Lesson preview · Models and data
Reading data and claims
~8 min · Free to read
Imagine two newspapers report the same news. One says: “Sales tax rises by just 2 points.” The other says: “Sales tax jumps 10%!” The tax, a charge added to the price of things you buy, went from 20% to 22%. Both headlines are true. Numbers rarely lie outright. People mislead with true numbers by choosing what to measure and how to say it. A few checks catch most of these tricks.
Say a phone plan goes from 20 dollars to 23 dollars a month. The price has risen by 3 dollars. As a share of the old price, that’s 3 ÷ 20 = 0.15, a 15% rise. This is the percentage change: always divide by the old value, the one you started from.
Divide the change by the starting value, then multiply by 100.
Rates need extra care, because they’re percentages already. The sales tax went from 20% to 22%. The plain gap between the two rates is 2 percentage points. As a share of where it started, the rate rose by 2 ÷ 20 = 10%. Both are true. When a headline reports a change in a rate, check which kind of change it means.
An index number compares a value with its level in a chosen base year, which counts as 100. If a price index stands at 120, prices are 20% higher than in the base year. If it then moves from 120 to 132, prices have risen by 12 ÷ 120 = 10%, not 12%. The rise in the index equals the percentage rise only when the index starts from 100.
Totals need care too. In 2024, Indonesia’s economy produced about 1.4 trillion dollars’ worth of goods and services, more than the Netherlands’ 1.2 trillion. But Indonesia had almost 16 times as many people. A country’s GDP is the value of the final goods and services it produces in a year. (Final means not used up in making something else.) Divide each country’s GDP by its population, and you get GDP per person: about 4,900 dollars in Indonesia and 67,000 in the Netherlands. Prices are lower in Indonesia, so a dollar goes further there. But even after adjusting for that, the Netherlands produced about 5 times as much per person. To compare how well off people are, use per-person figures.
Even per-person figures are averages, so they can’t show how evenly income is shared.
Key Term
Four traps in charts and claims
- A cut-off axis. If the bars start at 90 instead of 0, a gap of 2 can look enormous. Check where the axis starts.
- Picked dates. A trend can look good or bad depending on the year it starts. Ask what an earlier start would show.
- A third factor. Two things can rise together because something else drives both.
- Cause running backwards. Picture data showing that the biggest fires have the most fire engines at them. The engines don’t make the fires bigger: bigger fires get sent more engines.
The last two come down to one rule. Two things moving together (a correlation) doesn’t prove that one makes the other happen (causation): correlation is not causation.
Two of the three headlines used true numbers and still didn’t hold up. One started the clock at a spike; the other left out a third factor, income. The one that sounded like hype held up, because 4% to 5% really is a 25% rise. So checking the numbers isn’t enough: check what the headline makes them say.
Trap · Common Misconception
"A strong link must mean cause"
A strong link is still only a link. On its own, it can’t tell you whether A causes B, B causes A, or a third factor drives both. In the third headline above, internet use and long lives went together, but income could explain both. To test a cause, compare groups that are alike in every way except one. The fairest way is to sort people into the groups by lottery, so on average nothing else differs between them.
Tip
Three questions for any chart
- What exactly is measured? A total or a per-person figure? Percent or percentage points?
- What was chosen for you? Where does the axis start, and when do the figures start?
- What else could explain it? Look for a third factor, or for cause running backwards.
Check yourself · no marks
Country A has 10 million people and a GDP of 500 billion dollars. Country B has 100 million people and a GDP of 2,000 billion dollars. Which economy is bigger, and where is GDP per person higher?
Commit to one first. Guessing and being wrong beats reading the answer cold.
Practice · 1 / 6
Country A has 300 million people and Country B has 5 million. You want to know where the average person is better off. Which figure should you compare?
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