Practise a new skill: check what a percentage claim means

A confident answer can confuse a larger count with a better rate. Learn one small checking skill before asking a tool to explain it: calculate each rate using its own total, then name the comparison.

Practice goal: Calculate a count change and a percentage-point difference, then explain why neither alone establishes the cause of a change.

Use only the invented information below. Do not paste real emails, personnel records, customer details or confidential business records. Changing a name does not establish permission to upload a real record.

• [F1] These are invented desk-task tallies, not financial or customer records. Week A: 10 tasks due, 8 completed by their deadline. Week B: 20 tasks due, 12 completed by their deadline. Each task appears once within its week; the weeks have different task sets.
• [F2] On-time rate = on-time completions divided by tasks due, multiplied by 100. A percentage-point difference is the later rate minus the earlier rate. Relative count change = (later count minus earlier count) divided by earlier count, multiplied by 100; if the earlier count is zero, this relative formula is undefined.
• [F3] Worked mini-example: 3 of 4 is 75%; 4 of 5 is 80%. The rate rises 5 percentage points. The completion count rises from 3 to 4, or one third (about 33.3%). These are different comparisons.
• [F4] Authored feedback to audit: “Completions rose from 8 to 12, so the on-time rate improved by 50 percentage points. AI caused the improvement. You have mastered performance analysis.” No source identifies AI use, workload difficulty or a cause.
• [F5] First calculate both weekly rates, their percentage-point difference and the relative completion-count change. Correct the feedback in plain language. This practice has no calibrated mastery score.
• [F6] New self-check case: Week C has 25 tasks due with 15 on time; Week D has 20 due with 14 on time. Work this out before reading the answer below. Explain whether count and rate move in the same direction. No cause is supplied.

You can complete this on paper or in a local document. No external account, upload or purchase is needed.

Draft your answer before reading the correction. Optional: use only this fictional prompt in a tool your organization permits. Do not connect accounts, upload other files or send messages for this task.

Using only F1–F6, show the formula and denominator for each rate, the percentage-point difference and the relative count change for A→B. Explain the flaws in F4 without inventing a cause. Then solve the new C→D case and give one question that would be needed before evaluating why the pattern changed.

Complete fictional facts:
- [F1] These are invented desk-task tallies, not financial or customer records. Week A: 10 tasks due, 8 completed by their deadline. Week B: 20 tasks due, 12 completed by their deadline. Each task appears once within its week; the weeks have different task sets.
- [F2] On-time rate = on-time completions divided by tasks due, multiplied by 100. A percentage-point difference is the later rate minus the earlier rate. Relative count change = (later count minus earlier count) divided by earlier count, multiplied by 100; if the earlier count is zero, this relative formula is undefined.
- [F3] Worked mini-example: 3 of 4 is 75%; 4 of 5 is 80%. The rate rises 5 percentage points. The completion count rises from 3 to 4, or one third (about 33.3%). These are different comparisons.
- [F4] Authored feedback to audit: “Completions rose from 8 to 12, so the on-time rate improved by 50 percentage points. AI caused the improvement. You have mastered performance analysis.” No source identifies AI use, workload difficulty or a cause.
- [F5] First calculate both weekly rates, their percentage-point difference and the relative completion-count change. Correct the feedback in plain language. This practice has no calibrated mastery score.
- [F6] New self-check case: Week C has 25 tasks due with 15 on time; Week D has 20 due with 14 on time. Work this out before reading the answer below. Explain whether count and rate move in the same direction. No cause is supplied.

Authored flawed sample, not an actual provider response:

Week A is 80%; Week B is 120%. The rate increased 50 percentage points because AI helped. Fifteen on-time tasks are always better than 14, so D must also have a worse rate.

1. Use the correct total for each week. B has 20 tasks due, so 12 ÷ 20 × 100 = 60%, not 120%. A is 8 ÷ 10 × 100 = 80%.

2. The rate changes 60% − 80% = −20 percentage points. The count changes (12 − 8) ÷ 8 × 100 = 50%. A rise in completed tasks can accompany a fall in the on-time rate.

3. No AI exposure, workload explanation or causal comparison is supplied. Remove the claim that AI caused an improvement. Different tasks and totals limit comparisons; these tallies alone cannot explain why they changed.

4. A correct answer to a few items is evidence about those answers, not mastery of business analysis. Check the new case yourself, and retain a note about the denominator error.

5. For the new case, 15 ÷ 25 = 60% and 14 ÷ 20 = 70%. The rate rises 10 percentage points while the completion count falls by 1, or 1 ÷ 15 ≈ 6.7%. The opposite directions are consistent.

One supported correction:

A→B: A: 8 ÷ 10 × 100 = 80%; B: 12 ÷ 20 × 100 = 60%. The on-time rate fell 20 percentage points. The on-time count rose from 8 to 12, a 50% relative increase. No cause or AI contribution is established.

New C→D case: C: 15 ÷ 25 × 100 = 60%; D: 14 ÷ 20 × 100 = 70%. The rate rose 10 percentage points; the count fell 1 (about 6.7% relative to 15). Ask what changed in the task mix before trying to explain the pattern. A different task mix is a question, not an observed cause.

Check your answer:

• Use 10 and 20 as the A/B denominators, not the same total for both.
• Distinguish −20 percentage points from +50% count change.
• Show 60% and 70% for C/D and explain the count/rate divergence.
• Remove invented AI exposure, cause and mastery claims.
• Keep your calculations and correction note; try a different invented case later without copying this answer.

Different wording can satisfy these checks. Recheck the facts after any rewrite.

When practising another skill, ask for a small task, a complete source or rule and worked feedback. Check the explanation against that source, then try a different example. A tool-generated quiz, praise or score is not proof of lasting skill. For specialist business decisions, use the appropriate expertise and evidence; this arithmetic exercise supplies no financial advice.

Primary guidance checked on 2026-10-12. The references support source checking, privacy boundaries and clear presentation; the task facts and sample answers are invented. Use the references for their stated checking, privacy or formatting guidance. They do not establish tool performance, professional competence or approval of a real workflow.

• Generative Artificial Intelligence Profile
• Use Clear and Understandable Content
• Protecting Personal Information: A Guide for Business

Keep real work within your organization’s approved data and review process. These exercises do not establish tested accessibility, time savings, job competence or a professional qualification. No provider trial or human professional review is claimed.

Start free Module 1: account sign-in is required; no card is needed. Or read general AI learning guidance. Keep your practice answer in your own local document if you want to return to it; this page does not save it to your account.