Methods of Demographic Analysis Questions and Answers

Answer: C

The pair that is not matched correctly is fertility analysis with the formula for qx. The expression 2Mx divided by (2 + Mx) is the conversion of the central death rate into the probability of dying, which belongs to mortality and life table analysis, not to fertility analysis.

The stable population equation, the gravity form P1P2/D12 for migration, and the exponential projection Pt = P0 e^(rt) are matched to the right topics. So option C is the exception.

The correct formula for the probability of dying, qx, from the central death rate mx is 2mx divided by (2 + mx), which is used in building life tables, so it is a mortality formula and cannot stand for fertility analysis.

Answer: B

The component method of population projection requires age specific fertility rates, together with age specific mortality rates and migration, since it projects each age group forward and adds the births to the youngest age group.

The Gompertz method and the exponential growth method use only the overall growth trend, and the balancing equation method is for estimating population change from births, deaths and migration. None of those needs age specific fertility rates.

Answer: C

The pair that is not matched correctly is SMAM as a measure of migration. SMAM is the singulate mean age at marriage, a measure of the age at which people marry, so it relates to nuptiality and not to migration.

The crude birth rate is a measure of fertility, the infant mortality rate a measure of mortality, and the net reproduction rate a measure of population growth in terms of replacement. All three are matched correctly.

Answer: D

The doubling time of a population growing at the rate r is the natural logarithm of 2 divided by r. With exponential growth P = P0 e^(rt), the population doubles when e^(rt) = 2.

The other forms use the logarithm of e, which equals 1, or put a factor of 2 in the wrong place, so they do not give the doubling time.

The value of the natural logarithm of 2 is about 0.693, so a population growing at 1 per cent a year doubles in about 69 years, which is the familiar rule of 70.

Answer: B

The gross reproduction rate equals the net reproduction rate when there is no mortality, because the NRR is the GRR reduced by the survival of women to each childbearing age. If every woman survives, the reduction vanishes and the two are equal.

A zero growth rate or replacement level means the NRR is 1 but the GRR is then higher than 1, and closure to migration has nothing to do with the relation between the two.

The NRR is calculated by multiplying the age specific fertility rates of women by the survival ratios, so with perfect survival the multiplier is one at every age, and the NRR cannot differ from the GRR.

Answer: A

The correct matching is a-iv, b-iii, c-ii, d-v. The singulate mean age at marriage was devised by Hajnal, the theory of population is Malthus's, the abridged life table is credited to Greville, and the stable population theory was developed by Coale.

The other codes give the theory of population to Gompertz or Coale, which is wrong, since Gompertz is known for the mortality law.

Answer: D

The statement that is not true for a stable population is that the net reproduction rate equals the gross reproduction rate. They are equal only when there is no mortality, and in a real stable population the NRR is lower than the GRR since some women die before the end of childbearing.

NRR = e^(rT) is true for a stable population, as is the equality of the birth and death rates to 1/e0 when r is zero, and the age composition c(a, t) stays constant in time.

Answer: B

The crude death rate is based on the total population (i), the general fertility rate on the female population of reproductive age (iii), the infant mortality rate on per thousand live births (ii) and the gross reproduction rate on female births (iv), so the second code is correct. The other codes interchange the denominators, for example basing the crude death rate on live births. A rate is defined by its denominator, and the denominators listed in the second column decide which rate is which.

Answer: C

Age standardisation of fertility is used to compare fertility in two population groups, so the third option is correct per the key. By applying a common age distribution to the age specific rates of both populations, the differences due to age composition are removed and the comparison is made on fertility itself. It does not compare age distributions, nor remove differences in fertility. The method is applied to remove the effect of differences in age structure when two populations are compared. The other options describe other uses of standardisation and so are rejected.

Answer: B

The survival ratio from age 15 to age 45 is computed as l45 over l15 according to the key, so the second option is correct. It is the proportion of the 15-year-old survivors in the life table radix who live to age 45. The first option uses person-years lived and the third mixes the two, so neither agrees with the key. The key is the official answer, though some texts use the L column for census survival ratios.