Evidence · Intermediate · About 6 min
Interpret statistics
Keep the numbers honest
Both sides · Cross-examinationRead the case: The four-day workweek
Resolution A four-day, 32-hour standard work week should replace the current five-day, 40-hour model
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. Say who the group is. Two percentages can both be correct and still answer completely different questions.
Know the difference between a count, a percent change and a percentage-point change. The math is usually easy. Picking the right number decides what you are actually claiming.
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
Is it people, jobs, tasks or a rate?
Say who is counted
Keep the comparison group in the sentence.
Describe the change right
Percentage points and percent change are not the same.
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
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 is about the 90 people who answered, not everyone.
- All workers
72 of all 120 workers reported that preference: 60%.
We know nothing about the 30 who didn’t answer. Saying “all workers” overstates it.
- Output change
Tasks rising from 100 to 104 is a 4% relative increase.
This measures output. Don’t mix it with the survey numbers.
A correct number still needs the right claim attached to it.
Test the reasoning
Read the practice case
Resolution A four-day, 32-hour standard work week should replace the current five-day, 40-hour model
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 case: Meritocracy as practiced
Resolution Meritocracy as practiced in modern societies is a harmful fiction that should be rejected
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
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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 case
Calculate each group’s shortlist rate and the percentage-point difference. Explain one claim this arithmetic cannot establish.
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
You can return to the practice whenever you want.
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 practice 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 you repeat a percentage.
- Using correct math to suggest a cause you have not shown.
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