Science Puzzle
The Money Bag That Grew Too Much
A magazine runs a story about people's savings, with a picture chart. Average savings have gone up from £1,000 to £2,000, so the artist has drawn the 2025 money bag twice as tall as the 2015 one, keeping its shape the same.
The numbers are correct and the big bag really is exactly twice as tall. So what's misleading about the chart?
The Answer
To keep its shape, the bag had to get twice as wide as well as twice as tall. So it covers four times as much of the page, and the eye reads it as four times as much money.
We judge pictures by how much space they take up, not by measuring their height. Doubling both the height and the width multiplies the area by 2 × 2 = 4. You could fit four of the small bags into the outline of the big one. And because a bag looks like a solid object, it can even suggest a volume eight times bigger (2 × 2 × 2). The chart says "double" but shouts "four times" or more.
The writer Darrell Huff warned about this exact trick, with money bags, in his 1954 book How to Lie with Statistics. Later, the data designer Edward Tufte suggested measuring how much a chart exaggerates by comparing the change shown in the picture with the change in the data. Here, the picture shows a 300% increase in area for a 100% increase in savings.
There are honest ways to draw it. Use a bar chart, where only the height changes and the widths stay the same. Or, if you want pictures, show one bag for 2015 and two identical bags side by side for 2025.
The principle: Honest charts. In a picture chart, size should change in only one direction; scaling a shape in two or three dimensions exaggerates the difference it is meant to show.