 74 | .0669 | .0701 |
Table D.—Births and Deaths of Children under Five Years of Age.
| Year | Births. | Deaths. | Deaths. | Deaths. | Deaths. | Deaths. |
| Year | Births. | 0–1. | 1–2. | 2–3. | 3–4. | 4–5. |
| Males. |||||||
| 1880 | 9,893 | 986 | 183 | 60 | 54 | 31 |
| 1881 | 9,590 | 987 | 204 | 60 | 49 | 49 |
| 1882 | 9,712 | 934 | 178 | 82 | 63 | 56 |
| 1883 | 9,843 | 1,079 | 206 | 72 | 57 | 35 |
| 1884 | 10,131 | 870 | 145 | 77 | 55 | 36 |
| 1885 | 10,020 | 970 | 176 | 74 | 45 | 31 |
| 1886 | 9,872 | 1,027 | 162 | 56 | 50 | 81 |
| 1887 | 9,725 | 987 | 154 | 86 | 53 | 27 |
| 1888 | 9,641 | 752 | 140 | 57 | 36 | 33 |
| 1889 | 9,514 | 798 | 134 | 57 | 34 | 47 |
| 1890 | 9,293 | 775 | 114 | 54 | 45 | 42 |
| 1891 | 9,377 | 942 | 160 | 59 | 31 | 43 |
| 1892 | 9,101 | 910 | 132 | 77 | 41 | 42 |
| Females. |||||||
| 1880 | 9,448 | 819 | 174 | 72 | 46 | 33 |
| 1881 | 9,142 | 744 | 187 | 65 | 57 | 38 |
| 1882 | 9,297 | 744 | 155 | 71 | 54 | 50 |
| 1883 | 9,359 | 916 | 190 | 61 | 43 | 36 |
| 1884 | 9,715 | 703 | 156 | 81 | 41 | 30 |
| 1885 | 9,673 | 786 | 124 | 57 | 47 | 35 |
| 1886 | 9,427 | 872 | 152 | 74 | 38 | 30 |
| 1887 | 9,410 | 808 | 157 | 63 | 43 | 29 |
| 1888 | 9,261 | 584 | 117 | 58 | 42 | 37 |
| 1889 | 8,943 | 658 | 116 | 45 | 41 | 23 |
| 1890 | 8,985 | 663 | 100 | 43 | 29 | 29 |
| 1891 | 8,896 | 725 | 122 | 47 | 36 | 28 |
| 1892 | 8,775 | 684 | 112 | 60 | 44 | 31 |
Table E.—New Zealand Life Table, 1881—91.
Males.
| $x$ | $l_{x}$ | $d_{x}$ | $p_{x}$ | $q_{x}$ | $x$ | $l_{x}$ | $d_{x}$ | $p_{x}$ | $q_{x}$ |
| 0 | 10,000 | 967 | .9033 | .0967 | 40 | 7,376 | 61 | .9917 | .0083 |
| 1 | 9,033 | 164 | .9818 | .0182 | 41 | 7,315 | 63 | .9913 | .0087 |
| 2 | 8,869 | 68 | .9924 | .0076 | 42 | 7,252 | 67 | .9909 | .0091 |
| 3 | 8,801 | 44 | .9950 | .0050 | 43 | 7,185 | 69 | .9904 | .0096 |
| 4 | 8,757 | 37 | .9958 | .0042 | 44 | 7,116 | 72 | .9899 | .0101 |
| 5 | 8,720 | 34 | .9961 | .0039 | 45 | 7,044 | 77 | .9891 | .0109 |
| 6 | 8,686 | 31 | .9964 | .0036 | 46 | 6,967 | 81 | .9885 | .0115 |
| 7 | 8,655 | 28 | .9968 | .0032 | 47 | 6,886 | 84 | .9878 | .0122 |
| 8 | 8,627 | 23 | .9973 | .0027 | 48 | 6,802 | 87 | .9872 | .0128 |
| 9 | 8,604 | 20 | .9977 | .0023 | 49 | 6,715 | 90 | .9866 | .0134 |
| 10 | 8,584 | 18 | .9979 | .0021 | 50 | 6,625 | 92 | .9862 | .0138 |
| 11 | 8,566 | 18 | .9979 | .0021 | 51 | 6,533 | 94 | .9856 | .0144 |
| 12 | 8,548 | 18 | .9979 | .0021 | 52 | 6,439 | 97 | .9848 | .0152 |
| 13 | 8,530 | 19 | .9977 | .0023 | 53 | 6,342 | 103 | .9839 | .0161 |
| 14 | 8,511 | 21 | .9975 | .0025 | 54 | 6,239 | 108 | .9826 | .0174 |
| 15 | 8,490 | 25 | .9971 | .0029 | 55 | 6,131 | 116 | .9812 | .0188 |
| 16 | 8,465 | 28 | .9967 | .0033 | 56 | 6,015 | 122 | .9797 | .0203 |
| 17 | 8,437 | 32 | .9962 | .0038 | 57 | 5,893 | 130 | .9780 | .0220 |
| 18 | 8,405 | 35 | .9958 | .0042 | 58 | 5,763 | 138 | .9761 | .0239 |
| 19 | 8,370 | 39 | .9954 | .0046 | 59 | 5,625 | 144 | .9743 | .0257 |
| 20 | 8,331 | 41 | .9950 | .0050 | 60 | 5,481 | 145 | .9736 | .0264 |
| 21 | 8,290 | 43 | .9948 | .0052 | 61 | 5,336 | 149 | .9720 | .0280 |
| 22 | 8,247 | 45 | .9946 | .0054 | 62 | 5,187 | 156 | .9700 | .0300 |
| 23 | 8,202 | 45 | .9945 | .0055 | 63 | 5,031 | 162 | .9077 | .0323 |
| 24 | 8,157 | 45 | .9944 | .0056 | 64 | 4,869 | 172 | .9649 | .0351 |
| 25 | 8,112 | 43 | .9947 | .0053 | 65 | 4,697 | 193 | .9589 | .0411 |
| 26 | 8,069 | 43 | .9947 | .0053 | 66 | 4,504 | 205 | .9545 | .0455 |
| 27 | 8,026 | 42 | .9947 | .0053 | 67 | 4,299 | 214 | .9501 | .0499 |
| 28 | 7,984 | 43 | .9946 | .0054 | 68 | 4,085 | 221 | .9459 | .0541 |
| 29 | 7,941 | 44 | .9945 | .0055 | 69 | 3,864 | 222 | .9426 | .0574 |
| 30 | 7,897 | 46 | .9941 | .0059 | 70 | 3,642 | 212 | .9418 | .0582 |
| 31 | 7,851 | 48 | .9939 | .0061 | 71 | 3,430 | 201 | .9414 | .0586 |
| 32 | 7,803 | 49 | .9987 | .0063 | 72 | 3,229 | 194 | .9401 | .0599 |
| 33 | 7,754 | 50 | .9935 | .0065 | 73 | 3,035 | 187 | .9382 | .0018 |
| 34 | 7,704 | 52 | .9933 | .0067 | 74 | 2,848 | 185 | .9353 | .0047 |
| | | | | | 75 | 2,663 | ⋅ ⋅ | ⋅ ⋅ | ⋅ ⋅ |
| 35 | 7,652 | 51 | .9932 | .0068 | | | | | |
| 36 | 7,601 | 54 | .9929 | .0071 | | | | | |
| 37 | 7,547 | 55 | .9927 | .0073 | | | | | |
| 38 | 7,492 | 57 | .9925 | .0075 | | | | | |
| 39 | 7,435 | 59 | .9920 | .0080 | | | | | |
Table E.—New Zealand Life Table, 1881—91—continued.
Females.
| $x$ | $l_{x}$ | $d_{x}$ | $p_{x}$ | $q_{x}$ | $x$ | $l_{x}$ | $d_{x}$ | $p_{x}$ | $q_{x}$ |
| 0 | 10,000 | 817 | .9183 | .0817 | 40 | 7,498 | 62 | .9917 | .0083 |
| 1 | 9,183 | 155 | .9831 | .0169 | 41 | 7,436 | 61 | .9918 | .0082 |
| 2 | 9,028 | 64 | .9929 | .0071 | 42 | 7,375 | 61 | .9918 | .0082 |
| 3 | 8,964 | 42 | .9953 | .0047 | 43 | 7,314 | 60 | .9917 | .0083 |
| 4 | 8,922 | 33 | .9964 | .0036 | 44 | 7,254 | 61 | .9816 | .0084 |
| 5 | 8,889 | 29 | .9967 | .0033 | 45 | 7,193 | 61 | .9915 | .0085 |
| 6 | 8,860 | 27 | .9970 | .0030 | 46 | 7,132 | 63 | .9912 | .0088 |
| 7 | 8,833 | 22 | .9974 | .0026 | 47 | 7,069 | 65 | .9909 | .0091 |
| 8 | 8,811 | 20 | .9978 | .0022 | 48 | 7,004 | 66 | .9905 | .0095 |
| 9 | 8,791 | 18 | .9980 | .0020 | 49 | 6,938 | 69 | .9900 | .0100 |
| 10 | 8,773 | 16 | .9981 | .0019 | 50 | 6,869 | 75 | .9892 | .0108 |
| 11 | 8,757 | 18 | .9980 | .0020 | 51 | 6,794 | 78 | .9885 | .0115 |
| 12 | 8,739 | 18 | .9979 | .0021 | 52 | 6,716 | 82 | .9878 | .0122 |
| 13 | 8,721 | 20 | .9977 | .0023 | 53 | 6,634 | 86 | .9870 | .0130 |
| 14 | 8,701 | 23 | .9974 | .0026 | 54 | 6,548 | 90 | .9863 | .0137 |
| 15 | 8,678 | 26 | .9970 | .0030 | 55 | 6,458 | 93 | .9856 | .0144 |
| 16 | 8,652 | 28 | .9967 | .0033 | 56 | 6,365 | 98 | .9846 | .0154 |
| 17 | 8,624 | 32 | .9963 | .0037 | 57 | 6,267 | 103 | .9835 | .0165 |
| 18 | 8,592 | 35 | .9960 | .0040 | 58 | 6,164 | 109 | .9824 | .0176 |
| 19 | 8,557 | 36 | .9957 | .0043 | 59 | 6,055 | 114 | .9811 | .0189 |
| 20 | 8,521 | 38 | .9956 | .0044 | 60 | 5,941 | 117 | .9803 | .0197 |
| 21 | 8,483 | 40 | .9953 | .0047 | 61 | 5,824 | 122 | .9790 | .0210 |
| 22 | 8,443 | 41 | .9951 | .0049 | 62 | 5,702 | 128 | .9776 | .0224 |
| 23 | 8,402 | 42 | .9950 | .0050 | 63 | 5,574 | 135 | .9758 | .0242 |
| 24 | 8,360 | 44 | .9948 | .0052 | 64 | 5,439 | 143 | .9738 | .0262 |
| 25 | 8,316 | 45 | .9946 | .0054 | 65 | 5,296 | 162 | .9694 | .0306 |
| 26 | 8,271 | 46 | .9944 | .0056 | 66 | 5,134 | 172 | .9664 | .0336 |
| 27 | 8,225 | 48 | .9942 | .0058 | 67 | 4,962 | 182 | .9633 | .0367 |
| 28 | 8,177 | 48 | .9941 | .0059 | 68 | 4,780 | 188 | .9607 | .0393 |
| 29 | 8,129 | 50 | .9939 | .0061 | 69 | 4,592 | 191 | .9585 | .0415 |
| 30 | 8,079 | 50 | .9937 | .0063 | 70 | 4,401 | 191 | .9566 | .0434 |
| 31 | 8,029 | 52 | .9935 | .0065 | 71 | 4,210 | 195 | .9537 | .0463 |
| 32 | 7,977 | 54 | .9933 | .0067 | 72 | 4,015 | 204 | .9492 | .0508 |
| 33 | 7,923 | 55 | .9930 | .0070 | 73 | 3,811 | 219 | .9424 | .0576 |
| 34 | 7,868 | 58 | .9927 | .0073 | 74 | 3,592 | 243 | .9323 | .0677 |
| | | | | | 75 | 3,349 | ⋅ ⋅ | ⋅ ⋅ | ⋅ ⋅ |
| 35 | 7,810 | 60 | .9923 | .0077 | | | | | |
| 36 | 7,750 | 62 | .9920 | .0080 | | | | | |
| 37 | 7,688 | 63 | .9918 | .0082 | | | | | |
| 38 | 7,625 | 63 | .9917 | .0083 | | | | | |
| 39 | 7,562 | 64 | .9916 | .0084 | | | | | |