Week 15 — A Rate Is Not a Count: Reading Fertility, Momentum, and Population Change — Traditional alternative (no AI)

Instructors: publish this instead of the adaptive version if you prefer, and unpublish or delete the adaptive one.

Assignment 14 of the term — read the world's fertility figure and three illustrative population cases, work out what they say, choose the right course tool for a population question, and explain to someone outside sociology why a falling birth rate does not mean a shrinking population.

This week you learned how demography reads births, deaths, and moves, how the total fertility rate is built from age-specific birth rates, why a falling rate can still come with more births, how the demographic transition models population change, and how cities and social movements change a society. In Week 1 you learned to compare places by rate rather than by count, and in Week 2 you learned to read any statistic four ways; this week you use those habits on population. In this assignment you work four short problems, interpret each one, choose the right course tool for a population question, and explain a finding to someone who has never studied sociology. This week's lecture tutorial, quiz, discussion, and Sociology in Action Workshop practice the same ideas from other angles.

The task

You will use these figures, the first from this week's chapter and the rest invented for this assignment:

• Our World in Data's presentation of the United Nations World Population Prospects: the global total fertility rate was 2.3 children per woman in 2023, against 4.9 in the 1950s. The total fertility rate is the average number of children a woman would have at the current age-specific birth rates; it is a rate, not a count of children.
• An illustrative country (invented for this assignment): its age-specific birth rates for seven five-year age groups, ages 15 to 49, are 10, 60, 110, 90, 50, 20, and 10 births per 1,000 women a year.
• An illustrative country (invented for this assignment): in the first year, 60,000 women are in their childbearing years and have births at 110 per 1,000 women; 20 years later, 90,000 women are in their childbearing years and have births at 80 per 1,000 women.
• An illustrative town (invented for this assignment): 45,000 people, with 1,080 births and 405 deaths in one year.

Work these four problems, showing your arithmetic:

1. The global total fertility rate was 4.9 children per woman in the 1950s and 2.3 in 2023. By how many children per woman did it fall?
2. An illustrative country's age-specific birth rates for seven five-year age groups are 10, 60, 110, 90, 50, 20, and 10 births per 1,000 women a year. What is its total fertility rate, in children per woman?
3. In an illustrative country, 60,000 women have births at 110 per 1,000 women in the first year, and 20 years later 90,000 women have births at 80 per 1,000 women. How many more births are there in the later year?
4. An illustrative town of 45,000 people records 1,080 births and 405 deaths in one year. What is its natural increase per 1,000 people?

Beside each answer, add one brief interpretation of what that value shows and one limit of it. For problem 1, say what the total fertility rate measures and over whom, say whether the figures show a correlation, a cause, or neither, and explain why the fall does not by itself show that the world's population is shrinking. For problem 2, explain why the result is a synthetic rate that describes no real woman's children, and say what it cannot tell you. For problem 3, name the idea that explains why births rose while the rate fell. Then answer a classmate who asks, "Will this country's population shrink because its birth rate fell?": choose the course tool that fits best (the four data questions, population momentum, the demographic transition model, or one of the three perspectives), justify the choice from the case, and explain why one plausible alternative tool fits less well. For problem 4, explain what natural increase leaves out, and why the town could still shrink or grow faster because of migration.

Explain it to a non-expert

Your neighbor has never studied sociology and reads a headline: "Birth rates have collapsed: the world's population is about to shrink." She asks whether that is true. Write a 3–5 sentence message to your neighbor that explains in everyday words what the total fertility rate counts and does not count, says the world's rate fell from 4.9 in the 1950s to 2.3 in 2023, explains in plain words why a falling rate can still come with more births, notes that the figure describes the fall without explaining it, and names one limit of the figure. Explain any technical term in everyday words. More than one accurate message can be defensible.

For a different, ungraded example, imagine a friend who hears that each customer at a neighborhood café now orders fewer drinks per visit and asks whether the café must be selling fewer drinks. Model answer: "Not necessarily. Drinks per customer is an average for each visitor, not the café's total. If many more customers come in, the café can sell more drinks in all even while each one orders fewer. The limit is that the average alone cannot tell you how many customers came, so you need the count too."

Use that pattern for your message to your neighbor, with your own explanation and evidence.

Show your arithmetic. A reader should be able to reproduce every number you report from the values above without guessing which values or steps you used.

After this assignment

This is the last assignment of the course. Next comes the finals week, which carries the final exam. The final's study guide, its exam-prep tutorial, and the Final Practice Exam help you prepare. The choose-the-tool step in problem 3 is the same move the final asks of you: read a question, pick the course idea that fits, and say why another one fits less well.

Deliverables

Submit a single data-reading report containing:

• the four answers, each with the arithmetic shown and a brief interpretation of what that value shows and one limit of it;
• your choice of course tool for the classmate's question, with its justification and the alternative that fits less well;
• your message to your neighbor, explaining what the total fertility rate counts, giving the 4.9 and 2.3 figures, explaining why a falling rate can still come with more births, noting that the figure describes the fall without explaining it, and naming one limit; and
• a one-line restatement of the values you used, so your results are reproducible.

Keep it to roughly one page. Clear and correct beats long.

Choose how you show it. Present your report as written text, or as a recorded audio or video explanation of about three minutes with a transcript, or as a labelled diagram of the population figures with a short note. Every form is graded by the same scoring criteria. Submit in any accessible file type or as a link; a recorded response may be submitted as audio or video with a transcript, or as text.

How you'll be graded

The full analytic rubric is attached to this assignment in Canvas.

Academic integrity and AI use

This version is designed to be completed without AI: do the computations, the interpretations, and the writing yourself, without any AI tool. You may use a calculator or a spreadsheet for the arithmetic. Submitting AI-generated work as your own, or copying another student's numbers, is an integrity violation under the course policy.

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