Evidence · Intermediate · About 6 min
Interpret statistics
Keep the unit and denominator attached
Both sides · Cross-examinationRead the fictional case: The four-day workweek
Resolution A four-day, 32-hour standard work week should replace the current five-day, 40-hour model
Fictional practice brief: ten volunteer office teams with 120 workers tried a 32-hour week for four weeks. Of 90 survey respondents, 72 preferred it. Weekly completed tasks rose from 100 to 104 across the same teams, while new software was also introduced. Customer coverage, pay, and long-term output were not measured.
A percentage is a share of a specific group. State who is in the denominator. Two percentages can both be correct while answering different questions.
Distinguish a count, a relative change and a percentage-point difference. The calculation can be simple; choosing the right measure determines what your argument actually claims.
Fictional practice record
72 ÷ 90 = 80% of respondents preferred the shorter week.
72 ÷ 120 = 60% of all workers reported that preference. The 30 nonrespondents’ views are unknown.
Name the unit
Identify whether the figure concerns people, roles, tasks or a rate.
Choose the denominator
Keep the comparison group explicit.
Describe the change
Separate percentage points from a relative percentage change.
The same 72 workers, two different statements
Resolution A four-day, 32-hour standard work week should replace the current five-day, 40-hour model
Fictional practice brief: ten volunteer office teams with 120 workers tried a 32-hour week for four weeks. Of 90 survey respondents, 72 preferred it. Weekly completed tasks rose from 100 to 104 across the same teams, while new software was also introduced. Customer coverage, pay, and long-term output were not measured.
- Respondents
72 of 90 respondents preferred the shorter week: 80%.
This describes people who answered the survey.
- All workers
72 of all 120 workers reported that preference: 60%.
This does not tell us whether the 30 nonrespondents preferred it.
- Output change
Tasks rising from 100 to 104 is a 4% relative increase.
This is an output measure, not four percentage points in the preference survey.
A correct figure still needs the right claim attached to it.
Test the reasoning
Read the fictional practice case
Resolution A four-day, 32-hour standard work week should replace the current five-day, 40-hour model
Fictional practice brief: ten volunteer office teams with 120 workers tried a 32-hour week for four weeks. Of 90 survey respondents, 72 preferred it. Weekly completed tasks rose from 100 to 104 across the same teams, while new software was also introduced. Customer coverage, pay, and long-term output were not measured.
Your turn
Both sides · Constructive speechCalculate each group’s shortlist rate and the percentage-point difference. Explain one claim this arithmetic cannot establish.
Read the fictional case: Meritocracy as practiced
Resolution Meritocracy as practiced in modern societies is a harmful fiction that should be rejected
Fictional practice brief: twenty of 100 applicants received interview coaching. Eight of those twenty and twelve of the other eighty were shortlisted. The record does not compare qualifications, explain who received coaching, or measure later job performance.
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Coached: … Uncoached: … Difference: … This does not establish…
Try it aloud
Use the timer for a spoken attempt if it helps. Practice without recording, then note what you would improve.
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Review and continue
Resolution Meritocracy as practiced in modern societies is a harmful fiction that should be rejected
Read the practice task and fictional case
Calculate each group’s shortlist rate and the percentage-point difference. Explain one claim this arithmetic cannot establish.
Fictional practice brief: twenty of 100 applicants received interview coaching. Eight of those twenty and twelve of the other eighty were shortlisted. The record does not compare qualifications, explain who received coaching, or measure later job performance.
Your response
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One model response
Eight of 20 coached applicants is 40%; 12 of 80 uncoached applicants is 15%. The difference is 25 percentage points. The arithmetic establishes a rate difference in this fictional record, not that coaching caused it; qualifications and allocation were not compared.
The coached group contains 20 applicants.
The uncoached group has a different size.
Subtracting rates gives a percentage-point difference.
Each rate uses its own group’s denominator. The answer distinguishes a measured difference from the explanation for it, leaving the observation available for a further argument.
Review the performance
- EvidenceI use the correct denominator for each rate.
- ClarityI distinguish percentage points from relative change.
- ArgumentsI describe the claim the calculation actually supports.
Choose one move to improve, revise your response, then try it aloud.
Common mistakes to avoid
- Dropping “of whom” when repeating a percentage.
- Using correct arithmetic to imply an unsupported cause.
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