How to life expectancy is calculated ?

 Life expectancy is a statistical measure of the average time a person is expected to live, based on various factors like age, gender, and location. It is typically calculated using life tables (also known as actuarial tables or mortality tables). Here's how it is calculated step by step:

1. Gather Mortality Data

• Collect data on the number of people alive at the beginning of each age interval (e.g., 0–1 years, 1–2 years, etc.).
• Collect data on the number of deaths during each age interval for a specific population.

2. Calculate Age-Specific Mortality Rates

• For each age interval, calculate the probability of dying, usually denoted as $q_x$, where $x$ is the age.

$$q_x = \frac{\text{Number of deaths at age } x}{\text{Number of people alive at age } x}$$

3. Calculate Survivorship

• Determine the proportion of people surviving to each age, denoted as $l_x$. This is typically calculated starting with $l_0$, the total number of people born.

$$l_x = l_{x-1} \times (1 - q_{x-1})$$

4. Determine the Number of Years Lived at Each Age

• Estimate the average number of years people live within each age interval (denoted as $L_x$).
  For most age intervals:

$$L_x = \frac{l_x + l_{x+1}}{2}$$

For the last age interval:

$$L_\text{last} = \frac{l_\text{last}}{\text{mortality rate for last interval}}$$

5. Calculate Total Years Remaining

• Calculate the total number of years lived by all people beyond a given age, denoted as $T_x$:

$$T_x = \sum_{y=x}^\infty L_y$$

6. Compute Life Expectancy

• Divide $T_x$ by $l_x$ to find the average number of years remaining at age $x$, denoted as $e_x$:

$$e_x = \frac{T_x}{l_x}$$

For example:

• At birth ($e_0$), life expectancy is the total expected years an average newborn will live.
• At age 50 ($e_{50}$), life expectancy is the additional years a 50-year-old is expected to live.

Other Factors to Consider

• Gender: Males and females often have different life expectancies due to biological and social factors.
• Location: Life expectancy varies by country, region, and even socioeconomic status.
• Health Advances: Vaccinations, nutrition, and healthcare improvements can influence life expectancy trends.

Key Tools

• Governments and researchers use demographic surveys, census data, and population health records to compile the necessary mortality data.
• Advanced statistical models, such as those used by the UN or WHO, incorporate additional factors like disease prevalence and healthcare access.