MCAT content library / Psychology & sociology / Population pyramids and demographic change
Build two different age structures from the same starting population and explain why their totals can match.
About 18 minutes, including the worked examples and checks.
On this page
Read age structure as a record of people
A population pyramid shows how residents are distributed across age groups, commonly with two sex categories on opposite sides. Bar width represents a count or share, not a birth rate. The AAMC includes population pyramids, projections, growth and decline, Malthusian theory, and demographic transition.1
A wide youngest group is consistent with many surviving recent births, but its size also depends on mortality and migration. A narrow group can have several histories. Before explaining a shape, check the age-bin widths, the axis units, the measurement date, and which people the dataset includes.
Advance cohorts, then add the specified components
A cohort-component projection moves existing age groups forward while applying survival and migration assumptions and adding surviving births. A projection is conditional on these inputs. Changing an assumption can change the result without making the underlying arithmetic inconsistent.2
The figures and numbers here are original teaching data. The initial population contains 1,000 people, equally divided between recorded categories F and M. Counts are equal at each age by design; the labels describe these records. We project one ten-year interval, keeping the geographic boundary and category definitions fixed.
- Exactly 90% of each initially under-50 age group survives the interval; exactly 80% of the initial 50+ group survives.
- Surviving initial residents age ten years. The oldest group remains open-ended, so it receives survivors from 40–49 as well as retaining survivors already 50+.
- Scenario A adds 80 surviving newborns per recorded category and has no migration.
- Scenario B adds 60 surviving newborns per category and 20 net arrivals per category aged 20–29 at the endpoint. No other migration occurs.
Newborn counts already describe those alive at the endpoint, all aged 0–9. Do not apply the initial-resident survival percentages to them again. The specified migrants arrive at the endpoint, so they are not exposed to this interval’s survival adjustment. These are deliberately simplified timing assumptions.
| Age at measurement | Initial | After 10 years: A | After 10 years: B |
|---|---|---|---|
| 0–9 | 100 | 80 | 60 |
| 10–19 | 90 | 90 | 90 |
| 20–29 | 80 | 81 | 101 |
| 30–39 | 70 | 72 | 72 |
| 40–49 | 60 | 63 | 63 |
| 50+ | 100 | 134 | 134 |
| Total per category | 500 | 520 | 520 |
Trace one cohort instead of one row
The initial 0–9 group contains 100 people per category. Its survivors appear in 10–19: 100 × 0.90 = 90. They do not remain in the 0–9 row. That youngest row is replaced by the surviving births added during the interval.
Similarly, initial 10–19 residents become 20–29. In A, that bin contains 90 × 0.90 = 81 per category. In B, the same 81 survivors are joined by 20 endpoint arrivals, producing 101. The extra 20 are supplied by migration; they are not evidence that survival exceeded 100%.
The open-ended 50+ bin needs two contributions: 60 × 0.90 = 54 survivors from 40–49, plus 100 × 0.80 = 80 survivors already 50+. Its projected total is 134 per category in both scenarios. Omitting either group loses people; advancing the entire old 50+ bin out of the population would invent an age boundary.
The same total can hide different age structures
Scenario A has 520 residents per category, or 1,040 overall. Scenario B also has 520 per category: 20 fewer newborn survivors are offset by 20 more arrivals. Both populations grow 4% from the original 1,000, but B contains fewer young children and more residents aged 20–29.
For the same stipulated service that enrolls every resident aged 0–9, A implies 160 enrollees and B implies 120. Equal total growth therefore does not imply equal demand for an age-specific service. Actual use would require assumptions about eligibility and participation; the count alone supplies only the relevant age population.
The broad 50+ bin also illustrates a plotting trap. It covers more possible ages than any ten-year bin. Its greater width does not mean a single birth cohort was larger or that each individual is more likely to survive. A count pyramid combines the history of multiple demographic components.
Use demographic theories as models of change
The conventional demographic-transition model describes a shift from high birth and death rates toward lower rates: mortality falls while births remain relatively high, growth accelerates, and later fertility decline narrows the birth–death gap. Low birth and death rates form a further phase. The key comparison is the gap between rates, not whether one rate falls in isolation.3
If annual births fall from 40 to 30 per 1,000 while deaths fall from 35 to 10 per 1,000, natural increase rises from 5 to 20 per 1,000. Fewer births per resident can coexist with faster natural growth. The model offers a pattern to test; it does not supply a universal timetable, establish an inevitable next phase, or rank cultures. Migration can also alter total growth independently of that birth–death gap.
Malthusian theory emphasizes potential tension between population growth and subsistence. Malthus contrasted unchecked multiplicative population growth with additive growth in food supply. Preventive checks restrain reproduction; positive checks restrain population through increased mortality. Here positive identifies the type of check, not a beneficial outcome.4
To evaluate such an argument, inspect its growth assumptions. An original model starting with 100 people and food for 100, multiplying population by 1.5 each interval while adding food for 40, gives 150 versus 140 after one interval and 225 versus 180 after two. The projected shortfall follows those rules. It does not prove that food production, fertility, distribution, or mortality must follow them in every actual population.
Keep the initial population, transition rules, and interpretation separate. Cohort arithmetic states what follows from supplied assumptions. Evidence is needed to decide whether those assumptions describe the setting and how well the proposed demographic explanation fits.
ACTIVE PRACTICE · POPULATION REASONING
Keep the Total, Change the Age Structure
Begin with the original 1,000-person population and the passage’s ten-year survival assumptions. The simplified data have identical counts for the two recorded categories F and M. The projected per-category age counts, excluding births and migration, are 0, 90, 81, 72, 63, and 134.
Projected total: people (initially 1,000). Residents aged 0–9:; residents aged 20–29:. Each side has the same counts by construction.
Scenario A: 1,040 total, 160 young children. Scenario B: also 1,040 total, but 120 young children and 202 residents aged 20–29.
The 50+ interval is open-ended, not a ten-year cohort. Newborns are survivors at the endpoint; arrivals occur at the endpoint, so neither receives another survival adjustment. Population totals do not establish actual service use.
Check your reasoning
Choose an answer before opening its feedback. Each option explains the reasoning behind that choice.
Check 1
A population has 120 people aged 10–19 at the start of a ten-year projection. Exactly 85% survive; none migrates. What contribution does this initial cohort make to the projected population at the endpoint?
A. 102 people in the 20–29 age group.
Correct. The survivors total 120 × 0.85 = 102, and each is ten years older. They contribute to 20–29, not the row with their starting ages.
B. 102 people in the 10–19 age group.
Review this choice. The survival calculation is correct, but the cohort ages during the projection. The endpoint 10–19 group comes from younger residents and any applicable migration.
C. 120 people in the 20–29 age group.
Review this choice. The destination age group is correct, but the calculation ignores 15% mortality. Only 102 of the initial 120 survive.
D. 18 people in the 20–29 age group.
Review this choice. Eighteen is the number who do not survive: 120 × 0.15. The projected cohort contains the 102 survivors.
The principle to carry forward
Follow the same people to their new ages, applying survival before interpreting the endpoint row.
Check 2
Two ten-year projections start with the same population and use identical survival assumptions. Relative to A, projection B has 40 fewer surviving newborns and 40 additional net migrants aged 30–39 who arrive at the endpoint. No other input differs. Which comparison follows?
A. B has fewer people overall because fewer births necessarily mean lower total growth.
Review this choice. The 40 fewer newborn survivors are exactly offset by 40 endpoint migrants. Births alone do not determine the total when migration differs.
B. The totals match, but B has fewer children and more people aged 30–39.
Correct. The net difference in total population is −40 + 40 = 0. The age distribution still changes because the two adjustments enter different bins.
C. The totals and all age-group counts match because the two changes cancel.
Review this choice. They cancel only in the total. Fewer newborn survivors change the youngest group; the added migrants change the 30–39 group.
D. B has more people overall because migration does not enter the age-structure calculation.
Review this choice. Migration contributes to both the total and the migrants' endpoint age groups. Here the added migrants offset the reduced newborn survivors rather than increasing the total above A.
The principle to carry forward
Offsetting components can preserve population size while changing its composition.
Check 3
In two successive observations, a population's annual birth rate changes from 42 to 35 per 1,000 and its death rate from 37 to 12 per 1,000. Migration is zero. Which conclusion is warranted without assuming the later course of the rates?
A. Natural increase shrank, and lower fertility establishes that the population entered numerical decline.
Review this choice. The birth–death gap grew from 42 − 37 = 5 to 35 − 12 = 23 per 1,000. Births still exceed deaths, so the data do not show natural decline.
B. Natural increase grew, and the transition model fixes the date when births will next fall below deaths.
Review this choice. The gap did grow, but a general model supplies no date or guarantee that the rates will cross. Additional assumptions would be required.
C. Natural increase grew, but these observations do not determine the subsequent path of birth rates.
Correct. The gap rises from 5 to 23 per 1,000 because mortality falls more than births do. This is consistent with a transition pattern, while future rates remain unspecified.
D. Natural increase stayed constant, because both the birth rate and the death rate moved downward.
Review this choice. The directions alone do not determine their difference. Births fell by 7 per 1,000 and deaths by 25, so natural increase grew by 18 per 1,000.
The principle to carry forward
Compare the rate difference numerically, then keep the observed interval distinct from an assumed future.
Continue learning
Related lessons
- Fertility and mortality: make the denominator match
- Migration, population change, and immigration status
Browse psychology & sociology · MCAT content library
MCAT preparation and roadmap · Aim High, Score Higher
Sources
2. Office for National Statistics: National Population Projection Methodology
3. OpenStax: Demography and Population
4. Thomas Malthus: An Essay on the Principle of Population (1798)