Singulate mean age at marriage refers to the average age at first marriage (average number of years of single life), before a certain age (defined at 50), of population born in the same year. Singulate mean age at marriage is a common indicator in the study of marriage. It is not affected by the age structure of population; besides, it also covers marriage cases registered abroad.

Singulate mean age at marriage is calculated from the proportions of never-married by age and gender. The basic assumption involved in the calculation is that the change in the proportions of never-married from age x to age x+1 is a measure of the proportion of a birth cohort who married at the age of x+1.

Example: To calculate the singulate mean age at marriage of females in Macao according to the 2011 Population Census by using the proportions of never-married females by age group, and assuming that mortality of females aged 16-54 is so low that it can be ignored:

Age group(x) 　　 Proportion of never-married females (%) P(x)
16-19 　　　　　　99.0
20-24 　　　　　　84.5
25-29 　　　　　　53.5
30-34 　　　　　　27.4
35-39 　　　　　　16.8
40-44 　　　　　　11.4
45-49　　　 　　　 8.9
50-54　　　　　　 7.8

Steps for calculation
(1) Based on a birth cohort of 100 females at present marital status:
A.　Number of years of single life between age 16-49
A = ΣP(x) x 5 （x refers to age groups from 16-19 to 45-49）
Formula: (84.5 + 53.5 + 27.4 + 16.8 + 11.4 + 8.9) x 5 + 99.0 x 4 = 202.5 x 5 + 396 = 1408.5

(2) B.　Number of years of single life between age 0-49
B = A + 1 600（16 years x 100 persons = 1 600 years）
Formula: 1,408.5 + 1,600 = 3,008.5

(3) C.　Proportion of never-married females by age 50
C = (P(45-49) + P(50-54)) ÷ 2
Formula: (8.9 + 7.8) ÷ 2 = 8.4

(4) D.　Number of years of single life of never-married females by age 50
D = C x 50
Formula: 8.4 x 50 = 420.0

(5) E.　Number of years of single life of females married before age 50
E = B – D
Formula: 3,008.5 - 420.0 = 2,588.5

(6) F.　Proportion of married females at age 50
F = 100 - C
Formula: 100.0 – 8.4 = 91.6

(7) G.　Singulate mean age at marriage of females
G = E ÷ F
Formula: 2,588.5 ÷ 91.6 = 28.3

In this example, 91.6 out of 100 females born in the same year have married by age 50; their total number of years of single life before marriage is 2,588.5, and the singulate mean age at marriage is 28.3.