Percentage points versus relative percentage
Both compare percentages, but they use different calculations. Always say which one you mean.
W5's course data contain 3,059 passes among 4,108 full-time registrations (74.464%) and 429 among 557 part-time registrations (77.020%). The difference is about 2.555 percentage points, or 2.6 points rounded to one decimal.
The relative increase is (77.020-74.464)/74.464 times 100, about 3.432%. State which comparison you report. If you subtract only the already rounded 77.0 and 74.5, you get 2.5; retain raw fractions until the final rounding.
Source: W5 PDF pp. 3-51, 53. The lecture uses both a constructed 200-student support example and a synthetic 4,665-registration course dataset. They are different tables with different units.
Practice problems
Supplementary study questions on the lecture concepts — not verbatim exam questions. Each answer counts toward spaced review.
1. Conceptual understanding
Definitions and distinctions.
A rate rises from 40% to 50%. What is the percentage-point increase?
A rate rises from 40% to 50%. What is its relative increase?
2. Application
Apply the concept to a case or calculation.
A rate moves from 20% to 30%. What is the percentage-point increase?
For the same move from 20% to 30%, what is relative increase?
3. Interpretation and limitations
Evaluate assumptions and justify conclusions.
Why must a relative percentage change name a reference?
The original rate is 0%. What happens to ordinary relative percent increase?
Explain it in writing
Self-checked, not marked. Write a few sentences, then compare with the example answer. Your writing is saved as you type.
Show an example answer
Rounding each rate first can change the final displayed difference. Use the full fractions and round the final comparison once.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?
Show an example answer
It is a rise of 10 percentage points. Relative to 20%, the increase is 10/20=50%.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?