What you will learn
- Identify a denominator and time period.
- Distinguish average, median, and percentage-point change.
- Rewrite a numerical claim with its important limitations.
Ask what was counted
A number is an answer to a particular counting question. Before deciding whether it is impressive, recover that question. Who was included, what qualified as an event, over what period, and who collected the information? A shop reporting thirty complaints has told you little about service quality until you know whether it served one hundred customers or ten thousand. The count may also include repeat complaints from the same person.
Suppose two workshops report eight and twelve successful participants. If their class sizes were ten and forty, the success rates are eighty percent and thirty percent. Even then, ask whether success meant attendance, passing a test, or finding a job. Changing the definition can change the apparent winner without changing anyone’s experience.
Rebuild the comparison
A price moving from fifty to sixty rises by ten units, or twenty percent of its original price. A price moving back from sixty to fifty falls by about sixteen point seven percent. Percentage changes depend on the starting value. If a completion rate rises from forty to fifty percent, it increases by ten percentage points, or twenty-five percent relative to the original rate. These are different descriptions of the same change.
When reading a graph, inspect the vertical scale, the beginning and end dates, and whether equal distances represent equal quantities. A cropped axis can make a small movement look dramatic. That does not automatically make a chart dishonest; it means the visual impression needs a numerical check.
Look beneath the average
Imagine five delivery times: two, three, three, four, and eighteen days. Their mean is six days, while their median, the middle observation after sorting, is three days. Neither figure tells the whole story. The mean includes the effect of the very late delivery; the median describes the central observation. Someone promising a delivery date should also care about the risk of a long delay.
Ask about the spread and relevant subgroups. An overall satisfaction score can improve because the business served more easy cases, even if service within each case type did not improve. Compare like with like before treating a higher average as evidence of better performance.
Match the claim to the evidence
A survey of volunteers describes the people who answered, not automatically everyone who could have answered. A relationship between study time and scores does not alone prove that additional hours caused higher scores; prior preparation and support could matter too. Uncertainty is a reason to narrow a conclusion, not to dismiss every number.
Use a measured sentence: “Among the people who responded during this month, this outcome was reported; we do not yet know whether nonrespondents had the same experience.” Then decide whether the remaining uncertainty changes your action. A rough count may suffice for ordering chairs, while an expensive commitment deserves stronger evidence.
A fictional training comparison
Maya, a warehouse assistant, sees two evening courses advertising successful graduates. One reports forty graduates and another twenty. She asks for class size, completion definition, and the period covered. The first total spans four years; the second covers one year. Neither provider tracks all graduates’ employment.
Maya creates a table with comparable information and leaves missing cells blank. She chooses to attend introductory sessions before paying. Her improvement is not discovering a universally best school; it is refusing to let incomparable totals make the decision for her.
Audit one numerical claim
- Copy a real numerical claim without personal information.
- Record population, period, unit, denominator, and source.
- Recalculate one comparison and write two plausible alternative explanations.
- Rewrite the claim so that its scope is visible.
Further reading
- ONS: Employee earnings in the UK, definitionsThe definitions distinguish median earnings from the mean. All numerical examples in this lesson are invented.