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🔷 TOPIC (x) — VITAL STATISTICS

Syllabus topic (x) of 10 · runs until the end of the syllabus

Covers: Objectives & sources · key terms (density, CBR, CDR, natural increase, life expectancy, IMR, neonatal, MMR) · Fertility — CBR, GFR, SFR, TFR · Mortality — CDR, SDR, STDR · ⭐ GRR · ⭐ NRR · ➕ added: NRR ≤ GRR, ASFR modal age, MMR denominator conventions 🎯 Asked in the papers: 2024 · Q80 — match the measures of mortality/fertility

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Study and measurement of vital factors related to health and growth of community. It includes — - Marriage

• Births
• Deaths
• Sickness
• Migration and so on.

1. Introduction

1.1 Objectives

• To implement and evaluate health related schemes (National Health Programs).
• To determine community health related infections, epidemics and find solution.
• To use the data as primary tool in research activities.
• Administrative purposes.

"Branch of Biometry that deals with data and law of human mortality, morbidity & demography".

1.2 Sources of Vital Statistics

• Civil Registration system.
• National Surveys.
• Health Surveys.
• Sample Registration system.

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2. Key Terms

1. Population Density: Population per square Area / Region (Pop. / $Km^2$)
2. Crude Birth Rate: Number of Births / 1000 people.
3. Crude Death Rate: Number of Deaths / 1000 people.
4. Natural Increase: (CBR - CDR) per year in percentage (%).
5. Life Expectancy: How long people in certain countries are expected to live.
6. Replacement Rate: The rate that is needed to replace both parents.
7. Age dependency: Percentage of population that depend on economic support (e.g; pension for elderly, school for young).
8. Age Dependency Ratio: $\frac{\text{Number of dependents } (0-14 \text{ \& } 65+)}{\text{Pop. } (15-65) \text{ age}}$
9. Abortion Ratio: Number of Abortions per hundred pregnancies.
10. Abortion Rate: Number of Abortions per thousand women (15-44) age.

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11. Emigration Rate: Number of Emigrants per thousand population per year.

12. Immigration Rate: No. of Immigrants per thousand population per year.

13. Brain Drain: Emigration of highly trained, skilled people from country.

14. Effective literacy rate: Number of Literates with age more than or equal to 7 to the population with age more than or equal to 7 in year. $\text{Eff. L.R} = \frac{\text{No. of Literates } (Age \ge 7 \text{ years})}{\text{Total Pop } (Age \ge 7 \text{ yrs}) \text{ in a year}} \times 100$

15. Infant mortality Rate: $\frac{\text{Number of Infant deaths in a year}}{\text{No. of live births in a year}} \times 1000$

16. Neonatal Mortality Rate: $\frac{\text{Deaths under one month}}{\text{No. of live birth}} \times 1000$

17. Post-neonates Mortality Rate: $= \frac{\text{Death between 1}^{\text{st}} \text{ and 11 complete months}}{\text{No. of live births}} \times 1000$

18. Maternal Mortality Rate: $\frac{\text{No. of death of mother due to maternity}}{\text{No. of live births}} \times 1,00,000$

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3. Fertility

"Natural capacity to give birth to an offspring"

Fecundity capacity to bear (how many) child births.

3.1 Fertility Rate / Natality Rate / Birth Rate

Measure of rate of growth in population due to births in a specific period.

• Expressed in per thousand women per year.
• Child Bearing Age (India) $\rightarrow$ (15 - 49) years.

3.2 Methods of Calculating the Birth Rate

1. Crude Birth Rate (CBR)
2. General Fertility Rate (GFR)
3. Specific Fertility Rate (SFR)
4. Total Fertility Rate (TFR)

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(i) Crude Birth Rate (CBR)

$CBR = \frac{\text{No. of Live Births}}{\text{Population of that region in that time period}} \times 1000$

$CBR = \frac{B_t}{P_t} \times 1000$

Q. No. of live births in particular area is 3000, If the total population is 3 lac. Calculate crude Birth rate. Sol $CBR = \frac{B_t}{P_t} \times 1000 = \frac{3000}{3,00,000} \times 1000$ $= \frac{3000}{300} = \text{==10==}$

Q. Find the crude birth rate for given data.

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Sol $CBR = \frac{B_t}{P_t} \times 1000$ $= \frac{250}{\text{Males + Females}} \times 1000$ $= \frac{250}{9500 + 10000} \times 1000 = \frac{250}{19500} \times 1000$ $= \frac{2500}{195} = \text{==12.82==}$

(ii) General Fertility Rate (GFR)

$GFR = \frac{\text{No. of live Births}}{\text{No. of women (15-49)}} \times 1000$

$GFR = \frac{B_t}{\sum_{15}^{49} P_t} \times 1000$

For the Above Data: $GFR = \frac{250}{7500} \times 1000 = \frac{2500}{75} = \text{==33.33==}$

(iii) Specific Fertility Rate (SFR)

Fertility Rate taking the factors which affect it like; Marriage, Age, migration etc. $SFR = \frac{\text{No. of births in specific class}}{\text{Total women in that class}} \times 1000$

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ASFR = $\frac{\text{No. of Births in that particular age group}}{\text{Total No. of women in that group}} \times 1000$

(iv) Total Fertility Rate (TFR)

(a) For equal intervals = $\frac{(\sum \text{ASFR}) \times \text{interval}}{1000}$ (b) For unequal intervals = $\frac{(\sum (\text{ASFR} \times \text{interval}))}{1000}$

Case (b) — unequal intervals $TFR = \frac{\sum (\text{ASFR}) \times i}{1000} = \frac{1574.99}{1000} = \text{==1.574==}$

Quick Recap

1. $CBR = \frac{B_t}{P_t} \times 1000$
2. $GFR = \frac{B_t}{\sum_{15}^{49} P_t} \times 1000$
3. $SFR = \frac{\text{No. of Births (specific class)}}{\text{Total women (section)}} \times 1000$
4. $TFR = \begin{cases} (i) = \text{interval} \Rightarrow \frac{(\sum \text{ASFR}) \times i}{1000} \\ (ii) \neq \text{interval} \Rightarrow \frac{(\sum \text{ASFR} \times i)}{1000} \end{cases}$

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4. Mortality (Death Rate)

Number of deaths per thousand population in a particular area in specified time period.

4.1 Methods of Calculating the Death Rate

(1) Crude Death Rate (CDR) (2) Specific Death Rate (SDR) (3) Standardised Death Rate (STDR)

(i) Crude Death Rate (CDR)

$CDR = m = \frac{\text{No. of Annual Deaths}}{\text{Annual mean population}} \times 1000$

Q. Find the Male, Female and crude Death Rate from the given data.

Sol: $\text{Crude male Death Rate} = \frac{\text{No. of Male Deaths}}{\text{Total Male pop.}} \times 1000$ $= \frac{810}{1,00,000} \times 1000 = \frac{810}{100} = \text{==8.1==}$

$\text{Crude Female Death Rate} = \frac{\text{No. of Female Deaths}}{\text{Total Female pop}} \times 1000$ $= \frac{510}{85,000} \times 1000 = \frac{510}{85} = \text{==6==}$

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$\text{Crude Death Rate} = \frac{\text{No. of Deaths}}{\text{Total Pop.}} \times 1000$ $= \frac{1320}{\text{Male pop + Female Pop}} \times 1000 = \frac{1320 \times 1000}{1,00,000 + 85,000}$ $= \frac{1320}{1,85,000} \times 1000 = \frac{1320}{185} = \text{==7.135==}$

(ii) Specific Death Rate (SDR)

$SDR = m_i = \frac{\text{No. of Deaths (specific class)}}{\text{Total Pop. of that class}} \times 1000$

$SDR_{(0-20)} = \frac{120}{(15+15)1000} \times 1000 = \frac{120 \times 1000}{30,000}$ $= \frac{120}{30} = \frac{12}{3} = \text{==4==}$

$SDR_{(20-40)} = \frac{200}{40000} \times 1000 = \frac{200}{40} = \frac{20}{4} = \text{==5==}$

$SDR_{(40-60)} = \frac{250}{25000} \times 1000 = \frac{250}{25} = \text{==10==}$

$SDR_{(60-80)} = ?$ $SDR_{(80-\text{Above})} = ?$

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(iii) Standardised Death Rate (STDR)

$STDR = \frac{\sum m_i \times S_{pop}(i)}{\sum S_{pop}(i)}$

$m_i \rightarrow$ specific Death Rate $S_{pop}(i) \rightarrow$ Standard Population of $(i^{\text{th}})$ age group.

Q Find the standardized Death Rate for the Given Data.

$STDR = \frac{\sum m_i \times S_{pop}(i)}{\sum S_{pop}(i)} = \frac{2,71,700}{37,000} = \frac{2717}{370}$ $= \text{==7.34==}$

5. Reproduction Rates

5.1 Gross Reproduction Rate (GRR)

To get better view about the rate of population, gender of new born baby is taken into consideration.

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"Female children are potential future mothers and result in population increase"

Methods of calculating GRR

(1) If female births to "1000" are given. $GRR = \frac{\sum_{15}^{49} B_f}{1000}$

Q. Calculate the GRR for the given data

$\therefore GRR = \frac{\sum_{15}^{49} B_f}{1000} = \frac{1200}{1000}$ $GRR = \text{==1.2== per woman}$

(2) Female Population and female births are given $GRR = \sum_{15}^{49} \left[ \frac{B_f}{P_{xf}} \right] \times i$ $\rightarrow$ For unequal intervals

Q Calculate the GRR for the data given.

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(3) If total Fertility Rate and Male : Female ratio is given $GRR = \frac{TFR \times B_f}{\sum B}$

Q. If TFR = 1500 per thousand, Male : Female ratio is = 65:35 for new Born babies. Calculate GRR. Sol $GRR = \frac{TFR \times B_f}{\sum B} = \frac{1500 \times 35}{1000}$ (per 1000) $= \frac{15 \times 35}{1000} = \frac{525}{1000} = \text{==0.525== per woman.}$

Points to remember (GRR)

(i) If $GRR > 1 \rightarrow$ Population $\uparrow$ inspite of low birth rate (ii) If GRR < 1 \rightarrow Population $\downarrow$ inspite of low mortality (iii) If $GRR = 1 \rightarrow$ Population stagnant (population of females replacing themselves)

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5.2 NRR is Always Less Than or Equal to GRR

$\mathbf{NRR \le GRR}$

Why: GRR counts the daughters a woman would bear assuming she survives her whole reproductive span — it IGNORES mortality. NRR applies actual survival rates, so some of those daughters are removed. You can only ever lose women, never gain them — so NRR can never exceed GRR. They are equal only in the impossible case of zero mortality.

5.3 ASFR — Modal Value Between 20 and 25

The Age-Specific Fertility Rate rises from age 15, ⭐ peaks in the 20–25 age group (the modal childbearing age), then falls away to nearly zero by 49.

5.4 The MMR Denominator — Both Conventions

The notes above give Maternal Mortality Rate per 1,00,000 live births — that is the official WHO / SRS convention and is correct. ⚠️ But some textbooks and question papers state MMR "per 1,000 live births" — the 2024 paper did exactly this. Read the options and take whichever convention the question offers. The idea being tested is only that MMR is measured against live births, not against total population.

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5.5 Net Reproduction Rate (NRR)

Net Reproductive Rate is the extension or modified form of GRR where mortality / survival rates is also taken in Account.

**(i) If Female births, female population and survival rate is given ** $NRR = i \times \sum \left( \frac{B_f}{P_{xf}} \times 1000 \right) \times S$

• $i \rightarrow$ interval
• $B_f \rightarrow$ Female births
• $S \rightarrow$ Survival Rate
• $P_{xf} \rightarrow$ Female Population

Q. Calculate the net Reproductive rate for the given Data.

$NRR = i \times \frac{\sum \left( \frac{B_f}{P_{xf}} \times 1000 \right) \times S}{1000}$ $= 5 \times \frac{473.56}{1000} = 5 \times 0.473 = \text{==2.365==}$ Per Woman.

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Trick — survival rate from mortality rate, and back

$S.R = 10^{\text{no. of digits in mortality rate}} - \text{Mortality Rate}$ or $M.R = 10^{\text{no. of digits in survival rate}} - \text{Survival Rate}$

e.g If Survival Rate = 6, M.R = ? $M.R = 10^1 - 6 = 10 - 6 = \text{==4==}$

e.g If M.R = 63 what is survival Rate $S.R = 10^2 - 63 = 100 - 63 = \text{==37==}$

Important points about NRR

(i) If NRR > 1, Population will increase inspite of high death rate. (ii) If NRR < 1, Population will decrease inspite of high birth rate. (iii) If NRR = 1, Population will be stagnant.

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Case 3 of the trick

Q. $\frac{32146123}{2043212} = \frac{3214}{204} \xrightarrow{(-4)} \frac{3200}{200}$

$= \text{==16==}$ $16 \times 4 = \text{==64==} \rightarrow \text{factor to subtract.}$

$3214 - 64 = 3150$

$\frac{3150}{200} = \frac{315}{20} = \frac{31.5}{2} = \text{==15.75==}$ (Calculator = 15.73)

Q. Number of men is 151,781,326 and number of women is 156,964,212. Which options represent demographic sex Ratio. (PAA JKSSB 2020)

(a) 97.6 (b) 96.7 (c) 98.2 (d) 95.3

Sol $\text{Sex Ratio} = \frac{\text{No. of males}}{\text{No. of Females}} \times 100$

$= \frac{151,781,326}{156,964,212} \times 100$

$= \frac{151}{156} = \frac{150}{160} = \frac{15}{16}$ , $\frac{15}{16} \times 4 = \frac{15}{4} = \text{==3.75==}$

$= \frac{151 + 3.75}{160} = \frac{154.75}{160} \times 100$ $= \frac{154.75}{16} \times 10 = \frac{154.75 \times 5}{8} = 19.34 \times 5 = \text{==96.70==}$ (Calculator = 96.69)

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