A small neighborhood newsletter can make a large claim by choosing a familiar word. Support rose from 20% to 25%, the draft says, then calls that five percent more support. The subtraction is visible, but the description changes what has been calculated. Here is a wholly fictional pair of 200-person tallies, with invented counts and no claim about an actual neighborhood, survey method or trend. The aim is to write the arithmetic honestly before putting it in a headline.
| Fictional comparison | Calculation | Accurate description |
|---|---|---|
| 40/200 → 50/200 | 20% → 25%; 25 − 20 = 5 | Five percentage points higher |
| Relative change in share | (25 − 20) / 20 = 0.25 | 25% relative increase from the 20% starting share |
| A different, five-percent increase | 40 × 1.05 = 42; 42/200 = 21% | 20% → 21%, not 20% → 25% |
Write the counts before the percentages
In the first invented tally, 40 of 200 responses choose option A. Forty divided by 200 is 0.20, or 20%. In the second, 50 of 200 choose it: 50 divided by 200 is 0.25, or 25%. Both denominators are declared to be 200 for this example. Nothing establishes who those fictional respondents are or whether the two groups are comparable.
Keeping the counts visible exposes the scale: the second tally contains ten more responses for option A. That observation is different from saying ten additional residents changed their minds. The example supplies no identities, repeated respondents or follow-up observations that would justify that story. Equal group size is not evidence that the same people were asked.
Subtract the two percentages
The Office for National Statistics defines a percentage point as the difference between percentages. Following that distinction, 25% minus 20% is an increase of five percentage points. The unit tells a reader that the subtraction concerns two proportions. It should not be shortened to five percent more as though the words were interchangeable.
A careful sentence for these invented figures is: The share choosing option A is five percentage points higher in the second tally, moving from 20% to 25%. That wording preserves the two endpoints. It does not decide whether the difference is meaningful beyond this teaching example or explain why it occurred.
Ask what the relative change uses as its base
Relative increase answers another question: how large is the difference compared with the original amount? For the shares here, the calculation is (25 − 20) ÷ 20 = 0.25, or 25%. For the fictional counts, it is (50 − 40) ÷ 40 = 0.25 as well. The results agree because both tallies were given the same denominator.
A 25% relative increase is therefore compatible with a five-percentage-point increase in this example. Neither number is a more impressive version to choose for effect. They describe different relationships. Name the starting point when using the relative figure so readers can see what is being treated as the base.
Notice what a five-percent relative increase would produce
Starting from 40, a five-percent relative increase adds two, giving 42. With a denominator of 200, that would be 21%, not 25%. Starting from the 20% share directly gives the same result: 20% multiplied by 1.05 is 21%. This counterexample makes the wording problem concrete without borrowing a real poll.
The table keeps all three descriptions together. A printer, chart template or newsletter subscription cannot correct the unit for you. Before paying to reproduce the summary, compare the proposed wording with the actual operation: subtraction of proportions or division by a starting value. A tidy graphic can make a mislabeled calculation easier to repeat.
Keep arithmetic separate from a claim about the neighborhood
A defensible teaching headline would be: In this fictional example, option A moves from 20% to 25%—five percentage points. A real newsletter would need the actual source, dates, question, population and method before deciding what its headline can establish. The arithmetic alone supplies no sampling assessment, uncertainty test or causal explanation.
Do not repair an uncertain real comparison merely by changing percent to percentage points. Correct units are necessary for the numerical statement, but they do not make two unrelated questions or differently defined groups comparable. Keep that further enquiry visible. This example is complete when the reader can distinguish the calculations, not when a fictional neighborhood has been made to demonstrate growth.
Sources & further reading
Published sources for the details and examples discussed in this story.
