Percentages, rates and denominators
Interpret changes accurately by checking the base quantity and comparison.
What you will learn
- Distinguish percentage points from percentage change.
- Identify the relevant denominator.
- Translate a rate into an absolute count.
A percentage is meaningful only when its denominator is clear. A movement from 20% to 25% is five percentage points but a 25% relative increase. Both statements are correct, but they answer different questions.
Core method
A percentage is meaningful only when its denominator is clear. A movement from 20% to 25% is five percentage points but a 25% relative increase. Both statements are correct, but they answer different questions.
- Define the exact decision or claim before analysing detail.
- Use evidence that is relevant to the stated context.
- Record uncertainty instead of replacing it with confident wording.
Applied case
A course completion rate rises from 60% of 100 learners to 66% of 50 learners. The percentage increased, while the number completing fell from 60 to 33.
Apply the method
Write a one-sentence comparison that communicates both the rate and the absolute number without misleading the reader.
Review answer guidance
The completion rate rose by six percentage points, from 60% to 66%, but the smaller cohort meant that 33 learners completed compared with 60 previously.
Use in an assessment
Apply the method to the information provided in the task. A strong response makes its reasoning traceable and does not rely on specialist facts that are absent from the evidence.
- Read the requested outcome and constraints first.
- Eliminate responses that exceed the available evidence.
- Review whether the conclusion answers the precise question.