Use lessons 01–02 or equivalent skills before this exercise. You can revisit them from the lesson list.
A spreadsheet or calculator; optional local Python. Text-only AI can explain a plan but cannot establish that calculations ran.
Start with the idea
Distinguish percentage-point change from relative change.
Compare rates when groups have different totals. Name the measure you report. A numerical difference does not by itself prove what caused the change.
Percentage point: The direct difference between two percentages.
See the example and check your understanding
A made-up teaching example
Four errors in twenty tasks is twenty percent. Three errors in thirty is ten percent. The drop is ten percentage points, or a fifty percent relative reduction in the rate.
Ask yourself
Does “ten percentage points” mean the same thing as “ten percent relative reduction”?
Show the explanation
No. The first subtracts rates; the second divides the change by the starting rate. These constructed counts do not prove causation.
Start with these checks
- Check counts and the totals you divide by.
- Label the type of change.
- Do not assume tasks were equally difficult or that AI caused the change.
Use the different practice case below and check every requirement in its full instructions.
Full learning objectives
- Keep formulas and denominators.
- Distinguish percentage points from percent change.
- Use an independent spot-check.
Captions appear here during playback.
Verify calculations with executable evidence
Distinguish percentage-point change from relative change.
Video playback is unavailable. Read the descriptive transcript below, go directly to practice, or open the video file.
Source-based teaching example · Fictional data · Reviewed 2026-10-03. Microsoft Mark · locally synthesized. On a small screen, use fullscreen for diagram details or read the transcript.
Read the descriptive transcript
0:00 · What you will learn
Distinguish percentage-point change from relative change.
What appears on screen
Distinguish percentage-point change from relative change.
0:06 · The idea
Compare rates when groups have different totals. Name the measure you report. A numerical difference does not by itself prove what caused the change.
What appears on screen
Compare rates when groups have different totals. Name the measure you report. A numerical difference does not by itself prove what caused the change.
0:18 · One useful term
Percentage point. The direct difference between two percentages.
What appears on screen
The direct difference between two percentages.
0:26 · A worked example
Four errors in twenty tasks is twenty percent. Three errors in thirty is ten percent. The drop is ten percentage points, or a fifty percent relative reduction in the rate.
What appears on screen
Four errors in twenty tasks is twenty percent. Three errors in thirty is ten percent. The drop is ten percentage points, or a fifty percent relative reduction in the rate.
0:41 · Your turn to think
Does “ten percentage points” mean the same thing as “ten percent relative reduction”? Pause and decide before continuing.
What appears on screen
Does “ten percentage points” mean the same thing as “ten percent relative reduction”? Pause the video if you need more time.
1:00 · Why this answer works
No. The first subtracts rates; the second divides the change by the starting rate. These constructed counts do not prove causation.
What appears on screen
No. The first subtracts rates; the second divides the change by the starting rate. These constructed counts do not prove causation.
1:12 · Check 1
Check counts and the totals you divide by.
What appears on screen
Check counts and the totals you divide by.
1:17 · Check 2
Label the type of change.
What appears on screen
Label the type of change.
1:22 · Check 3
Do not assume tasks were equally difficult or that AI caused the change.
What appears on screen
Do not assume tasks were equally difficult or that AI caused the change.
1:29 · Now try a different case
Open the lesson and try its different practice case. Use every check in the full task. Watching alone does not mark the lesson complete.
What appears on screen
Open the lesson Try the new case Check and revise The full task and its requirements are in the linked lesson.
Watching explains the example. Complete the lesson practice to check what you can do. Explore all visual lessons →
The method
Keep the calculation method with the result: spreadsheet formula or code, input version, units and rounding. AI-generated numbers require verification. For important totals, use a small independent calculation and reconcile row counts. Decimal arithmetic can help with decimal quantities, but it does not decide the correct business rounding policy.
Define rates before calculating. A rise from 20% to 30% is ten percentage points and a 50% relative increase, not the same measure. Check zero denominators, omitted groups and whether the compared periods are equivalent. A passing parser or a polished chart does not validate the underlying arithmetic or question.
Choose your model, harness and offline route
Text-only assistant
Use supplied text. Ask for a plan or draft; do not claim browsing, code execution or file access that was unavailable.
Tool-enabled application or harness
Record which tools actually run, allowed files and actions, approval boundaries and observable results. Tools are optional unless the task needs them.
Local or cloud deployment
Inspect inference, retrieval, connectors, logs and storage separately. Use only authorized environments for real data; training fixtures are fictional.
Higher-capability or frontier model
Evaluate the exact task and configuration. Capability does not supply missing evidence or grant permission. No provider ranking or guarantee is implied.
Offline alternative
Use the supplied inputs and inspect the worked example manually. Builder exercises use local deterministic Python. No paid account or live model call is required.
Record the exact product/model label when available, tools actually used, inputs, permitted actions, observed output and checks. Live accounts or APIs may have external costs; they are optional and are not used by this page.
Read the general workflow guide →Worked example
Supplied input
Constructed counts: before 4 errors / 20 tasks; after 3 / 30. Rates: 20% and 10%.
A checked result
Rate falls by 10 percentage points; relative rate reduction is (20%-10%)/20%=50%. These constructed counts do not establish causation or real improvement.
Why this works
The denominator changed, so compare rates rather than raw errors. State both the measure and evidence boundary.
Try a different case
Independent counts: period A 6 errors / 40 tasks; period B 4 / 50. Calculate rates, percentage-point difference and relative reduction. Verify with a calculator or spreadsheet and keep the formula.
Download this task and checklist →Interactive practice / Fictional fixture
Separate rate and change measures
Use the supplied independent case above. Check the bounded decisions, then review your written artifact against the full acceptance criteria.
Everything runs in this browser. No AI model is called and no work is uploaded. Bounded checks cover specific facts and rules. Your writing is not graded: you review it yourself. Practice never marks a lesson complete automatically.
Avoid causal claims and state the denominators.
Try the task, run the checks, then revise. Checks are teaching feedback, not an instructor grade.
Observed browser simulation
This trace comes from the bounded local checker. It is not a Python run, model result or production tool execution.
Self-review
Locked. Write every written part, then run the checks. A few words is not an attempt.
This is self-review, not grading. Read our answers, then tick what your own work does. Ticks are optional. They stay on this page and are not saved or sent anywhere. A different answer can be just as good if it meets the lesson criteria.
Supported interpretation and comparability concern
A strong answer
Period A: 6 errors in 40 tasks, 15%. Period B: 4 errors in 50 tasks, 8%. The error rate was 7 percentage points lower in B. As a relative change that is about 46.7% (7 / 15). I cannot say why. The periods had different task counts, and I do not know if the tasks, the people or the way errors were counted stayed the same. Formula kept: (6/40 - 4/50) / (6/40).
A flawed answer
Errors fell from 6 to 4, a 7% reduction, which shows the new process works.
What is wrong with it: It compares raw counts when the task totals differ. “7%” mixes up percentage points with relative change. “Shows the new process works” is a causal claim nothing here supports.
Keep or restore your work
Drafts are not saved automatically. Save only fictional practice data. A browser draft may be lost if storage is cleared; download a copy to keep it.
Your steps
- Compute each rate using its own denominator.
- Calculate the two change measures separately.
- Write a supported sentence and name a comparability concern.
Check your work
- Rates are 15% and 8%.
- Decrease is 7 percentage points; relative reduction is approximately 46.7%.
- Do not infer causation or silently equate task difficulty.
After your attempt: review notes and a common mistake
“Seven percent reduction” confuses the measures. The relative reduction is 7/15, while the percentage-point decrease is 15 minus 8.
Different wording or a different justified decision can pass. Check your work against every requirement; these notes are not an automated grade.
Explain your approach
What would you inspect before attributing the change to AI?
Keep your artifact, one correction or decision, its evidence and one remaining limitation. Nothing on this page sends or uploads your work.
Check your understanding
Choose an answer to see feedback. This is a knowledge check, not instructor assessment.
Review your independent practice
Complete the supplied task before recording progress. Use the acceptance criteria and reveal the review notes after your attempt. Keep your artifact yourself; nothing is uploaded.
Not yet self-reviewed. Completion stays in this browser and does not issue a badge.
Optional deeper study
Explore the related general-course lesson → This opens the existing canonical lesson; it is optional depth, not another copy of this focused task.
Primary references
Revision 2026-10-03. Fictional examples, not observed provider results. Knowledge checks and completion records are self-study aids.