Spotting Missing Bases

Welcome back to Percentages in News and Statistics! This is the sixth and final lesson of the course, and it brings together everything we have built so far. Over the previous five lessons, we learned how to calculate percent changes, read percentage shares, estimate real counts, compare percentages across groups of different sizes, and distinguish percentage points from relative percent change. Now we turn our attention to a problem that shows up constantly in advertising, headlines, and everyday conversation: percent claims that leave out the base. A percentage without its base is like a fraction without a denominator — it looks precise but tells us surprisingly little. By the end of this lesson, you will be able to spot these incomplete claims and explain exactly what information is needed to evaluate them.

As we explored earlier in this course, every percentage describes a share of some specific group or quantity. That group or quantity is the base. When someone says "60% of registered voters support the policy," the base is clear: registered voters. We know exactly what 60% refers to, and we could estimate a count if we knew how many registered voters there are.

But what happens when someone simply says "60% support the policy"? Now we are left guessing. Is that 60% of all adults? Of people who were surveyed? Of people in one particular city? The number sounds solid, yet without its base it could mean very different things.

This lesson is all about building the habit of pausing and asking one powerful question: percent of what? That single question is your best defense against misleading statistics.

Not every incomplete claim is missing the same thing. In practice, vague percent statements tend to fall into three categories:

1. Missing base group — The claim does not say who or what was measured. For example, "80% agree that our product is the best" does not tell us whether that 80% comes from a random sample of shoppers, the company's own customers, or the company's employees.

2. Missing comparison — The claim states a change or advantage without naming what it is measured against. For example, "Our battery lasts 50% longer" invites the question: longer than what? A competitor's battery? The brand's previous model? An industry average?

3. Missing sample size or context — The claim may hint at a group but gives no sense of how large or representative it is. The classic "9 out of 10 dentists recommend…" sounds impressive until we ask: how many dentists were surveyed, and how were they selected?

The summary below shows these three kinds of missing information and the question each one should trigger.

Recognizing which piece is absent is the first step toward deciding whether a claim deserves our trust.