Percentages, rates and denominators
Interpret changes accurately by checking the base quantity and comparison.
Covered in this guide
- 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.
Always ask ‘percent of what?’
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.
A 50% rise from a tiny base
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.
Try this
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.
How quantitative items trap you
Write the numerator, the denominator and the time window. Options that drop the base or mix rates are usually wrong.