United States Life Tables and Actuarial Tables 1939 …

[Pages:154]FEDERAL SECURITY A G E N C Y

UNITED STATES PUBLIC HEALTH SERVICE

NATIONAL OFFICE OF VITAL STATISTICS

UNITED STATES LIFE TABLES and

ACTUARIAL TABLES

1939-1 941

BY

THOMAS N. E. GREVILLE

Actuarial Mathematician

/

Prepared under the supervision o/

HALBERT L. DUNN, M. D. .

CHIEF, NATIONAL OFFICE OF VITAL STATISTICS

UNITED STATES GOVERNMENT PRINTING OFFICE

WASHINGTON : I947

- For role by the Superintendent of Documents, U. S. Government Printing Office, Washington 45, D. C. Price 31.P5

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ACKNOWLEDGMENTS

Associated with Dr. Greville in the preparation of this based on life insurance experience; Messrs. W. R. . .

volume was Miss Elbertie Foudray, Actuarial Stdtis- Williamson: Robert J. Myers, and Harry Mehlman of

tieian, whose long experience in dew ograpliic analysis the a c t h h l stafl' of the Social Security Board, whose

I

and in the preparation of previous United States life counsel was frequently sought on. technical questions; ,

tables has been of the greatest value. Numerous mem- and Mr. Mortimcr Spiegelman of the Metropolitan

bers of the clerical and professional staff of the Bureau Life Insurance Co., who made aaumber of useful sugges-

of the Census, and more particularly its Vital Statistics tions and assisted, in checking some of the references.

Division, made important contributions. Dr. Iwao Ackno,wlcdgment is made a.lso to Mr. J. W. Butcher,

M. Moriyama, Chief of the Planning and Analysis Government Sta.tistician of Ncw Zealand; for making

Section of the Division, and Mr. Morris B. Ullman, available in aclva.nce of publicetion tlie 1934-1938 life

Statistician in the Office of the Statistical Assistant to tables for that country, nnd to the American Life

the Director, played an importaiit part in shaping many Convention and its former Actuary, Mr. F. Edward

decisions as to the arrangement of the tables and the Huston, for furnishing tables of commutation columns

manner of presen_tation of tihe test material. Miss based on the 1930-1940 Experience table of morjdity.

Maude Sharp mas responsible for the gencral editorial Thcse werc used in computing certain values presented

accuracy and uniformity of tables and text.

in table 0, 'part 111. R4r. Hugh H. Wolfenden, prom-

Thanks are also due to a number 'oI actuaries outside inent Canadian actua.ry and sta.tistician, was especiall?

the Bureau of the Census, who Assisted in various ways. generous in giving advice concerning the many teeh-

Among these should be mentioned Cspecially Mr. nical problcms which arose, and was freely consulted

John S. Thompson,' Vice President and Mathematician at every-stnge.of the work. His wide experience in the *

of the Mutual Benefit Life Insurance Co., and Mr. construction of mortality tables and his mastery of

Alfred N. Guertin, formerly Actuary of the Department abtua.ria1and statistical-theory have left their stamp on

. of Banking and Insurance of the State of New Jersey, every part of the volume. In acknowledging the con-

who made available mortality data at the very old ages tributions so generously made by actuaries outside the

Bureau of the Census, it should be understood that they

1 As this volunie was going to press it was learned that Mr. John S. ThompsGn has become President of the Mutual Benefit Life Insurance Co.

are not to be held accountable for any technical defects.

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CONTENTS '

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PART 1.-INTRODUCTION

Page

Plan and scope of this volume_ _ _ _ _ _ _ _ _ 3_ _ _ _ _ _ _ _ _ _ _ _ _ _

Accuracy of t h e tables

tJomparisons based on the life tables:

Variation by race and sex

2

Comparisons based on t h e life tables-Continued

Comparison with earlier United States life tables- - -

Cornparison with recent life tables for other countries

Page 10 14

PART 11.-LIFE TABLES

Page

Explanation of the columns of the life table _ _ _ _ _ _ _ _ _ _ _ _ 21

Use of life tables in estimating a n d forecasting popula-

T

tions he life

____ table

__ as

__________________ a frequency distribution-

_______

__

__ _______

__

____

~

-

~2~2 ~ 23

~

~

~

-

Page

24 24 25

PART 111.-ACTUAREAL TABLES

Page

Scope of the actuarial tables_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 55 Uses of the actuarial tables _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Comparison, with mortality tables based on the expe-

Mathematical notation employed in the actuarial tables-

rience of insured lives _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _5_5_

Page

57 57

PART 1V.-MATHEMATICAL THEORY A N D USE OF T H E ACTUARIAL TABLES

1';1L'e

Page

_ _ _ _ _ _ A.

General Mathematical Compound interest

- - Theory _ _ _ _ _ _ _

- - - - - - - - - - - - - - - - - - - -

_

8_ 5 85

_ B._ Ar_ ran.ge_ me_ nt a_ nd _ Use_of_ .th_ e A_ ctuarial Tables-Con. Use of thpactuarial tables in calculating single life

Pure endowment_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _8_5_ Annuities_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _85_ _

annuity surance

values and benefits- - - -

net - - - -

premiums

- - - - - - - - -

-

f -

or - -

-l-if_e_

in-

- - -

93

Temporary life annuity_ _ Commutation columns--

- _

__

__

__

_______________

__

__

__

__

__

__

________

_

85 86

Other types of annuities_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

86

Life assurances_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _8_7_

Joint life annuities_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _88

Use of !he actuarial tables in evaluating joint life

annuities--_-__---..-_----------------------

94

Evaluation of joint life annuities involving ages under 1 7 - - - - - - - - _ - - - - - - - - - - - - - - _ - - - - - - - _ - - - 95

Rqivtieerss_i_o_n_a_r_y_ _ _a_n_n_ _u_i_ti_e_s_ _ _a_n_d_ _ _l_a_s_t_ _s_u_ _rv_ _iv_ _o_r_. annu- * 89 Relation between annuities aud assurances-- - - - - - 89

Calculation of net values of reversiouary and last

survivor annuities, two or more lives- - c

-a_n_d_

_

_a-ss-u-r-a-n-c-e-s-

involving - - - - - - - - -

97

Formulas for joint life benefits ___ _ _ _ _ __ _ _ _ _ - :90

Estimation of joint life annuity values based on

B.

Arrangement and Use of

Elementary values- - -

the

- - -

Actuarial

- - - - - - - - -

T- -a-b_l-e-s

-

-

-

-

-

-

-

-

-

-

92 92

_ _ _ _ the separate life

white females

_

t_a_b_l_e_s_

_ f_o_r _

_w_h_ i_t_e_

_m_ _a_le_s_

_

a_

n_ _d

97

PART V.-METHOD OF CONSTRUCTION AND GRADUATION OF THE LIFE TABLES

~

l'nge

rage

A. Preliminary Adjustment of the D a t a _ _ _ _ _ _ _ _ _ _-_ _ _ _ _ 101 B. Calculation of t h e Rates of Mortality-Continued

_ _ _ _ .Accuracy of the data_ _ _ _ _ _ _ 101 _ _ _ ___ __ __ _ _ __ __.A_ dj.ustment of mortality rates at ages 0 t o 4 for

Completeness of birth registration - - - - - - - _._- - - 102

the effect of migration - - - - - - - - - - - - - - - - - 119

CMoemthpoldeteonf easdsjoufstrmegeinsttroaftiionnfaonf tindfaatnat_ _d_e_a_t_h_s___-_ _-_-

103 107

Grouping of ages for the computation mortality at ages 5 and over- - - - - - - -

of - - -

- r

ates - - - -

-o-f

120

Adjustment for incomplete reporting of infant deaths by subdivisions of the first year of life--- 108

General tality

procedhre at ages 5 a

nudseodvienr.

o. b. t.a.i.n.in. .g.

r. a. t.e.s.

o. f.

.m. o. .r-

122

_ _ _ _ _ _ Redistribution of "other races" deaths under 1 year

of a g e _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Unreported Estimation

ages at of July

1d,e1a9th40_ , p_ opu_ latio.n_ s _ _

_ _ __ _ _

- - - - -

_ _1_0_9_ _ _ 10_ 9 _

109

_

Pivotal value formulas employed- - - - _ _

Derivation of pivotal rates of mortality _ Tr_ eatm_ en_ t of_ the_ ve_ ry o_ ld a_ ges_ _ _ _ _ _ _ _ _

_

-..-

- -

____

-

_

_

_

-

_

Special adjustment of Negro d a t a_ _ _ _ _ _1_ 10 _ _ _O. sc_ ulat_ ory_ int_ erpolation formulas used- - - - - - - - - -

123 124 124 125

Estimation of foreign-born population under 5----

B. Calculation of the Rates of Mortality _ _ _ _ _ _ _ _ _ _ _ _ _ _

112 112

Test. of the graduation of the rates of mortality- - -

C. Calculation of Other Life Table Functions- - - _ _ - - - - -

126 133

Ba$c process for obtaining mortality ratcs at ages 115

Calculation Calculation

of of

1, a L._

n

-

d

-

d, - -

_ -

_

-

_

-

_ -

_

__ .. -

_ -

_ -

_

_

-

_ -

_

-

_-

_

_-

_ -

_ -

_

-

____

- -.

133 133

117

Calculation of T, and k, _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 134

APPENDIX

Page

A.

Method Used in Testing the Glover's' Separation Factors-- -

-A_ _p-p_ro_ -p-ri-a-te-n- e- ss_

_

of

- -

D. Procedure Used in Carrying Out the Makeham Grad-

135

uation of the Life Table for Total Whites_ _ _ _ _ _ _ _ _

B. Derivation of the Special Extensions of the Karup-

King Formula Rat,es at Ages

5Utsoed11faonrdI2n6tetropo3l1a_t_io_ n_

_ o_f_

_M_ _o_r_ta_l_i_ty_

136

C.

h,Iet,hod White

oMf aCleosmapnudtaWtihointeofFetmhealeAsc_ t_u_a_r_ia_ l_

_T_ a_ b_ l_e_s_ f_o_r

137

General considerations- - - - - - - - - - - - - - - - - - - - - - - Method of graduation eniployed- - - - - - - - - - - - Preliminary graduation- - - - - - - - - - - - - - - - - - - - - - - -

Final determination of the Makeham constants-- -

Modification of the basic life table values for use

finemt haelesa_c_t_u_a_r_i_a_l _t_a_b_ l_e_s_

Calculation of the force

_fo_of_r_mw_ o_h_ri_tta_el_i_mt_ya__l_e__s__

__a__n__d____w_h_i_te_

137 137

Junction with original val.ies at very young ages- -

Completion of the mortality table _ _ _ _ _ _ - - - - - - - - Test of t)e graduation _ _ _ _ _ _ _ _ _ _ _ 1_ _ _ _ _ _ _ _ _ _ _ _ _

Calculation of commutation columns and net

premiums_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _1_3_8 I

- Cahlacmuliazteiodnmoforottahlietrytatabbleles-d-e-r-iv-e-d- f-ro-m- - -th- e- -m- -a-k-e--

Poee

138 138 138 139 139 140 140 140

143

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CONTENTS

PRINCIPAL TABLES

Table

Page Table

Pago

LIFE TABLES FOR THE UNITED STATES: 1839-1941 ~

ACTUARIAL TABLES BASED ON THPJ LIFE TABLE FOR

1. Total population 26 _ _ _ _ _ _ _ _ _ _ _ _ _ _ r _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

WHITE FEMALES I N THE UNITED STATES: 103klQ41

_ _ _ _ 2.

3. 4.

5.

-6. 7. 8.

_ _ 9.

TTTTNWWNooooeehhtttggtaaaiiarrttllllooeefwmNfemfmeehmeamaamglietallreeeaasloesssll_ eee_ _ssss__-_ -___ _-__ ___-__ ______ _________ _-___ _ _________ _-__ __ _-___ ___ ____ _ _=___ __ ___ __ __-_-__ __ -___ _ -___-_ _ ____ _ ____ __-__ _ -___ _ . -___-___ _. _ _-__ _ _-__ __ -__ _ ___ _______ _-_--_ _ __ _ __ _ __ _23333344_60824028_ _ _ ___ _ . 222223_ 567890......_ __ EClo_ e_m4_ 2233m%%mpppe_ _neee_ upprrrtteecacc. a_ rrereetcc_ y_ ninneeotttnvn_ niiita_ t_ nnnlciiutttonn_ eeeel_ ttsrr_ ruee-eeem'rr-ss_ seett_ nt_ ss__--stt_---- - _ __a--_ __ _t- - __-____ _. . __ __ __-__ _ _______ __ __-_ _ __-____ _ -__-_ ___ _ ___ _ __ ___ _ _ ___ _ ___ ____ _ __-__ _ __-____ _ _______ _ _____ ___ ___ _ _ _- - __ _ _ _ __ 67_ 7777_ 1_ 39204:_ ---_ __ __ _

10. 11.

Total Other

orathceesr,rma caleess-___ _-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_

-_

-_

-_

-_

_-

_-_-_-_-_-

-

-

44 46

, Immediate whole life annuity, single and annual net premiums a t

(I

12. 13.

Other races, females_ Life table functions for

__.__

the first year

_____

of life-. - - - - - -

_ - -

_

.4_ 8 50

_31.._ 32.

_2_ pe_ rce_ nt i_ nte_ res_ t __ _ -_ _ __ _ __ _ ___ _

2% percent interest

_.

-__-_

__

__

_

_ - _ _ _ _7_5_ _ _ _ _ 76_

_

_

_

_

ACTUARIAL TABLES BASED ON THE LIFE TABLE FOR WHITE MALES IN THE UNITED STATES: 1838-1041

33.

3 percent interest _ L _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

77

34. 3%percent interest- - - _ _ _ _ _ _ _ - _ _ - _ _ _ _ _ _ _ _ _7_8_ _ _

35. 4 percent interest-- . . . . . . . . . . . . . . . . . . . . . . . . . .

79

14. Elementary yalues-- - - _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 58

Commutation columns ut-

. ACTUARIAL TABLES BASED ON THE MAKEHAMIZED

15.

1:;6:.

19.

_ _ - - - - - 2 percent 59 interest_ _ _ _ _ . _ _ _ _ _ _ _ _ _ . _M_ OR_ TAL_ ITY_T_ ABL_ E F_ OR_TO_ TA_ L W_ HITES I N THE

246 percent interest--

- - - - - - - - -.- - - - -. - 60

UNITED STATES: 1839-1941

3 ercent interest_ _ _ _ _ _ _ r _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

61

3 4

Y2 percent percent in

interest-________-_-^--------------

- terest-- _ _ _ _ _ _ _ __ _ _ _-

62 36. ._ 63_3_ 7.

_ Makeham constants__-

T_ ab_ le of_ un_ ifor_ m s_ enio.ri_ ty

_

_

__

__

__

__

__

__

__

__

_ _

- _

__

__

__

__

_-

_-

__

__

__

__

_ _

79 80

Immediate whole life annuity, bingle and annual net

38. Elementary values _ _ _ _ _ - _- __ _ _ _ _ _ _ _ 8_ 0 _ _ _ _

xz

22. 23. 24.

- premiums at-

_ _ _ _ _ 2 ercent iqterest, - -

2 g percent interest-- -

3 percent in!erest_- - 3>/2percent interest_ _ _ . 4 percent interest,-

-.

-

_. __

- - - - - - - - - - - - - - -e-- - - - -

_ _ _ _ .- .- - -1 - - - :_ - - - -.

_ _ _ _ _ _ _ _ _ _ - _ L _ _ _ _ _ _ _ _

-

_ _ _ - _ - _ c

_ _ _ _ ._ . . _ _

_ _ _ _ _ _ __ . _ . _ _

64

65 39.

66 40. _6_ 7 _ 41. _ 6-8_4_ 2.

Immediate life annuitie

2 percent interest_ _ _423_ %ppeeprreccreecnnettniitnnittneetrreeerssetts__t_____

s at-

____--_____-__________ ___________ _____________

____ __________ _____

_______-__-_1_-_____ _______

__

__

_

_

_8_1_

82 83 84

_

I

FIGUWS '

Figure

Page Flgure

Paac

-

L

_ _ - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 1. AnUnnuiatlerdatSetaotfems,o1r9ta3l9i-ty19p4e1r_1_,_0_0_0_,f_o_r_e_a_c_h_ _r_ac_ e_ _b_y_ _se_x_': 4

2. Annual rate of mortality per 1,000,by race and by

sex: United States, 1939-1941

5

3. Number of survivors out of 100,000 born alive, for

each race by sex: United States, 1939-1941_---_-- 6

8. Annual rate of mortality per 1,000 for white females:

'

death-re istration.Stat.es of 1900 and 1920,and the United h a t e s , a t 10-year intervals, 1900-1941__,,

9. Number of survivors out of 100,000live births, from recent life tables for selected countries, I. Males--

13 18

4. Nuamndbebryofsesxu:rvUivnoirtsedouSttoafte1s0,0,1090309-b1o9r4n1a_l_iv_e_,_b_y_ _ra_ c_ e_

10. Number of survivors out of 100,000live births, from

7

recent life tables for selected countries, 11. Females- 19

,

.

5. 6.

AvSetraatgees,f1u9tu39re-1l9if4e1ti_m_ _e_, _f_o_r_e_a_c_h_ _r_a_c_e_ _b_y_ _s_e_x_:_U_ _n_i_te_d 8'

Average future lifetime, by race and by sex: United States, 1939-1941---___-_-__----_-__--_-_9-_

11. Frequency distribution of ages at death in a cohort starting with 100,000 live births, based on the

--.. mortality of white males: United States, 1939-1941-

24

7. Annual rate of mortality per 1,000 for white males:

12. Ratio of Negro deaths in'selected age groups to Negro

- - death-registration States of 1900 and 1920,and the

United States, at 10-year intervals, 190O-1941_ - 12

deaths at ages 60-54 'in the same year: United

I States, 1933-1941-----------------------------

111

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UNITED STATES LIFE. TABLES AND ACTUARIAL

TABLES, 1939-1941

PART I

INTRODUCTION

Plan and scope of this volume

of incompleteness of reporting, except in the case of

The life tables in this volume are b a r d on the 1940 birth statistics.' How'ever, it is believed that the un-

census of population and the deaths of the 3-year period reported cases constitute, in general, a small percentage 1939-1941. Separate life tables have been prepared for of the totals involved, except in the case of data for each sex for each of three racial groups: white, Negro, very young children (including births). I n the latter

and other races. This is the first time official life tables case, a serious attempt has been made to introduce a -

1

have been prepared for races other than whites and suitable correction in the process of constructing the Negroes in the United States. Life -tables are also life tables.2 I t should be mentioned also that when

included for the total population of each sex, for the death itatistics are related to thh, corresponding poputotal population of each racial group without distinction lation data, as in the computation of rates of mor-

by sex, and for the entire population without distinc- tality, any incompleteness in the enumeration of the

tion by race or sex. Each of the 12 life tables is based population tends to offset whatever deficiency may

on data for the entire continental United States. Also exist in the reporting of deaths. It is believed, there-

included are certain actuarial tables derived from the fore, that errors of incomplete reporting are not likely,

life tables for white wales, white females, and total in general, .to be of sufficient magnitude to seriously

whites, to be used in calculating premiums and values affect the life table valu?!s fo`r white persons. How-

for life annuities, life assurances, and other monetafy ever, there is some indication that in the rural areas of

benefits contingent on death or survival. Other sections the South the reporting of Negro deaths may be appregive a brief synopsis of the elementary mathematical ciably less complete than the enumeration of Negroes

theory of life contingencies, including those involving in the ensu us.^ Since 49 percent of the total Negro

more than one life; instructions for using the actuarial population is found in the rural parts of the South, it is

tables, with numerical examples; and a complete ac- possible that mortality rates for Negroes may be some-

count of the methods and processes used in constructing what understated. There is a more serious possibility

the life tables. Because of the increasing interest in the of error in the case of the group of "other races" which

preparation of life tables on the part of demographers, includes Indians living on reservations, a class which

public health workers, and other groups, an effort has presents real difficulty from the standpoint of complete

been made to render this statement of methods and reporting and enumeration.

processes intelligible to readers having a reasonable Among the errors due to incorrect reporting, those

knowledge of mathematics and statistics, but without arising from incorrect statements of age are by far the

specific actuarial training. -For this reason, some of the most important class, as regards the construction of

explanations will doubtless seem to the actuary un- life tables. These errors in' age fall into two general

I

.necessarily full, and even somewhat tedious. An ap- types: (1) systematic errors, which arise from a pref-

pendix, intended primarily for actuariea, explains the' erence for ages ending with certain digits, such as 0, 5,

special pkcesses used in the construction of the actu- and the even numbers generally, and (2) errors charac-

arial tables, and certain other technical matters.

teristic of particular ages or periods of life. The sys-

Accuracy of the tables

tematic errors are believed to have been 1argely.elimi-

nated in the graduation of the data described in part

I

It is well known that the statistics on which these life tables are based are subject to various errors, the magnitude of which is, in most cases, diflicult to estimate with precision. These errors, whether found in .statistics of populations, deaths, or births, fall into

V. A typical example of an age error of the second type would be that described by Wolfenden4 as "a natural inclination-to overstate the age until the attainment of majority, and then to understate a t adult ages,

two general classes: (1) incompleteness or underenumeration, and (2) incorrect reporting of some of the

pertinent information, such as age, race, or sex. Very little specific information is available as to the extent

'1 see p. 102.

see pp. 1ae-108. 8 U. 8. Burmu of the Censuq, United States Abrldged LiJe Tables, IgSB, Urban and Rural, by Region#. ColorFandSrz, p. 5, June 1043. 4 Wolfenden,HughE.,Popukrlim Ratislies and Tlieir Compilation (Actuarial .%die#, No.3). p. 27. Actuarisl Society of Americs, NPWYork. 1925

1

:`,L ..

2

UNITED STATES LIFE TABLES AND ACTUARIAL TABLES

with some oveistatemcnt i n advanced years." Errors of this sort are not easy to-detcct, especially if the samc type of error occurs in both population and death statistics. Only in one instance, in which the effect was particularly noticeable, has any adjustment bcen made for such errors in the construction of the life tables in

this volume. This point is fully discussed in part V.

Errors in the reporting of race probably are rclatively infrequent, except in the case of persons ,of mixed white and Indian blood. Thcre is no general agreement as to what proportion of Indian blood entitles one to be called an Indian, and it is likely that the information furnished on death ccrtificates mny often fail to be consistent in this respect with the definition adopted in the population census. Any error arising from this source could scarcely be of sufficient magnitude to have any appreciable influence on mortality rates for the white population, but could easily have a disturbing effect on those for "other races." It is believed that any errors in the reporting of s'ex would not be sficiently numerous to seriously affect any of-the life tables.

In addition to errors resulting from actual inaccuracies in the data, there are errors due to chance fluctuation in the numbcr of deaths: that is, what is known as sampling error. This is of importance only in fairly small classes, in which a small variation in the absolutc number of dcaths in a given age group may make a considerable difference in the rate of mortality. Tablc A, showing the total enumerated population and the total`deaths in thc 3-year period in each of the six subdivisions of the population for which separate life tables were prepared, indicates the size of the exposure underlying each life table. Sampling errors tend to bc largely corrected by the graduation process, in which the mortality rates in each age group are adjusted so as to bring them into line with those in the neighboring age groups. In any case, it is believed that the effect of sampling error is negligible in the life tables for whitc persons, and of minor importance in thosc for Negroes, except at the very old ages. However, i t may havc significantly affected the results for "other racw."

If allowance is made for all the possi6le sources of error discussed above, thc life tables for whites and Negroes are believed to be sufficiently accurate and reliable for all ordinary purposcs. However, those for "other races" can be regarded only as reasonable approximations. For reasons explained in part V, this is also true of the life table values for subdivisions of the first year of life in all the tables.8

In connection with the accuracy of the tables, it

should be clearly understood that the values cannot be considered reliable, in most cases, t o anythirig like the number of decimal places or significant figures shown in the tables. The chief purpose of retaining

TABLEA.-i940 ENUMERATEPODPULATIONS, AND TOTAL

DEATIIRSEPORTED IN 1939-1941, BY RACEAND SEX: UNITED STATES

.

RACE AND S E I

1940 1939-1941 population deaths f

~~

White:

____ _ _ _ _ Mnlc ____ ____________ ___ ___ Fcmalc

_ _ ._ _ _ _.__ -_ .-_ .-_- _ __ __ _ __ __ _ __ __ .... _ 55. 89_ .,_ 47_ 4686_ _ .,5_ 3428.. 2_ __.21_ ,,004083_ ,,61290_ 2 ___.

Ncgro:

_____ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Male_.-_ .- -_ __

Fcmnlc_.-_ .-_ .

_

_

_

_ - -_ ..- -_-___ __ _ __ _ __ ___ -_--.-.._ _ .86_ -,,5_ 29_ 66_9,,4_ 0_ 8_ 308_ _ _.__22_8426,._44QW_ 4

_

.

Other races:

_ _ _ _ _ _ ___ _ _ Male.- ._ .-- -.---

_ _ _ _ _ _________________ Female ~

- - - - -__ .-_ ..- - -_- . --._

344,006

13,803

~ _ _ . . _ _ _ _ _ _ 24_ 4,86_ 1 _ _8_ .21_ I _ _ _ _

additional figures beyond those which can be regnrdqd

as dependable is to secure a reason-abledegree of smooth-.

ness in the res&. This is always desirable, and in many of the uses to which life tables are put excessive roughness is a serious inconvenience. A further reason exists in the. case of the actuarial tables, because of the mathematical relationships which hold between different actuarial-functions, such as the values of life annuities and assurances. The actuary wishing to make use of the tables is inconvenienced if, because of excessive rounding, these relationships do not hold with a fair degree of precision.

Comparisons based on the life tables

Variation by race and sex-The most usual measure

of the comparative longevity of different populations

is the average duration of life, also called the expecta-

tion of life at birth. This is the average number of

years lived by the members of a specified cohort, or

closed group of pcrsons, assumed to be subject through-

out life to the life table rates of mortality. A compm- * ison on this basis is given in table B. This table indi-

cates that females live, on &e average, longer than

males, white persons longer than Negroes, and Negroes

not quite so long as those of "other races." There is,

however, some objection to the use of the average dura-

tion of life as a standard of comparison because the

method of calculating it gives great weight to the relatively large number of deaths occurring in the first year *

`

of life. Thkinfluence may be entirely eliminated hy

considering instead the average lifetime remaining to

those members of the cohort who survive to age 1,. .

This comparison is presented in table C, which shows,

in general, about the same relationships ns table B.

However, the differences between the corresponding

values for Negroes and "other races" are slightly

increased now that thc effect of the high infafit mortal-

ity among "other races" is no longer reflected in the

figures.

3 In connectionwith tke distributionor "othk races" deaths by snhdivisionsof the flrst year of life, a correction was applied for snnrpling error. See p. 108.

6 See p. 108.

INTRODUCTION

TABLE C-AVERAGE FUTURELlFETlhfE 1N Y E A R S AT AGE 1,

BY RACEAND SEX:UNITEDSTATE?1,939-1941

RACE

I 1 I Bothsexes Male

Femf~le

-~~~

TABLEF.-SURVIVORSTO AGE 65 O I ~ TOF 100,000 LIVEBIRTHS,

-BY RACEAND SEX: UNITEDSTATES1,939-1941

RACE

I 1) I Bothsexes Male Female

I

_-______ ~ - All races__._._______65_ .76 __.6.4..00.___ 67.7_ 3 ________ -

White_ _ _ _ . _ _ ~ ._ __ ___ __ _._ .._ . 66..8_ .4_ _ ._ __ 6.4..9_ 8_ . 68.93 Negro_ _ _ _ _ . _ _ .~ ._ __._ __ . _ _ _ __ __ 57_ .1_ 5 _ __ . . _ _ h5.9_ 3 _ _58_ .46 _ Other raccs-. __..__ ~ ._ _ _._ ._ __ __ ._ _._ .%.90___58_ . $0___ 60.1_ 4

~

Another possible standard for comparing the longevity of different populations is provided by the median ' length of life, or `(probable lifetime," which is the age at which exactly half thc originallmembers of the cohort have died, and half are still alive. In other words, it is the age to which an infant born alive has just an even chance of surviving. The va.lues of the median length of life (shown in table D) are greater in every case than those of the average length of life: the difference ranging from 3.81 `yearsin the case of Negro females to 8.70 years in the case of females of "other races." The use of the probable lifetime as a measure of longevity results in a somewhat more favorable showing for "other races," as compared with Negroes, than when the average duration of life was used. I n fact, the probable lifetime of males of "other races" slightly exceeds-that of Negro females. The reverse was true of the corresponding average durations of life.

TABLED.-MEDIAN LENGTHOF LIFEIN YDARSB, Y RACEAND

SEX: UNITEDSTATES1, 939-1941

BACE

1 11 1 ' Bothsexes , Male

Female

\

I

II

I

In considering the mortality and longevity of the group of "other races," it should be kept in mind that

this is a heterogeneous class made up of elements which differ widely both in the general level of mortality and in its incidence by age. The racial composition of the group is s h o h in table G , and age-specific death rates for the principal races separately appear in table H, together with comparablc figures for whites and Negroes.

TABLEG.-POPULATIONOF OTHERRACES,B' Y SPECIFIERDACE AND SEX: UNITEDSTATES1,940

RICE

I 1)POPULATION ,Total Ma&ZI

PERCEKT R P RACE

11 -

Total Male IFemai

_ _ _ _ _ Totalotherraces

--58__ 8,8_ 87__3_ _44,_ 0_ 06__ 2_ 44,8_ _81 _--1-00.0 100.0 100.0

Indian_ _ _ _ _ _3_ 33,96_ 9 .1.71.,4_ 27 _ 162_ ,642_ _ 56._ 7 _49_ .8 _ _ 66.4

Chinese______..7_ 7,5.04.._57_ ,38_ 9 _20_ ,115__1_ 3.2

16.7

8.2

Jap8nCS3_______.12.6..94.7__7_ 1,9_ 67 __ 54,9_80_ 21.6

20.9

22.4

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Filipino_____._.4.5,.56_ 3 ._39_ ,72_ 3 _5_ ,840___ 7.7

Allother

4,904

3,500 1,404

0.8

11.6 1.0

2.4 0.B

1 All except white and Negro

TABLEH.-DEATH RATESPER1,000ENUMERATPEODPULATION,

- I-1- BY AGE, RACE,AND SEX:UNITEDSTATES1, 939-1941 -

SEX AND AGE

-- White Negro Indian Chinese rapaneso Other

MALE

_ _ _ _ _ _ _ _ _ _ _ _ 0 4_ _ _ _ _ _1_ 3.2 _ _22_ .8 _ _ 35._ 8 . . _ 13.7_

5-9

__. 1.2

1. fi

3.3

11.0

10-14 ._____..1..1_._1.7___ 2.8

1.6

15-19

1.7

3.7

5.7

3.5

. %24 _______ 2.3___ 6.4._..7..5

25-29

___.... 2.5

7.8

8.6

4.7 5.0

3c-34____.___.3_.1 _.__ 9.7.. 8.3

6.9

- 35-39 _ _ _ _ _ . _ 4.2 - - -1_ 1.4 _ _8_ .2 _ 9.5

_ _ _ _ _ 40-44___~ __..-fi_ .1

15.7

9.6

12.8

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 45-49

9.1

20.8

13.0

17.1

_ _ _ 50-54--- _._- _~ . 13.7

29.4

_ _ 55-59- - -

.- - ~

__ - .

20.7

36.1

60-64_ _ ___ _ _ . _ _ .3_ 0.0 _ _ 43.8

16.3

23.8

24.1 30.1

.

38.3 47.7

_ _ _ _ _ _ _ 65-74- __.___..5_ 3.1 ___ 54.5.. 48.4

`75 and over

- 135.0

119.8

109.9

80.2 192.1

12.1

1.1 1.3

1.8 2.6 2.9 4.8 4.5

6. n

9.4 11.4

17.6 27.4 45.7. 110.0

12.7 11.6 1 2. 1

11.4 4.9

5. 1 4.7 7. 4

. 7. (i

12. 9

19.4 27. 5 59.6 02.2 103.7

10.4

.9 .7

1.2 1.8 2.0 24 3.1 4.3 6. 1

9.0 13.5 20.7 40. 8 120.8

18. 1

32.1

1.3

2.8

1.5

3.0

4.2

6.4

5.8

9.5

6.6

9.1

8.2

8.4

9.9 ' 9.4

14.0

9.6

17.6

11.2

25.7

16.0

32.4

21.9

40.0

28.0

44.9

43.0

86.5

103.7

13.7

1.0

1.5 -2.8 3.6 4.3 2.5 4.6 5.6 9.8 15.1 17.0 2R 2 42.5 93.8

9.4

10; 7

1.0

3.0

.E

11.4

1.5

1 2.7

1.9

14.5

3.3

12.5

2.5

15.5

3.3

1 4.4

3.9

18.5

6.7

23.2

7.9

45.3

13.9

57. 5

17.3

142.9

37.0

91.7

49.0 1388.9

1 Rate based on less than IO deaths.

UACE

~ - - Both sexes Male

Female

A more detailed comparison of life table values by

-~~ sex by race and is offered Allraces.__.._______92_ ,234___ 91. ,39.2.__9_ 3,116_________ figures 1 to 6, in which are

plotted graphically the values a t White______________92_ .951___92_ ,09.8 ___ 93,8_ 48 ________________ all ages of the rate

,

Negro_ _ _ . _ _ - _ _ . _ . _ _ _ _ _ Other races.________

__._87_.36_7 ___6_6,4_94_ . _ _ 82,_ 853 _ _8_ 2,41_ 2

_ _._ _88_83. .,2_3b_ 0l2__ _o__ f_`m_ __o_ rta_ li_ ty,_ th_ e

_ nu_ mb_ er_o_ f survivors

out

of

100,000

live births, and the average future lifetime for each of

the 12 life tables. These graphs bring out certa,in

, FIGUREl.-ANNWAL RATE OF MORTALITPYER 1,000, FOR EACHRACE BY SEX:*UNITEDSTATES, 1939-1941

100

90

80

7c

I

P

.

3c 2c

I

I

I

I

I

45

50

55

60

t

Age in years

-

 ................
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