How Not to Be Wrong

Jordan Ellenberg presents mathematics as a way to examine everyday arguments. The publisher's description emphasizes interpretation rather than a list of calculation rules. The following Nuxflo example explores how a correct number can support a misleading comparison.

Two ways to describe the same change

A club's attendance rises from 20 people to 30. That is an increase of 10 people, or 50% of the starting attendance. Another club rises from 200 to 230, an increase of 30 people or 15%. Which grew more?

Both answers can be correct under different definitions. The first grew faster relative to its starting size; the second added more people. A headline that says only “Club A grew more than Club B” leaves the measure unstated. Before accepting the comparison, decide whether the question concerns growth rate, extra seats needed, or total reach.

Check what happens when the direction reverses

If the first club falls from 30 back to 20, the decrease is about 33%, not 50%. The denominator is now 30. A 50% increase followed by a 50% decrease would leave 15 people, below the starting 20.

Try another pair yourself: a workshop grows from 40 to 50 registrations and then returns to 40. The increase is 25%; the decrease is 20%. Writing the starting and ending counts beside each percentage makes the asymmetry visible without advanced mathematics.

Ask whether a straight-line story is justified

Two observations also do not establish a lasting trend. If attendance rose by ten this month, adding ten every month forever may soon exceed the room's capacity. There may be seasonal effects, repeat visitors, or a one-time event. The arithmetic of a projection can be flawless while its assumptions are implausible.

Choose this book when you enjoy following a mathematical idea through several settings. Use it to ask better questions about definitions and assumptions, not to treat calculation as a substitute for understanding where the data came from. For a closer look at survey selection, read Naked Statistics.