Vital Statistics

Abdullah Al Mahmud

Concept of Vital Statistics

That branch of biometry which deals with data and laws of human mortality, morbidity, and demography.

Arthur Newsholme \(\downarrow\)

the whole study of mankind as affected by heredity or environment in so far as the results of this study can be arithmetically stated.

Rates & Ratios

Dependency Ratio
Sex ratio
Population density
Crude Birth Rate (CBR)
General Fertility Rate (GFR)
Age-Specific Fertility Rate (ASFR)
Total Fertility Rate (TFR)

Gross Reproduction Rate (GRR)
Net Reproduction Rate (NRR)
Net Fertility Rate (NFR)
Crude Death Rate (CDR)
Age-Specific Death Rate (ASDR)

Rate vs Ratio

Dependency Ratio

\[d = \frac{P_{0-14}+P_{65+}}{P_{15-64}}\times100\] Where

\(P_{0-14}\) = The no. of children aged between 0 & 14
\(P_{65+}\) = The no. of people aged 65 or older
\(P_{15-64}\) = The no. of people aged between 15 and 64

\(d = 103\%\) means there are 103 dependents for every 100 working-age people

\(d = 70\%\) means there 70 dependents for every 100 working-age people

DR Example

Age Group	Population (millions)
0-14 (Youth)	40
15-64 (Working-Age)	120
65+ (Elderly)	20

Find the Dependency Ratio and explain

Reveal Answer

\[ \text{Dependency Ratio} = \left( \frac{\text{Youth} + \text{Elderly}}{\text{Working-age population}} \right) \times 100 \]

\[ \text{Dependency Ratio} = \left( \frac{40 + 20}{120} \right) \times 100 = \left( \frac{60}{120} \right) \times 100 = 50\% \]

DR Insight

Dependency Ratios of two different cities are

\(d_1 = 101\%\) and \(d_2 = 98\%\)

Which city has more dependent people per 100 working people?

Write the interpretation of each value.

Sex Ratio

\(SR = \frac MF \times 100\)

Suppose a town has the following population data:

Males: 52,000
Females: 50,000

\[ \text{Sex Ratio} = \left( \frac{\text{Number of Males}}{\text{Number of Females}} \right) \times 100 \]

\[ \text{Sex Ratio} = \left( \frac{52,000}{50,000} \right) \times 100 = 104 \]

SR Explanation

In this example, the sex ratio is 104, which indicates that there are 104 males for every 100 females in the town.

IF SR = 95, what does it mean?

Population Density

\(D = \frac PA\)

P = Total Population

A = Area

Density Example

City	Total Population	Total Land Area (km²)
City A	1,000,000	500
City B	2,500,000	1,250

Find the densities

Reveal Answer

\[ \text{Population Density} = \frac{1,000,000}{500} = 2,000 \text{ people/km}^2 \]

\[ \text{Population Density} = \frac{2,500,000}{1,250} = 2,000 \text{ people/km}^2 \]

Both cities have the same population density of 2,000 people per square kilometer.

Density Example 02

City	Total Population	Total Land Area (km²)
Tokyo, Japan	37,435,191	2,194
New York City, USA	8,804,190	783
Mumbai, India	20,667,656	603

Reveal Answer

City	Population Density (people/km²)
Tokyo, Japan	17,063
New York City, USA	11,243
Mumbai, India	34,285

Crude Birth Rate

\(CBR = \frac BP\times 1000\)

B = Total no. of alive children in a year

P = Average/Mid-year population of that region in that time

CBR Example

If a country has 500,000 live births in a year and a mid-year population of 50,000,000:

Reveal Solution

\[ \text{CBR} = \left( \frac{500,000}{50,000,000} \right) \times 1,000 = 10 \text{ births per 1,000 people} \]

Explanation: There are 10 live births per 1,000 people in the population per year.

General Fertility Rate

GFR is used to estimate the number of live births in a year per 1,000 women of childbearing age (typically ages 15-49)

\(\displaystyle GFR = \frac{B}{F_{15-49}}\times 1000\)

B = Total number of live births in a year

\(F_{15-49}\) = Total number of women in reproductive age group (15-49)

GFR Example

A country has:

Number of live births in a year: 300,000
Number of women aged 15-49: 10,000,000

Reveal Answer

\[ \text{GFR} = \left( \frac{300,000}{10,000,000} \right) \times 1,000 = 30 \text{ births per 1,000 women} \]

Therefore, the General Fertility Rate in this example is 30 births per 1,000 women of childbearing age.

Age-Specific Fertility Rate

ASFR is used to analyze fertility patterns across different age groups

\(\displaystyle ASFR_i = \frac{B_i}{F_i}\times 1000\)

\(B_i\) = Total number of live births in a year by the women in ith age group

\(F_i\) = No. of women in ith age group

Total Fertility Rate

Total Fertility Rate (TFR) of a population is the average number of children that are born to a woman over her lifetime if:

they were to experience the exact current age-specific fertility rates (ASFRs) through their lifetime.
they were to live from birth until the end of their reproductive life.

\(\displaystyle TFR = 5 \sum_{i=1}^7ASFR_i = 5 \sum_{i=1}^7 \frac{B_i}{F_i}\times 1000\)

5 for class interval

Uses of Fertility Rates

Fertility Rate	Use Case
GFR	Measures fertility of women aged 15-49
ASFR	Analyzes fertility rate specific to age groups
TFR	Estimates total children a woman would have
GRR	Measures the number of daughters born to women
NRR	Measures net reproduction rate, accounting for mortality
NFR	Measures fertility rate in a given population

Gross Reproduction Rate

\(\displaystyle GRR = 5 \sum_{i=1}^7\frac{G_i}{F_i}\times 1000\)

\(G_i =\) Total number of girl babies born in a year by the women in ith age group

Net Reproduction Rate

\(\displaystyle NRR = 5 \sum_{i=1}^7\frac{G_i}{F_i}\times S_i\times 1000\)

\(S_i =\) Survival rate of women of reproductive age group (15-49)

Net Fertility Rate

\(\displaystyle NFR = 5 \sum_{i=1}^7\frac{B_i}{F_i}\times S_i\times 1000\)

GRR Implications

GRR = 1: Replacement level (each woman has, on average, one daughter).
GRR > 1: More than one daughter per woman on average, suggesting potential population growth.
GRR < 1: Fewer than one daughter per woman on average, indicating a population decline in the long term (if other factors remain constant).

NRR Implications

NRR = 1: The population is at replacement level, meaning each woman has, on average, one daughter who survives to reproductive age.

NRR > 1: More than one daughter survives per woman, indicating the population is growing over time.

NRR < 1: Fewer than one daughter survives per woman, suggesting the population is declining in the long term.

Implications

GRR > 1: Number of potent women increasing
GRR = 1: Number of potent women remains constant. There is no change in population
NRR > 1: The number of potent women more than that of previous year; population increasing
NRR = 1: No change in population
GRR = NRR: No new-born girls dies before reaching last potent age

Numerical Problem

Find CBR, GFR, ASFR, TFR, GRR, & NRR

Age	# Women	# Newborn	# Baby boys	Survival probability
15-19	7806000	521435	272342	0.980
20-24	6781000	846256	422247	0.977
25-29	5840000	412342	206122	0.972
30-34	5434000	326268	183134	0.960
35-39	5675000	211810	111440	0.942
40-44	6083000	69750	34380	0.895
45-49	5361000	42354	22462	0.854

Total population = 109,027,142

Solutio to Rates

Age Group	# Women \(\times 1000\) \(F_i\)	# Newborn \(B_i\)	# Baby boys	Survival probability \(S_i\)
15-19	7806	521435	272342	0.980
20-24	6781	846256	422247	0.977
25-29	5840	412342	206122	0.972
30-34	5434	326268	183134	0.960
35-39	5675	211810	111440	0.942
40-44	6083	69750	34380	0.895
45-49	5361	42354	22462	0.854

Natural Growth Rate (NGR)

NGR = CBR - CDR

\(\displaystyle \frac BP \times 1000-\frac DP \times 1000 = \frac {B-D}P \times 1000\)

Growths

Geometric Growth

\(P_o =\) Initial population

\(P_n =\) Final population

\(n =\) Number of period (year, month, etc)

\(r =\) Rate of increase

Population after 1 year, \(P_1 = P_o + P_or = P_o(1+r)\)
Population after 2 years, \(P_2 = P_1 + P_1r = P_1(1+r) = P_o(1+r)^2\)
Population after n years, \(P_n = P_o(1+r)^n\)

Growth Problems

Time required for population to get doubled/tripled in certain rate
Rate required for population to get doubled/tripled in certain time

Exponential Growth

Geometric: \(P_n = P_o(1+r)^n\)

If n is fragmented in smaller periods

Like 100 % in 1 year \(\rightarrow\) 50 % in each half-year

\(P_n = P_o(1+\frac{r}{n})^n\)