06 / 12 · Read a set of numbers
From 20% to 30%: what actually changed?
Separate percentage points, relative change, and a combined rate.
Builds on Same average, different experience
Go to practice ↓A question to keep in mind
A completion rate goes from 20% to 30%. Did it rise by 10% or 50%?
It rose by 10 percentage points, or by 50% relative to the starting rate. Picture two groups of 100 people: 20 finish in the first, 30 in the second. That is 10 more per 100; compared with the original 20, the extra 10 is half as many again.
Percentage points come from subtraction: 30 - 20 = 10. Relative growth also divides by the starting value: (30 - 20) / 20 = 50%. Both descriptions are correct when their units are stated. A relative increase of 10% from 20% would give 22%, not 30%.
A second trap appears when groups differ in size. Add the actual counts before calculating a combined rate. A class of 10 and a class of 90 should not receive equal weight just because each has one reported percentage.
Work through an example
- Difference in rates: 30 - 20 = 10 percentage points.
- Relative increase: 10 / 20 = 0.5 = 50%.
- A precise sentence: 'From 20% to 30%, up 10 percentage points, or 50% relative to the starting rate.'
Your turn
0 / 3A rate rises from 20% to 30%. Fill in both kinds of change.
Read solution · does not award completion
- Percentage-point increase: 10 points
- Relative increase: 50 %
It rises by 10 percentage points and by 50% relative to the starting rate.
A class of 10 has 9 passes. A class of 90 has 45 passes. What are the combined passes, total students, and pass percentage?
Read solution · does not award completion
- Total passes: 54
- Total students: 100
- Combined pass rate: 54 %
There are 54 passes among 100 students, so the rate is 54%, not the simple average of 90% and 50%.
A score goes from 40 to 60. Which sentence is precise?
Read solution · does not award completion
It increased by 20 score points, which is 50% of the starting score.
60 - 40 = 20 score points; 20/40 = 50%. A score point and a percentage point are not interchangeable units.
Apply this lesson to an AI answer · synthetic teaching example
A polished answer gets the percentage wrong
In this synthetic example, a task completion rate rises from 20% to 30%. An assistant writes:
The completion rate increased by 10%, so the improvement was small.
Which change is 10, and what does the size tell us?
Think first, then inspect the reasoning
- Subtract the rates: 30% − 20% = 10 percentage points.
- Relative to the starting rate, (30% − 20%) ÷ 20% = 50% growth.
- Neither number tells us the practical importance or cause on its own. Check group sizes, costs and how the comparison was made.
A conclusion supported by the information
The completion rate rose by 10 percentage points, a 50% relative increase. Its practical importance needs more context.
Check every reported increase against its baseline. A high writing-quality score does not verify arithmetic.
See the executed checker caseBring it back to your own work
Choose two percentages and describe their difference both in percentage points and relative to the starting rate.
Statistical literacy: directory, audit and transfer assessment
How do I retain independent judgment when using AI here?
Keep your own answer before consulting an AI candidate. Check sources, calculations, inference and conditions; explain adoption or rejection. Then solve a new-context task independently and apply the checks to this lesson.
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