Rate vs Ratio

Dependency Ratio

DR Example

Find the Dependency Ratio and explain

DR Insight

Dependency Ratios of two different cities are

$d_1 = 101\%$ and $d_2 = 98\%$

1. Which city has more dependent people per 100 working people?

2. 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

Find the densities

Density Example 02

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:

• 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

• 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:

1. they were to experience the exact current age-specific fertility rates (ASFRs) through their lifetime.
2. 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

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

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

Total population = 109,027,142

Solutio to Rates

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

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