Counts, rates and honest wording
A count says how many; a rate says what share of the eligible cases. Comparing rates needs percentage points or relative change, clearly named.
W6 p. 7 uses constructed registrations: full-time 60 passes out of 100; part-time 18 out of 20.
| Study mode | Passed | Did not pass | All registrations | Pass rate |
|---|---|---|---|---|
| Full-time | 60 | 40 | 100 | 60/100 = 60% |
| Part-time | 18 | 2 | 20 | 18/20 = 90% |
A count chart answers a workload question: full-time has more passes (60 versus 18). A rate chart answers a chance-per-registration question: part-time has the higher pass rate (90% versus 60%). Both are correct; the title and axis label must say which question the chart answers, and the denominator should be visible.
Comparing two rates has two defensible forms (W6 p. 8). From 60% to 90%:
- Absolute difference: 90%-60% = 30 percentage points.
- Relative increase: (90-60)/60 = 50%, relative to 60%.
"Increased by 30%" is wrong for either reading. Name the unit: "30 percentage points higher" or "50% higher relative to 60%".
A dashboard flags; it does not explain (W6 p. 29). Participation = active ÷ eligible × 100, where active means at least one login in the stated week.
| Course | Previous week | Current week | Change |
|---|---|---|---|
| C1 | 82/100 = 82% | 80/100 = 80% | -2 points |
| C2 | 30/40 = 75% | 24/40 = 60% | -15 points |
| C3 | 18/20 = 90% | 18/20 = 90% | 0 points |
For C2 the change is -15 percentage points, or (60-75)/75×100 = -20% relative. A drop like this is a prompt to investigate: a deadline moved, a logging outage, a change in who is eligible, or real disengagement. In C3 each student is 1/20 = 5 points, so small groups move in large steps.
Source: W6 PDF pp. 1-37. Most numbers in the lecture are illustrative or constructed for teaching; pp. 26-27 reuse the Week 5 synthetic registration counts. The Week 6 lab manual (L6) practises Week 5 EDA reasoning and is worked through section by section in Lab work.
The Week 5 unknown-outcome bounds and the Week 6 rule to name the denominator: one cohort gives 75% among known outcomes but 60%–80% for everyone.
Practice problems
Supplementary study questions on the lecture concepts — not verbatim exam questions. Each answer counts toward spaced review.
1. Conceptual understanding
Definitions and distinctions.
Full-time: 60 passes of 100. Part-time: 18 of 20. Which has the higher pass rate?
A pass rate rises from 60% to 90%. Which statement is correct?
2. Application
Apply the concept to a case or calculation.
Which chart answers “Which mode produces more passes to process?”
C1 participation goes from 82/100 to 80/100. What is the change?
3. Interpretation and limitations
Evaluate assumptions and justify conclusions.
C2 falls from 75% to 60%. What is the relative change?
A dashboard shows C2 participation fell 15 points. What is the right response?
Explain it in writing
Self-checked, not marked. Write a few sentences, then compare with the example answer. Your writing is saved as you type.
Show an example answer
The difference is 30%−20% = 10 percentage points. The relative increase is (30−20)/20×100 = 50%.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?
Show an example answer
It falls from 75% to 60%, which is −15 percentage points or −20% relative. The drop is a flag to investigate, for example eligibility changes, logging problems or deadlines, not proof of disengagement.
Check: did you answer the question, use evidence or working, and avoid claiming more than the evidence supports?