Back to the on-screen lesson ·
Data and maps make choices about people: undercounts shift seats and money, framing can stigmatize, and precise locations can expose; adjusting and protecting are part of the work.
Paper packet. Every task here also exists on screen, where it is checked automatically; answers written on paper are not assessed by Nydus. When you are back at a device, enter your answers there.
By the end of this lesson you will be able to measure an undercount, estimate a true population, and judge a map by whom it counts, how it frames and what it reveals.
You have made and read maps, measured with layers, and weighed samples and outliers. This last lesson asks who the data is about, and what the choices made in collecting and mapping it do to them.
| Term | What it means |
|---|---|
| Undercount | People a count misses; the net undercount is those missed less those counted twice. |
| Coverage | The share of a population a count or survey reaches. |
| Apportionment | Dividing the seats in the House of Representatives among the states by population. |
| Aggregation | Reporting data for areas rather than individuals, to protect privacy. |
| Informed consent | Agreement to take part, given with an understanding of what the data will be used for. |
| Redlining | Marking neighborhoods as risky for lending, historically by their residents' race. |
Every data set and map makes choices about the people it describes.
Another way: picture
Picture a class photo where the photographer only waited for the students already standing in front. The quiet kids at the back, the ones who arrived late, and the ones who were absent never appear. Years later, the photo is all anyone has of that class, and it tells the story of only some of them.
Another way: steps
Design starts with the audience and question. Label the mapped quantity and unit, specify the reporting period, and show class breaks without ambiguous endpoints. Distinguish zero, missing and suppressed data. Use labels or patterns as well as color so the main comparison remains readable without red-green discrimination. Check text at the intended print or screen size. Include a suitable scale representation and orientation where needed, plus source organization, dataset edition, collection date, CRS and relevant processing notes. A resized scale bar stays meaningful only when resized consistently with the map; a copied numeric scale may become wrong.
Ethical communication also asks whose experience is excluded. An address can identify a household even after removing a name. Before release, assess whether small cells or combinations of maps reveal individuals. Aggregate, suppress or restrict access when appropriate, explain the loss of detail, and seek informed community input. Do not invent consent or present a technical map as community approval. A well-labeled uncertain result is more useful than a precise-looking claim that its data cannot support.
Investigate a local question such as access to public drinking fountains or the distribution of shade near public walking routes. Use public nonpersonal data with appropriate reuse permission, or construct and label a fictional study area. Define your population, time period, audience and a measurable claim before opening the tools. Choose at least one vector layer with attributes and one raster layer. Explain why these representations fit the question, inspect provenance and accuracy, and select a suitable analysis CRS. Keep the original data and a source inventory.
Create a GIS project in software available to you. Import the layers, verify positions against independent reference features, transform working copies where necessary, and inspect attributes for missing or duplicate keys. Join a relevant attribute table, then perform a justified buffer or network operation and an overlay. Explain why the operation answers your question and what it excludes. If a network is unavailable, limit the claim to proximity; do not rename a circle a walking-time service area. If your question requires an interpolated surface, document observations and validation; otherwise explain why interpolation would add unsupported assumptions.
Save the project, derived layers and a reproducible processing log naming inputs, settings, software version and outputs. Include at least one independent validation check, such as withheld observations or reference locations, and report disagreements. Repeat the analysis with a different resolution or boundary definition, keeping other choices fixed. Compare both the values and the decision. Create a readable map with scale, legend, units, dates, source metadata and a text alternative that communicates the main evidence. Write a short argument connecting the result to the question, considering an alternative interpretation and discussing privacy, omissions and uncertainty. Submit the project, data inventory, log, validation table, sensitivity comparison, map and argument. A map image alone is insufficient.
This investigation requires a human reviewer to inspect the files and the reasoning. For each criterion award 0 for absent or misleading work, 1 for partial work with a consequential unresolved weakness, or 2 when the specified evidence is present and defensible.
| Criterion | Evidence for 2 points |
|---|---|
| Question and data fitness | Defines place, population, period and claim; justifies vector, raster and attributes using provenance, resolution and positional accuracy. |
| Reference systems and operations | Shows an appropriate CRS, verifies alignment, checks join keys and explains correct spatial operations and their assumptions. |
| Reproducibility | Another reviewer can reopen the project and rerun the recorded inputs, transformations and settings to recover the submitted result. |
| Validation and sensitivity | Uses a genuinely separate reference check, reports discrepancies and compares a controlled resolution or boundary change. |
| Communication and ethics | Supplies readable scale, legend, units, sources and a text alternative; identifies omissions, privacy risks and affected groups without claiming unverified consent. |
| Interpretation | Connects evidence to the question, considers an alternative and limits the conclusion to the data and robustness demonstrated. |
The proposed completion criterion is at least 10 of 12 points, with no zero and full marks for reference systems and operations, reproducibility, and communication and ethics. Revise a misleading spatial claim or unsafe disclosure before acceptance. Ask a reviewer to inspect your project, data inventory, processing log, validation results, map and interpretation. Demonstrate a GIS operation or help the reviewer reproduce a recorded step. Ask for criterion scores, reasons and specific revision requests, then revise your work using that feedback. Automated quizzes do not assess this project.
The Constitution requires a count of everyone in the United States every ten years. The count decides how the 435 seats in the House are divided among the states, guides how districts are drawn, and steers hundreds of billions of federal dollars a year.
No count is perfect. The Census Bureau checks each one with a follow-up survey and publishes estimates of who was missed and who was counted twice.
The Bureau's review of the 2020 census estimated that it missed about 3.3 percent of Black residents and nearly 5 percent of Hispanic residents, and counted young children poorly, while it overcounted non-Hispanic White residents by about 1.6 percent.
The total came out close, but the shares did not. When some groups are missed and others double-counted, places where the missed groups live lose their fair share of seats and funding.
If a count reached only a share of a group, the estimated true size is the count divided by that share. A count of $900$ young children with a ten percent miss suggests about $900 \div 0.9 = 1000$.
Adding ten percent of the count instead, $990$, falls short, because the ten percent is of the true size, not of the count.
After the 2020 census an average House district held about 761,000 people. The last seats are decided by thin margins: the Census Bureau noted that New York would have kept a seat it lost with 89 more people counted.
Funding works the same way at smaller scales. Programs for schools, roads, health care and housing use census counts for a decade, so each person missed can cost a community for ten years.
A map is an argument. Shading a neighborhood in alarming red, labeling it by its problems, or choosing class breaks that make a small difference look large can shape how outsiders see it, and how lenders, insurers and officials treat it.
The same data mapped with neutral colors and honest breaks, and with the neighborhood's assets shown too, tells a different story.
Location data can identify people. A map of individual homes with a sensitive attribute, such as an illness or immigration status, can expose the people in them even without names. Phone location records can reveal where someone sleeps, works and worships.
Agencies protect people by aggregating to areas, suppressing counts that are too small, and adding careful statistical noise, as the Census Bureau began doing for its 2020 data.
Maps made from outside can miss what residents know: a path everyone uses, a sacred site, a flood that never made the records. Participatory mapping invites the people of a place to draw and correct the map themselves.
Tribal nations, for example, have mapped their own lands and place names, restoring knowledge that official maps left out or renamed.
Checking an answer. An adjusted count is always larger than the count. An undercount rate divides by the true population, so it is a little smaller than the miss divided by the count.
Dividing the count by the share counted is allowed because the count equals the true size times that share. Dividing the miss by the true population is allowed because a rate describes the share of everyone, counted or not.
Asking who made a map is allowed, and necessary, because every map selects: no map can show everything.
The same tools that can harm can also reveal harm. Overlaying pollution sources, tree canopy, heat and income has shown cities where to plant trees, where to enforce clean air rules and where to invest.
The difference lies in who asks the questions, who is included in the answers, and whether the people described have a say in what is done.
For the 2020 census, the Census Bureau adopted a method called differential privacy. It adds carefully measured random noise to published counts, so that no one can work backward from the tables to identify a person, while totals for states and large areas stay accurate.
The noise matters most for small places. A census block of a dozen people may be published with a count a few people off, which can confuse a small town's planning or a study of a rural community. Supporters point to the real risk that detailed tables could be matched with commercial data to reveal individuals; critics point to the harm of inaccurate small-area counts. The debate shows that privacy and accuracy are both values, and protecting one can cost the other.
The most common slip is dividing the miss by the count rather than the true size. Another is adding the undercount percent of the count instead of dividing by the share counted.
A third is treating a map as a neutral photograph. A fourth is publishing precise locations of vulnerable people because the data happened to be available.
Every lesson in this course has been about choices: scale, projection, classes, layers, resolution, samples. This one adds the question that runs under all of them: who does the choice serve, and who does it leave out?
In the 1930s, the federal Home Owners' Loan Corporation graded neighborhoods in hundreds of American cities for mortgage lending, coloring the safest green and the riskiest red. Neighborhoods where Black residents and immigrants lived were marked red, often regardless of the condition of their homes.
Lenders followed such grades for decades, withholding loans from red neighborhoods and deepening their decline. Researchers who have overlaid the old maps with modern data find that many formerly redlined neighborhoods still have lower home values, fewer trees and hotter summer streets.
The maps, now digitized and public, are a lesson in how a map can do more than describe a place: it can help decide what happens to it.
The 2020 census was taken during a pandemic, which closed offices and delayed door-to-door visits, and after a fierce debate over a proposed citizenship question that the Supreme Court blocked. Many communities worried their residents would not respond.
Cities, states and nonprofits ran outreach through churches, schools and local radio. Afterward, the Bureau's follow-up survey found that the total was close but that Black and Hispanic residents and young children had been undercounted, and some groups overcounted, a pattern seen in earlier censuses too.
Those estimates are used to plan the next count, and a few states gained or lost a House seat by margins far smaller than the undercounts, which is why counting everyone is a question of fairness, not only of arithmetic.
It is natural to think of data and maps as simply recording what is there, so that arguing with them is arguing with facts. But people decide what to count, whom to reach, how to group and how to color, and each decision can favor some and harm others.
Treating a map as a choice, not a mirror, is what lets a reader ask who made it, who is missing, and whom it serves.
A survey estimates $1000$ residents; the census counted $950$. Find the miss.
$1000 - 950 = 50$
People missed.
Divide by the true population.
$50 \div 1000 = 0.05$
A share of everyone.
Convert to a percent.
$5\%$
The undercount rate.
Name the slip of dividing by the count.
$50 \div 950 \approx 5.26\%$
The wrong whole.
A count found $1900$ renters and missed about $5$ percent. Find the share counted.
$1 - 0.05 = 0.95$
Ninety-five percent reached.
Divide the count by the share.
$1900 \div 0.95 = 2000$
The estimated true size.
Find the people missed.
$2000 - 1900 = 100$
Renters not counted.
Name the slip of adding five percent.
$1900 \times 1.05 = 1995$
Five short.
Say why renters are missed.
$\text{they move more often}$
And share homes.
Suppose a county gets $1500$ dollars per resident a year and its count missed $2000$ people. Find one year's loss.
$1500 \times 2000 = 3000000$
Dollars.
Multiply by the years.
$3000000 \times 10 = 30000000$
Until the next census.
Express it in millions.
$30\ \text{million dollars}$
Over a decade.
Say where it would have gone.
$\text{schools, roads, clinics}$
Programs using the count.
Say how counties respond.
$\text{outreach before census day}$
Trusted local messengers.
Say what a county can do after.
$\text{challenge the count}$
Through the Bureau's review.
Find the true population.
$4800 + 200 = 5000$
Everyone.
Divide the miss by it.
$200 \div 5000 = 4\%$
The undercount rate.
Find the percent counted.
A follow-up survey estimates that a neighborhood has $800$ residents, but the census counted $776$. What percent of residents did the census miss?
Complete the worked solution: a town's census counted $48000$ residents, and a follow-up survey estimates it missed $2000$. Find the true population, the percent missed and the percent counted.
Find the true population.
$\text{counted} + \text{missed} =$ t
Everyone who lives there.
Find the percent missed.
$\text{missed} \div \text{true} \times \text{a hundred} =$ p
The undercount rate.
Find the percent counted.
$\text{a hundred} - \text{percent missed} =$ q
The coverage.
Say who is missed most often.
$\text{young children, renters}$
People who move or share homes.
Match each practice to the problem it guards against.
| exposing individuals through their locations | studying people who never agreed to it | a mapmaker missing what residents know | readers unable to check or date the claim | |
|---|---|---|---|---|
| reporting counts by census tract, not by address | ||||
| asking people before recording where they live | ||||
| showing a draft map to the neighborhood it describes | ||||
| printing the data's source and date on the map |
In a county, a census counted $900$ young children, $1900$ renters and $4800$ homeowners. Follow-up surveys suggest it missed $10$, $5$ and $4$ percent of each group. Fill in the estimated true size of each group.
| people | |
|---|---|
| young children, estimated | |
| renters, estimated | |
| homeowners, estimated |
A count misses $10$ percent of a group. Write the group's estimated true size as a function of the number counted, $x$.
Answer:
Suppose federal programs send a county about $1800$ dollars per counted resident each year, and its census count missed $250$ residents. How many dollars could the county lose over the ten years until the next census?
Answer: dollars
After the 2020 census, an average congressional district held about $761000$ people. Suppose a state's count missed $152200$ residents. What fraction of an average district is that?
Answer: districts
Mark supported audit sentences addressing disclosure, readability and interpretation limits. A fictional draft maps requests from 2 households as exact address points without names. Its red-green legend lacks labels and units; scale and source date are absent.
This task has no paper form; do it on a device.
Lesson test: one question per skill, one attempt each, no hints. Your answers are checked when you submit.
A count misses $5$ percent of a group. Write the group's estimated true size as a function of the number counted, $x$.
Answer:
You can reason about the ethics of representation. Explain how an uneven census count can shift seats and funding between places.
27. Your turn: a town counted $4800$ and missed an estimated $200$. What percent was missed?, step 3
$96\%$
The coverage.