Methods of Demographic Analysis Questions and Answers

Q: Death rates are standardised to :

Death rates are standardised to eliminate the differential influence of one or more variables.Crude death rates of two populations are not comparable when the populations differ in composition, above all in age (and sex) structure: an older population has a higher crude rate even if each age group is healthier. Direct or indirect standardisation applies the age-specific rates to a common standard population (or vice versa), removing the effect of those compositional variables.Standardised rates are comparative indices, not estimates of 'ideal' or 'actual' rates, and they have nothing to do with correcting death registration.

Q: Which one of the following population growth model is not matched correctly ?

The model that is not matched correctly is Gompertz : Pt = BCt.The arithmetic model is Pt = Po(1 + rt), the exponential model is Pt = Poert, and the logistic curve is Pt = K / (1 + ea + bt), all as printed in options A, B and C.The Gompertz curve is a double-exponential, usually written as Pt = K abt, or log Pt = log K + (log a) bt. The form BCt is a simple exponential in t, so it is the one that does not match.

Q: The double time (t) of a given population growth rate (r) is

The official key gives t = log e2 / r, which stands for the natural logarithm of 2 divided by the growth rate.If a population grows at a constant rate r, then Pt = Poert. It doubles when Pt / Po = 2:\[ \begin{aligned} e^{rt} &= 2 \\ rt &= \log_{e} 2 \\ t &= \frac{\log_{e} 2}{r} \end{aligned} \]Option B is the printed form of this result (the log to the base e of 2). Option A has no base, so with common logarithms it would give 0.301 / r, which is wrong. Options C and D have a factor 2r in the denominator, which would make the doubling time half as long as it should be.

Q: Match the following List - I with List - IIList-IList-II(a) Regional model life tables(i) Hajnal(b) Singulate mean age marriage(ii) Brass(c) Theory of stable population(iii) Lotka(d) P/F Ratio method(iv) Coale Semeny(v) Sheps

The correct matching is a-iv, b-i, c-iii, d-ii.The regional model life tables are the work of Coale and Demeny (the booklet prints 'Coale Semeny'), the singulate mean age at marriage is Hajnal's measure, the theory of stable population is associated with Lotka, and the P/F ratio method of estimating fertility is Brass's.Sheps, (v), is a name from the study of fertility and reproduction and is not the author of any of the four items, so the codes that use it are wrong.

Death rates are standardised to :

A.obtain an estimate of ideal rates
B.eliminate the differential influence of one or more variables
C.adjust them with registration of deaths
D.obtain correct estimate of actual rates

Exam Year(s)

MH SET - 2019, SET Exam - 2019,

Answer: B

Death rates are standardised to eliminate the differential influence of one or more variables.

Crude death rates of two populations are not comparable when the populations differ in composition, above all in age (and sex) structure: an older population has a higher crude rate even if each age group is healthier. Direct or indirect standardisation applies the age-specific rates to a common standard population (or vice versa), removing the effect of those compositional variables.

Standardised rates are comparative indices, not estimates of 'ideal' or 'actual' rates, and they have nothing to do with correcting death registration.

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Which among the following rate is referred as probabilistic rate ?

A.Migration rate
B.Crude death rate
C.Marriage rate
D.Crude birth rate

Exam Year(s)

UGC NET - 2012,

Answer: C

The official key names the marriage rate as the probabilistic rate.

A rate in demography can be a ratio of events to the whole population living in the year, or a probability, the chance that a person at risk will experience the event. The marriage rate is the one the textbook behind this question treats as a probability of marrying among those exposed.

The crude death rate and the crude birth rate are plain event-to-population ratios and are not called probabilistic in that scheme, and the migration rate is also a simple ratio of movers to the population. So the key sets the marriage rate apart from the other three.

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Death rates are standardized to

A.eliminate the differential influence of one or more variables.
B.obtain an estimate of the ideal rates.
C.correct under registration of deaths.
D.obtain correct estimate of actual rate.

Exam Year(s)

UGC NET - 2012,

Answer: A

Death rates are standardised to remove the differing influence of one or more variables, such as age, from the comparison.

The crude death rate of two populations cannot be compared fairly if their age structures differ, since an older population will have more deaths in any case. Standardisation applies the rates to one standard population, so the difference caused by age (or sex or another variable) is eliminated and what remains reflects the real difference in mortality.

It does not estimate an ideal rate, since there is no such thing. It does not correct the under-registration of deaths, which needs a separate adjustment, and it does not give a corrected figure for the actual rate, because the standardised rate is only a comparison figure.

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Which one of the following is not matched correctly ?

A.Average age of child : Length of generation
B.A group of people related to marriage or adoption : Household
C.Net Reproduction (NRR) equal to unity : Replacement level
D.A married woman having no birth : Zero parity

Exam Year(s)

UGC NET - 2012,

Answer: A

The official key picks the pair of average age of the child with the length of generation as the one not matched correctly.

The length of generation is the average age of mothers when their daughters are born, not the average age of the child, so the first pair is wrong.

A net reproduction rate equal to one is the replacement level, and a married woman with no birth is of zero parity, so those two pairs are right. The pair of a group related by marriage or adoption with the household is loose, since a household is a group living together and a group related by marriage or adoption is a family, but the key accepts it and counts the first pair as the clearly wrong one.

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Match an item from List - I with an item from List - II :

List - I	List - II
a. Theory of Stable Population	i. William Brass
b. Singulate Mean age at marriage	ii. Lotka
c. Intermediate variable framework	iii. Hajnal
d. P/F Ratio	iv. Davis and Blake

Codes : a b c d

A.i iii ii iv
B.i ii iii iv
C.ii iii iv i
D.iii ii i iv

Exam Year(s)

UGC NET - 2012,

Answer: C

The correct matching is the theory of stable population with Lotka, singulate mean age at marriage with Hajnal, the intermediate variable framework with Davis and Blake, and the P/F ratio with William Brass, that is ii iii iv i.

Lotka developed the mathematics of stable populations. Hajnal introduced the singulate mean age at marriage as an indirect measure from census marital status. Davis and Blake set out the intermediate variables. Brass's P/F ratio method estimates fertility from parity and current fertility.

The first, second and fourth sets assign a method to the wrong person, for example the stable population theory to William Brass, so only the third is right.

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Stationary population is a model that

A.excludes migration
B.holds fertility constant
C.has fixed mortality rates
D.All the three above

Exam Year(s)

UGC NET - 2012,

Answer: D

A stationary population is a model with all three features: it has no migration, a constant fertility and fixed mortality rates, so the numbers and age structure stay the same over time. Births equal deaths and the growth rate is zero.

Since each of the first three statements is a part of the definition, any one of them alone is incomplete, and the correct choice is that all the three above are true.

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Which one of the following population growth model is not matched correctly ?

A.Arithmetic : \(P_{t} = P_{o}(1 + rt)\)
B.Exponential : \(P_{t} = P_{o}e^{rt}\)
C.Logistic : \(P_{t} = \frac{K}{1 + e^{a + bt}}\)
D.Gompertz : \(P_{t} = BC^{t}\)

Exam Year(s)

UGC NET - 2012,

Answer: D

The model that is not matched correctly is Gompertz : P_t = BC^t.

The arithmetic model is P_t = P_o(1 + rt), the exponential model is P_t = P_oe^rt, and the logistic curve is P_t = K / (1 + e^{a + bt}), all as printed in options A, B and C.

The Gompertz curve is a double-exponential, usually written as P_t = K a^{b^t}, or log P_t = log K + (log a) b^t. The form BC^t is a simple exponential in t, so it is the one that does not match.

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The double time (t) of a given population growth rate (r) is

A.\(t = \frac{\log 2}{r}\)
B.\(t = \frac{\log e^{2}}{r}\)
C.\(t = \frac{\log e}{2r}\)
D.\(t = \frac{\log e^{2}}{2r}\)

Exam Year(s)

UGC NET - 2012,

Answer: B

The official key gives t = log e² / r, which stands for the natural logarithm of 2 divided by the growth rate.

If a population grows at a constant rate r, then P_t = P_oe^rt. It doubles when P_t / P_o = 2:

\[ \begin{aligned} e^{rt} &= 2 \\ rt &= \log_{e} 2 \\ t &= \frac{\log_{e} 2}{r} \end{aligned} \]

Option B is the printed form of this result (the log to the base e of 2). Option A has no base, so with common logarithms it would give 0.301 / r, which is wrong. Options C and D have a factor 2r in the denominator, which would make the doubling time half as long as it should be.

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How many years it takes the population to double with a growth rate of 1.0 ?

A.70 years
B.46 years
C.140 years
D.28 years

Exam Year(s)

UGC NET - 2012,

Answer: A

A population growing at 1.0 per cent a year doubles in about 70 years.

From the previous result:

\[ t = \frac{\log_{e} 2}{r} = \frac{0.693}{0.01} \approx 69.3 \]

The 'rule of 70' gives the same figure at once: divide 70 by the rate in per cent, 70 / 1.0 = 70 years.

The other options correspond to other rates: 46 years would need a rate of about 1.5 per cent, 140 years about 0.5 per cent, and 28 years about 2.5 per cent.

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10.

Match the following List - I with List - II

List-I	List-II
(a) Regional model life tables	(i) Hajnal
(b) Singulate mean age marriage	(ii) Brass
(c) Theory of stable population	(iii) Lotka
(d) P/F Ratio method	(iv) Coale Semeny
	(v) Sheps

A.a-iv, b-i, c-iii, d-ii
B.a-i, b-iii, c-ii, d-iv
C.a-ii, b-iii, c-v, d-iv
D.a-v, b-iv, c-iii, d-ii

Exam Year(s)

UGC NET - 2012,

Answer: A

The correct matching is a-iv, b-i, c-iii, d-ii.

The regional model life tables are the work of Coale and Demeny (the booklet prints 'Coale Semeny'), the singulate mean age at marriage is Hajnal's measure, the theory of stable population is associated with Lotka, and the P/F ratio method of estimating fertility is Brass's.

Sheps, (v), is a name from the study of fertility and reproduction and is not the author of any of the four items, so the codes that use it are wrong.

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