Johnston] 



NAVAHO POPULATION 



213 



CALCULATION OF STABLE POPULATION AGE DISTRIBUTIONS FROM 

 MODEL LIFE TABLE VALUES ' 



The derivation of an age distribution for a stable population from 

 selected model life table values and an assumed rate of natural in- 

 crease is illustrated in appendix table 2. The procedure can be out- 

 lined in the following steps: 



Appendix Table 2. — Illustration of procedure for deriving a stable population 

 age distrit)ution from given model life table values 



1 Assumed midpoint, 

 if =25000-K.75) (91553) =25000+68665=93665 

 3t,m = (i.9)(9i553)-(.(2.1)(88513) =173951+185877=359828 

 4to"' = 25000+ (2.65) (91553) + (2. 1) (88513) = 25000+242615+ 185877 = 453492 



Step 1. An appropriate model life table and assumed rate of nat- 

 ural increase must be decided upon initially. This selection must 

 depend, of course, upon the intended purposes of the calculation. In 

 developing the hypothetical age distributions shovs^n in table 36, model 

 life table values and rates of natural increase vrere selected in order 

 to represent plausible rates of fertility and mortality which might 

 have been observed among the Navaho population at different periods 

 in the past. 



Step 2. The midpoint of each age group {a) is multiplied by the 

 assumed rate of natural increase (r) . 



Step 3. The values of e'"'' are obtained directly from a table of 

 descending exponential functions. 



Step Jf. The Z^ values which correspond to the basic q^ values of 

 the selected model life table are next obtained directly from the basic 

 United Nations source.* 



' The development, uses, and limitations of these model life tables are described in 

 United Nations, 1955 b. The basic L, values utilized in the construction of the hypothet- 

 ical age distributions given In the present analysis were provided in a later development of 

 these models given in United Nations, 1956. 



* United Nations, 1956, table iv, pp. 78-79. The model shown in appendix table 2 is 

 "Level 80," identified by a life expectancy at birth (for both sexes combined) of 60.4 years. 



