Demographic and Official Statistics
Core concepts
Understand the core demographic measures: crude birth and death rates, age-specific rates, total fertility rate, life expectancy, infant mortality, and standardised mortality ratios. Know the difference between crude and standardised rates and why direct and indirect standardisation matter when comparing populations with different age structures. Understand life tables (l_x, d_x, q_x, e_x), population projections, the components method, and the demographic transition. Be familiar with census methodology, vital registration, and the definitions used in official statistics.
Traps
- Comparing crude death rates across countries with very different age structures.
- Confusing the total fertility rate with the crude birth rate; TFR is a synthetic cohort measure.
- Misreading q_x (probability of dying) as m_x (central death rate).
- Treating mid-year population as the denominator when the correct exposure differs.
- Confusing natural increase with total population change, which includes net migration.
- Using indirect standardisation when direct is possible; indirect is a fallback when age-specific rates are unavailable.
Worked example
A population has 12,000 births and a mid-year population of 600,000: crude birth rate = 12,000/600,000 × 1,000 = 20 per 1,000. If age-specific rates for a standard population give an expected 9,000 deaths and 10,000 are observed, the standardised mortality ratio is 10,000/9,000 × 100 = 111, indicating 11% higher mortality than expected. Rule of thumb: rates use mid-year population as the denominator and are usually expressed per 1,000.