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Indian Statistical Service Examination Demography & Vital Statistics: practice questions

Indian Statistical Service Examination (with Indian Economic Service) · India · Union Public Service Commission

Original practice questions written to the published syllabus · not past papers
10worked here, free
98written to this exam in this subject
9syllabus units

What this subject covers

Measuring populations and their change: sources of demographic data, fertility, mortality and migration measures, life tables, population growth models and projection, which the Indian Statistical Service and national statistical offices examine and rural and farm-household studies use.

In the exams: UPSC ISS Statistics IV (heavy, reported); SSC CGL JSO (present); light in ICAR exams

Where the 98 questions fall

How our questions for Indian Statistical Service Examination spread across the units of Demography & Vital Statistics. Difficulty: 23 easy, 61 medium, 14 hard.

Life tables: construction and uses; abridged life tables19
Measures of fertility: crude, general, age-specific and total fertility rates; GRR and NRR11
Measures of mortality: crude, age-specific and standardised death rates; infant mortality11
Migration measures10
Population projection: component method10
Stable and stationary populations10
Sources of demographic data: census, civil registration and sample registration9
Population growth models: exponential and logistic curves9
Rural and farm-household demography9

10 practice questions, worked

Choose an answer, then open the working. Each explanation says why the right answer is right and why the others are not.

1 · Sources of demographic data: census, civil registration and sample registration · medium

A dual-record sample registration system combines continuous recording of births and deaths by a local enumerator with which second element?

  1. Verbal autopsy interviews for every recorded birth
  2. An independent periodic survey whose records are matched to the continuous ones
  3. Hospital records of all births and deaths occurring anywhere in the whole country
  4. Verbal autopsy interviews carried out for every birth recorded by the enumerator
Answer and working

B. An independent periodic survey whose records are matched to the continuous ones

Matching two independent sources allows estimation of events missed by both (as in capture-recapture), correcting for under-recording.

Further reading: Preston, Heuveline and Guillot, Demography; Pollard, Yusuf and Pollard, Demographic Techniques; Keyfitz and Caswell, Applied Mathematical Demography; UN Principles and Recommendations for Population and Housing Censuses

2 · Measures of fertility: crude, general, age-specific and total fertility rates; GRR and NRR · medium

Where mortality is low, replacement-level fertility corresponds to a TFR of about what value?

  1. 1.0 child per woman
  2. 3.0 children per woman
  3. 2.1 children per woman
  4. 2.5 children per woman
Answer and working

C. 2.1 children per woman

Two children replace the parents; the extra 0.1 allows for more boys than girls at birth and some female deaths before the end of reproduction. Where mortality is higher, replacement TFR is higher.

Further reading: Preston, Heuveline and Guillot, Demography; Pollard, Yusuf and Pollard, Demographic Techniques; Keyfitz and Caswell, Applied Mathematical Demography; UN Principles and Recommendations for Population and Housing Censuses

3 · Measures of mortality: crude, age-specific and standardised death rates; infant mortality · medium

Death rates per 1,000 are 5 (under 50) and 20 (50 and over) in district A. A standard population has 70,000 under 50 and 30,000 aged 50 and over. What is A's directly standardised death rate?

  1. 12.5 per 1,000
  2. 25.0 per 1,000
  3. 9.5 per 1,000
  4. 15.5 per 1,000
Answer and working

C. 9.5 per 1,000

SDR = (5 × 70,000 + 20 × 30,000)/100,000 = 9.5 per 1,000. 12.5 is the unweighted average of the two rates.

Further reading: Preston, Heuveline and Guillot, Demography; Pollard, Yusuf and Pollard, Demographic Techniques; Keyfitz and Caswell, Applied Mathematical Demography; UN Principles and Recommendations for Population and Housing Censuses

4 · Life tables: construction and uses; abridged life tables · medium

Which constant appears in Reed and Merrell's formula ₙqₓ = 1 − exp(−n ₙmₓ − a n³ ₙmₓ²)?

  1. a = 0.5
  2. a = 0.08
  3. a = 0.008
  4. a = 1.0
Answer and working

C. a = 0.008

Reed and Merrell fitted a = 0.008 empirically from many life tables.

Further reading: Preston, Heuveline and Guillot, Demography; Pollard, Yusuf and Pollard, Demographic Techniques; Keyfitz and Caswell, Applied Mathematical Demography; UN Principles and Recommendations for Population and Housing Censuses

5 · Migration measures · medium

A district grows from 500,000 to 540,000 between censuses, with 120,000 registered births and 50,000 deaths. What is the net migration by the vital statistics method?

  1. +40,000
  2. +110,000
  3. -30,000
  4. −70,000
Answer and working

C. -30,000

Net migration = (P_t − P₀) − (B − D) = 40,000 − 70,000 = -30,000: a net loss. +40,000 is the total change; −70,000 the negative of natural increase.

Further reading: Preston, Heuveline and Guillot, Demography; Pollard, Yusuf and Pollard, Demographic Techniques; Keyfitz and Caswell, Applied Mathematical Demography; UN Principles and Recommendations for Population and Housing Censuses

6 · Population growth models: exponential and logistic curves · medium

A population grows from 100 million to 150 million in 10 years. What is the geometric annual growth rate?

  1. 4.05% per year
  2. 5.00% per year
  3. 4.14% per year
  4. 15.00% per year
Answer and working

C. 4.14% per year

(1 + r)¹⁰ = 1.5, so r = 1.5^0.1 − 1 = 4.14%. 4.05% is the continuous (exponential) rate.

Further reading: Preston, Heuveline and Guillot, Demography; Pollard, Yusuf and Pollard, Demographic Techniques; Keyfitz and Caswell, Applied Mathematical Demography; UN Principles and Recommendations for Population and Housing Censuses

7 · Population projection: component method · easy

In a cohort-component projection, 50,000 women aged 20-24 have a five-year survival ratio ₅L₂₅/₅L₂₀ = 0.98 and no migration is assumed. How many will be aged 25-29 five years later?

  1. 51,000
  2. 49,000
  3. 50,000
  4. 1,000
Answer and working

B. 49,000

50,000 × 0.98 = 49,000. 1,000 is the number expected to die.

Further reading: Preston, Heuveline and Guillot, Demography; Pollard, Yusuf and Pollard, Demographic Techniques; Keyfitz and Caswell, Applied Mathematical Demography; UN Principles and Recommendations for Population and Housing Censuses

8 · Stable and stationary populations · medium

What did Lotka show about a closed population with constant age-specific fertility and mortality?

  1. It always declines to extinction
  2. Its age distribution keeps oscillating for ever without settling down
  3. It always declines to extinction, because rates cannot stay constant
  4. It converges to a fixed age distribution and a constant growth rate
Answer and working

D. It converges to a fixed age distribution and a constant growth rate

Whatever the starting age structure, the population becomes stable: fixed proportions by age and constant intrinsic growth rate r.

Further reading: Preston, Heuveline and Guillot, Demography; Pollard, Yusuf and Pollard, Demographic Techniques; Keyfitz and Caswell, Applied Mathematical Demography; UN Principles and Recommendations for Population and Housing Censuses

9 · Stable and stationary populations · hard

A stable population has intrinsic birth rate 0.035 and intrinsic rate of natural increase 0.015. What is the intrinsic death rate?

  1. 0.020
  2. 0.050
  3. 0.015
  4. 0.035
Answer and working

A. 0.020

In a stable population d = b − r = 0.035 − 0.015 = 0.020.

Further reading: Preston, Heuveline and Guillot, Demography; Pollard, Yusuf and Pollard, Demographic Techniques; Keyfitz and Caswell, Applied Mathematical Demography; UN Principles and Recommendations for Population and Housing Censuses

10 · Stable and stationary populations · medium

A herd keeps a constant size of 600 cows, and cows remain in the herd for 5 years on average. How many replacement heifers enter each year, by stationary-population reasoning?

  1. 600
  2. 3,000
  3. 30
  4. 120
Answer and working

D. 120

In a stationary population, annual entries = population/average duration (CBR = 1/e₀): 600/5 = 120.

Further reading: Preston, Heuveline and Guillot, Demography; Pollard, Yusuf and Pollard, Demographic Techniques; Keyfitz and Caswell, Applied Mathematical Demography; UN Principles and Recommendations for Population and Housing Censuses

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Read the subject

Demography & Vital StatisticsThe full study manual, free Indian Statistical Service ExaminationFormat, sections and how it has changed

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