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.
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- 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?
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- 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?
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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.
Bring it back to your own work
Choose two percentages and describe their difference both in percentage points and relative to the starting rate.