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A demographer studies human populations quantitatively: how many people are present, how their characteristics are distributed, and how births, deaths and human migration change those counts. The work connects population census definitions and statistical sampling to statistical estimation and mathematical models of population dynamics. A forecast must distinguish observed counts from assumptions about future rates.^[ref]

For example, in a closed demographic cohort with $n_a(t)$ people aged $a$ and common one-year survival probability $s_a(t)$ conditional on that count, a basic projection isA cohort of 1000 people with survival probability $0.998$ contributes an expected 998 survivors to the next age class. Births create a new youngest class, and human migration requires additional terms. This elementary calculation illustrates why a demographer works with age structure and explicit statistical parameters, rather than extrapolating a single total without assumptions.

A demographic cohort is a group defined by experiencing a specified event during the same interval, then followed through time. A birth cohort consists of people born in a stated period; other examples group people by year of immigration or first diagnosis. It is not the same as all people of a given age in a single cross-section.

Ignoring migration, a birth cohort with 1000 initial members and 950 survivors ten years later has ten-year survival proportion $950/1000=0.95$. Comparing that with the proportion of today's ten-year-olds among today's residents answers a different question, because births, deaths and human migration have affected the denominator. Cohort analysis separates changes experienced by a group as it ages from changes between successive groups. For a cohort defined by birth year $c$, calendar year and age satisfy $t=c+a$, which creates an exact dependence in attempts to estimate age, period and cohort effects simultaneously.

Demography measures the size, composition and change of human populations. It combines population censuses, registrations of births and deaths, and statistical sampling with mathematical models of population dynamics. A population census refers its counts to a specified time and territory; collecting questionnaires on different days should not silently change the reference date.^[ref]

For a fixed territory, a demographic accounting identity iswhere $B,D,I,E$ count births, deaths, immigration and emigration during the intervening period. For example, $N(t_0)=10000$, $B=140$, $D=90$, $I=80$ and $E=110$ give $N(t_1)=10020$. This demographic balancing equation distinguishes natural increase from net human migration; it does not assume an exponential growth law.

Counts also need denominators. A birth rate compares births with the relevant population exposure, rather than comparing raw birth totals between differently sized human populations. Changes in age composition can alter an aggregate rate even when the underlying age-specific rates remain fixed, motivating analysis by demographic cohorts.

A human population for quantitative demography is the collection of people satisfying a stated territorial, residence and time definition. Its size $N(t)$ is a count; its age or other composition describes how that count is distributed between subgroups. A resident population and the people physically present on a particular night can have different sizes.

For example, a town with 10000 residents and 200 births during one year has an approximate crude birth rate of 20 births per 1000 residents per year if its midyear population is 10000. A town with 20000 residents and the same birth count has approximately half that rate. Raw event counts therefore cannot replace denominators. Population censuses and the demographic balancing equation connect successive measurements, while demographic cohorts allow changes in composition to be tracked.