Free ATI TEAS 7 Mathematics guide
October 2026 - Absolute & Relative Change Study Guide for nursing students in
Absolute change is the raw difference between two values. Relative change expresses that difference as a percentage of the starting value. The distinction matters because a small absolute change can be a large relative one, and questions are written to see whether you notice which is being asked for.
The two measures
| Formula | Units | Answers | |
|---|---|---|---|
| Absolute change | new − original | Same as the data (falls, pounds, mg) | How much did it move? |
| Relative change | (new − original) ÷ original × 100 | Per cent | How big was the move compared with where it started? |
Why the two can disagree completely
A ward that goes from 2 infections to 3 has an absolute change of 1 and a relative change of 50%. A ward that goes from 200 to 220 has an absolute change of 20 and a relative change of 10%. The second ward moved twenty times as much in absolute terms and far less in relative terms.
Neither figure is the honest one on its own. Which matters depends on the question: absolute change tells you the size of the effect on the ground, relative change tells you whether it is a big shift for that particular starting point.
Reading a question carefully
Worked example
A clinic's monthly appointments fell from 320 to 272. Give the absolute and the relative change.
- Absolute:
272 - 320 = -48, so a decrease of 48 appointments. - Relative: divide by the original —
48 ÷ 320 = 0.15. - Convert: 15%.
- Check what the question asked for. "By how many" wants 48; "by what percentage" wants 15%.
Absolute change: a fall of 48 appointments. Relative change: a fall of 15%. The wording of the question — "how many" against "what percentage" — is what selects between them.
Relative change always divides by the original value. Dividing by the new value is the commonest error in the whole topic, and it produces an answer that is always in the answer choices.
Percentage points are a third thing
When the data is itself a percentage, two different changes can be described.
- A vaccination rate rising from 60% to 66% is a rise of 6 percentage points.
- The same rise is a 10% relative increase, because
6 ÷ 60 = 0.10. - Both statements are correct and they are not interchangeable. A question that says "percentage points" wants the subtraction.
Terms to know
- Absolute change
- The raw difference between two values, in the units of the data.
- Relative change
- The change as a percentage of the original value.
- Percentage point
- The arithmetic difference between two percentages.
- Baseline
- The original value that a relative change is measured against.
- Magnitude
- The size of a change, ignoring its direction.
What the TEAS asks most
The same core ideas appear in different wording. If you can answer these without stopping to think, you have what this section requires.
By how much did the figure change?
Absolute change: subtract. The answer carries the units of the data.
By what percentage did it change?
Relative change: difference divided by the original, times 100.
Which of two changes is larger?
Ask which measure the question means. The answer can differ depending on which one you use.
The rate rose from 40% to 45%. Describe the change.
Five percentage points, or a 12.5% relative increase. Read which is wanted.
Key points
- Absolute change is a subtraction; relative change is a percentage of the original.
- Relative change always divides by the starting value.
- A small absolute change on a small base is a large relative change.
- Percentage points and percentages are different when the data is itself a percentage.
- Read the question wording: "how many" against "what percentage".
Review quiz
4 questions on this topic, each with the reasoning worked through. Pick an answer to see how it went, or open the explanation straight away.
-
Question 1 of 4
A ward recorded 15 medication errors last quarter and 12 this quarter. What is the relative change?
Show the answer and explanation
Correct answer: B. A decrease of 20%
3 ÷ 15 = 0.2, a 20% decrease. "A decrease of 3" is the absolute change rather than the relative one, 25% comes from dividing by the new figure of 12, and 80% is12 ÷ 15— the ratio of the two values rather than the change between them. -
Question 2 of 4
Ward A's infections went from 4 to 6. Ward B's went from 50 to 56. Which statement is correct?
Show the answer and explanation
Correct answer: B. Ward B had the larger absolute change; Ward A had the larger relative change.
Ward B moved by 6 against Ward A's 2, so B wins on absolute change; but A rose 50% against B's 12%, so A wins on relative change. This split is the whole point of the topic — the two measures can point in opposite directions.
-
Question 3 of 4
A hospital's hand hygiene compliance rose from 64% to 72%. Which statement is accurate?
Show the answer and explanation
Correct answer: B. It rose by 8 percentage points, a relative increase of 12.5%.
The subtraction gives 8 percentage points, and
8 ÷ 64 = 0.125gives the 12.5% relative rise. "Rose by 8%" is the sloppy phrasing the distinction exists to prevent, the third choice swaps the two measures, and the last mistakes the new value for the change. -
Question 4 of 4
A figure falls from 250 to 200. What is the relative change?
Show the answer and explanation
Correct answer: A. A decrease of 20%
50 ÷ 250 = 0.2, so a 20% fall. 25% is what you get by dividing by 200 — the new value instead of the original — "a decrease of 50" is the absolute change, and the last choice has the direction wrong as well.
Put this TEAS topic into practice
Build a set on absolute change and relative change and use the rationale on every question to reinforce what you just reviewed.
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