Start with a question that has a denominator
Suppose one area adds 20 residents to an initial 100, while another adds 90 to an initial 900. The second adds more people; the first grows faster relative to its starting population. Neither comparison is wrong. A useful claim says which question it answers.
The live investigation uses actual published Census counts. The small examples in this explanation are fictional arithmetic practice. Do not replace the real counts with the worked examples in your report.
Read the graph before making a claim
The chart uses the same −5% to +20% horizontal scale for every selected state. A bar left of zero indicates a decline; one right of zero indicates an increase. The printed numbers and table provide the same information without requiring color interpretation. Hiding a state changes which rows contribute to the calculation; it does not alter its recorded population.
Before including all eight states, predict whether a large starting population should receive the same influence as a small one. Your answer depends on whether your question concerns the average state rate or the combined population.
Reconstruct the two calculations
For each state, let P₀ be the 2010 resident count and P₁ the 2020 resident count, both measured in people. The difference D = P₁ − P₀ is also measured in people. The percentage change is 100 × D / P₀. Read it as “divide the change by the starting population, then express the ratio per hundred.” It is a change over the decade, not an annual rate.
For the fictional 100-to-120 and 900-to-990 example:
| Comparison | Calculation | Interpretation |
|---|
| Area A | 20 / 100 × 100 = 20% | Change relative to A’s starting count |
| Area B | 90 / 900 × 100 = 10% | Change relative to B’s starting count |
| Mean area rate | (20% + 10%) / 2 = 15% | Each area receives equal influence |
| Combined rate | (20 + 90) / (100 + 900) × 100 = 11% | Starting population determines influence |
The combined rate is a weighted mean of the two rates: A receives weight 100/1,000 and B receives 900/1,000. The calculation is 0.1 × 20% + 0.9 × 10% = 11%. These are arithmetic population weights, not survey sampling weights.
When nothing is selected, the mean has no rows and the combined rate has a zero starting denominator. The correct result is undefined, not a zero-percent growth claim. The empty state is useful evidence that a calculation needs a defined comparison set.
Conduct a reproducible sensitivity check
- Write a provisional claim for Texas and Wyoming before expanding the selection.
- Include all eight states and inspect both summaries. Identify the question each answers.
- Choose one state to exclude. Explain your reason before seeing the new result; do not hunt for an exclusion that makes a preferred story appear.
- Record the new comparison and capture it with your claim. Explain whether the conclusion changed or simply the population being described.
- Download the raw CSV and your analysis JSON. Recompute a row and both summaries independently. Compare unrounded values before discussing display rounding.
An analyst can disagree with an exclusion while reproducing the arithmetic exactly. Reproducibility establishes that the procedure can be followed; it does not establish that the selection or interpretation is sound.
What the observations cannot establish
Eight deliberately selected states do not represent the United States. Their average is not a national estimate. These historical totals also do not show individual moves, motives, births, deaths or the separate contribution of domestic and international migration. A causal claim about a policy needs a comparison design and evidence beyond a before/after state total.
A census attempts a population count, but coverage and processing problems may remain. Do not attach a survey-style sampling margin of error that this table does not provide. Nor should two aggregate snapshots be read as a record of what happened to the same individuals.
The lab preserves one published historical vintage. A later estimate, correction or population definition can legitimately differ. Compare definitions and dates before treating disagreement as an arithmetic error. Resident population and the population used for congressional apportionment are related but distinct measures; this extract uses resident population.
Independent application
Create a short methods appendix with the dataset title and release, state selection, formulas, rounding rule, exported files and limits. Give a partner a fresh inclusion rule and ask them to reproduce your result without your screenshot. Then explain the unfamiliar practice case below in your own words before revealing feedback. A reproducible number and a defensible social explanation are separate achievements.
Original Census Table E · Local eight-state CSV
