IB Biology HLDisease & ImmunityPaper 1 & 2~8 min read
Evaluating COVID–19 Data
Two formulas, and they look almost identical. The only thing you have to get right is what you divide by — and that depends on whether you are comparing two groups at one moment, or one group at two moments.
📘 What you need to know
Percentage difference compares two directly comparable values that occur at the same time.
Directly comparable means the values mean the same thing. Number of cases and number of deaths are not directly comparable.
Percentage difference = the difference between two values, divided by the average of the two values, times 100.
Percentage change compares two values from the same data set at different times.
Percentage change = the change, divided by the original value, times 100.
If the original number is larger, the result is a percentage decrease. If it is smaller, it is a percentage increase.
A decrease can be written as a negative number or described in words.
Which formula does this question want?
Read the question and ask one thing: are the two numbers from two different places at one time, or from one place at two different times? That single decision picks the formula for you.
Both formulas subtract one value from the other. The only thing that changes is the denominator, so that is the part to check before you press equals.
Percentage difference
A percentage difference calculation lets you compare two directly comparable values that occur at the same time — for example, the number of COVID–19 cases in two different countries at the same point in time.
What “directly comparable” means. The two values must mean the same thing. The number of cases and the number of deaths are two different types of value, so a percentage difference between them tells you nothing useful.
Percentage difference
percentage difference = ( difference between the two values ÷ average of the two values ) × 100
WE 1
Calculating a percentage difference
In the same week, Country A recorded 27 400 confirmed cases of COVID–19 while Country B recorded 9 800 confirmed cases. Calculate the percentage difference between them. (3 marks)
Step 1: the difference between the two values
27 400 − 9 800 = 17 600
Step 2: the average of the two values
(27 400 + 9 800) ÷ 2 = 37 200 ÷ 2 = 18 600
Step 3: put them into the formula
(17 600 ÷ 18 600) × 100 = 94.6%There was a 94.6% difference between the two countries that weekboth values are numbers of cases at the same time, so they are directly comparable — that is why this formula is allowed
That is the reason percentage difference uses the average. With two values measured at the same time, there is no reason to treat either one as the starting point.
Percentage change
A percentage change calculation compares two values from the same data set at different times — in other words, how a factor has changed over time.
Percentage change
percentage change = ( change ÷ original value ) × 100
Here one value did come first, so it is the natural baseline. That is why you divide by the original value and not by an average.
WE 2
A percentage increase
A country recorded 15 600 confirmed cases in one month and 21 450 confirmed cases the following month. Calculate the percentage change. (2 marks)
Step 1: the change
21 450 − 15 600 = 5 850
Step 2: divide by the original value
(5 850 ÷ 15 600) × 100 = 37.5%A 37.5% increase in confirmed casesthe original value is 15 600 because that month came first — using 21 450 gives the wrong answer
WE 3
A percentage decrease
Weekly hospital admissions fell from 4 820 to 3 615 after a vaccination campaign. Calculate the percentage change. (2 marks)
Step 1: the change
4 820 − 3 615 = 1 205
Step 2: divide by the original value
(1 205 ÷ 4 820) × 100 = 25.0%Step 3: say which direction it went
The original value was larger than the new value, so this is a decrease.
A 25.0% decrease, which can also be written as −25.0%never leave a change answer bare — write increase, decrease, or put the negative sign in
Watch your units and your rounding. If the data is given to the nearest whole number, quoting an answer to four decimal places looks careless. Two or three significant figures, plus a percentage sign, plus the word increase or decrease, is what a full–mark answer looks like.
The two formulas side by side
Percentage difference
Percentage change
Used for
Two directly comparable values at the same time
Two values from the same data set at different times
Typical question
Cases in two countries this week
Cases in one country in June and in July
Top of the fraction
The difference between the two values
The change
Bottom of the fraction
The average of the two values
The original value
Direction
Not applicable — neither value came first
State increase or decrease, or use a negative sign
🧠
Two words: Average for A difference, Original for the Other one
Difference and average both describe two things sitting side by side. Change and original both imply a starting point that came first.
💡 Exam tips
Check first whether the values are directly comparable. Cases and deaths are not.
Write the formula down before substituting. It earns method marks even if the arithmetic slips.
Show your working line by line: difference, then denominator, then the final calculation.
Always include the percentage sign and, for a change, the word increase or decrease.
Round sensibly — usually to one decimal place or three significant figures.
If a question gives you three numbers, decide which two are being compared before you touch the calculator.
⚠ Common mistakes
Dividing by the average when you needed the original value. This is the single most common error on these questions.
Dividing by the new value instead of the original. The original is the one that came first in time.
Comparing values that are not directly comparable, such as cases against deaths.
Forgetting to multiply by 100. You end up with a decimal instead of a percentage.
Leaving out increase or decrease. A percentage change without a direction is incomplete.
Copying the wrong number from a table. Underline the two values you are using before you start.
That completes Disease & Immunity. The whole unit is one long argument: pathogens try to get in, barriers stop most of them, the innate system handles what gets through, the adaptive system learns from it, and vaccines let us do that learning safely across a whole population.
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