Two calculations, one common mistake. Percentage difference and percentage change look almost identical, use almost the same numbers, and give completely different answers. This page is about telling them apart in the first five seconds of a question.
📘 What you need to know
Percentage difference compares two directly comparable values that occur at the same time — for example, cases in two countries this week.
Directly comparable means the values mean the same thing. Number of cases and number of deaths are not directly comparable.
Percentage difference = difference between the two values ÷ average of the two values, × 100.
Percentage change compares two values from the same data set at different times — how something has changed.
Percentage change = change ÷ original value, × 100.
If the original number is larger, it is a percentage decrease; if smaller, a percentage increase.
Both answers are expressed as percentages.
Which one does this question want?
Read the question and ask one thing: are the two numbers separated by place or by time?
Percentage difference is symmetrical — swap the two countries and you get the same answer. Percentage change is not, because one value is the starting point.
Percentage difference
This compares two values that occur at the same time and that are directly comparable. Neither value is more “original” than the other, so neither one can be the denominator — which is why you divide by the average of the two.
Percentage difference
(difference between the two values ÷ average of the two values) × 100
Directly comparable is the phrase to watch. The number of confirmed cases and the number of deaths are two different types of value, so a percentage difference between them means nothing at all. Cases versus cases, deaths versus deaths.
WORKED EXAMPLE
In one week, Region A recorded 24 600 confirmed cases and Region B recorded 3 900. Calculate the percentage difference between them. [3]
Step 1: find the difference24 600 − 3 900 = 20 700Step 2: find the average of the two values(24 600 + 3 900) ÷ 2 = 28 500 ÷ 2 = 14 250Step 3: substitute into the formula(20 700 ÷ 14 250) × 100 = 1.4526… × 100145 % (3 s.f.)both values are cases, in the same week — that is what makes this a difference
A percentage difference over 100 % looks wrong the first time you see it, but it is perfectly normal. When one value is much larger than the other, the gap between them can easily be bigger than their average.
Percentage change
This compares two values from the same data set at different times — how a figure has changed. Here one value clearly is the starting point, so that one goes on the bottom.
Percentage change
(change ÷ original value) × 100
WORKED EXAMPLE
A region recorded 52 400 cases in March and 41 300 cases in April. Calculate the percentage change. [3]
Step 1: find the change52 400 − 41 300 = 11 100Step 2: identify the original valueMarch is the earlier month, so 52 400 is the original value.Step 3: substitute into the formula(11 100 ÷ 52 400) × 100 = 0.21183… × 10021.2 % decrease (3 s.f.)the original value was larger, so this is a decrease — you can also write it as −21.2 %
WORKED EXAMPLE
Recorded deaths rose from 1 240 in one month to 1 612 the next. Calculate the percentage change. [2]
Step 1: find the change1 612 − 1 240 = 372Step 2: divide by the original value(372 ÷ 1 240) × 100 = 0.300 × 10030.0 % increaseoriginal value is the earlier figure, 1 240 — using 1 612 gives 23.1 % and no marks
WORKED EXAMPLE
A student calculates the percentage difference between the number of cases and the number of deaths in one country. Explain why this calculation is not valid. [2]
The rule being brokenPercentage difference can only be used for values that are directly comparable, meaning they measure the same thing.Why these are notCases and deaths are two different types of value, so the result would not describe anything meaningful.Not directly comparable, so the calculation has no meaninga valid comparison here would be deaths as a percentage of cases, which is a different calculation
Getting the marks in data questions
🧩 A routine that works under time pressure
Check the two values are directly comparable. If not, stop — the question is asking something else.
Decide: separated by place (difference) or by time (change)?
Write the formula down before substituting. It is often worth a mark by itself.
Show the subtraction as a separate line so the working is visible.
Substitute, calculate, and round to the number of significant figures the question asks for — 3 s.f. if it does not say.
Add the unit (%) and, for a change, the word increase or decrease.
Almost every mark lost on these questions is a working mark, not an arithmetic one. Write the formula, write the subtraction, write the substitution. Even if your calculator lets you down, three of the marks are already safe.
💡 Exam tip
Learn which denominator goes with which calculation: average for difference, original for change.
The original value is always the earlier one in time. Read the dates carefully.
State increase or decrease. A bare number is an incomplete answer for percentage change.
Keep full accuracy in your calculator and round only at the end.
If a question gives you a table, underline the two values you are using before you start.
Percentage difference values above 100 % are normal. Do not assume you have made a mistake.
⚠ Common mix-up
Dividing by the wrong thing. This is the single biggest source of lost marks in the whole skill.
Using the new value as the original. It changes the answer completely, as the deaths example shows.
Comparing values that are not directly comparable, such as cases against deaths.
Rounding too early. Round only the final answer.
Forgetting the percent sign, or forgetting to multiply by 100 at all.
Confusing percentage change with percentage point change. A rate rising from 4 % to 6 % is a 2 percentage point rise, but a 50 % change.
That is the end of Disease & Immunity. Go back to Pathogens and work forwards through the unit without your notes — if you can get from a pathogen entering the body all the way to a memory cell and a vaccine, you have this topic.
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