Lecture 28 — Summaries That Don't Mislead
Position in the course
This is lecture 28 of 32. It belongs to the course arc described in the course outline and uses the standard interactive case method: display, attempt (5 minutes), discuss, reveal, name the technique.
Learning objectives
- Choose mean vs median deliberately
- Read percentages with their bases
- Spot misleading summaries and fix them
By the end of this lecture students can do all three under time pressure, which is what the four cases exercise.
Prerequisite knowledge
Before this lecture: Lecture 25 — thinking with data
Assumed fluencies:
- mean vs median
- percentages and their bases
Preparation task: Bring one published statistic and guess its base.
Detailed topic outline
Core (mandatory):
- mean vs median under skew
- percentage bases and their traps
- the inspection paradox
- Simpson's paradox informally
Extension (optional enrichment):
- dashboard ethics
- defending a summary to a sceptical room
Case sequence
| Case | Title | Difficulty |
|---|---|---|
| cs-109 | The Salary Parable | Beginner |
| cs-110 | The Percentage Maze | Foundational |
| cs-111 | The Waiting-Time Twist | Intermediate |
| cs-112 | The Dashboard Defence | Advanced |
| cs-135 | The Split That Leaks | Expert |
Display each case full-screen from the student page (cases cs-109–cs-112); instructor pages cs-109–cs-112 under case-studies/instructor/ hold the full solutions, reveal guides, and discussion prompts. Applied additions cs-135 extend the session as optional extra attempts or homework; they share the lecture's theme but teach an applied, real-world angle.
Timing plan (120 minutes)
| Minutes | Segment |
|---|---|
| 0–10 | Framing: where this fits; recall of the previous lecture |
| 10–30 | Case 1 (cs-109): 5-minute attempt, then discussion and reveal |
| 30–50 | Case 2 (cs-110): same rhythm |
| 50–70 | Case 3 (cs-111): same rhythm, harder case |
| 70–75 | Break |
| 75–100 | Case 4 (cs-112): same rhythm, hardest case |
| 100–115 | Synthesis: name the techniques; misconceptions check |
| 115–120 | Exit questions, homework, next-lecture preview |
Timing flexes with the room: if a case ignites the class, let the discussion run and compress the synthesis; if the attempts stall, harvest partial attempts rather than extending the clock.
Worked examples
- cs-111 waiting-time twist: the bus paradox simulated with 100 simulated passengers and reconciled with the arithmetic.
Instructor demonstration to open the lecture: Salary parable (cs-109): add one billionaire to a row of nine salaries and watch the mean betray; the median holds.
Classroom activities
| # | Activity | Minutes | Format and prompt |
|---|---|---|---|
| 1 | Mean-vs-median showdown | 6 | Ten salary strips; instant votes, then the skew that decides them. |
| 2 | Percentage court | 7 | Three published claims are tried: is the base stated, and is the comparison legal? |
| 3 | Dashboard redesign | 6 | A misleading chart is redesigned under the constraint 'honest but still persuasive'. |
Board plan
- Left third: the case statement, kept visible for the whole cycle.
- Middle third: students' contrasting attempts (two maximum).
- Right third: the reference trace or table, revealed last.
- Bottom strip, written during the cycle: the name of the technique and the one-line invariant or rule this case taught.
Instructor explanation notes
Reading the room. Summaries are arguments, and this lecture teaches students to cross-examine them. The inspection paradox (cs-111) is the intellectual peak; simulation makes it believable.
Running the reveal. Ethics is treated as design under constraint (cs-112), not as a bolt-on sermon.
Lecture focus. One sentence to repeat verbatim: Every summary is an argument; cross-examine it.
Common misconceptions
- Defending a mean in the presence of obvious skew.
- Comparing percentages that use different bases.
- Sampling waits without noticing length bias — the inspection paradox.
- Optimising a dashboard for persuasion over honesty.
Each case's instructor page lists the specific wrong turn to expect; the reveal should address it by name.
Student practice exercises
Core:
- Recompute the salary parable's (cs-109) mean and median with and without the outlier.
- Untangle the percentage maze (cs-110): identify each base and restate the claims correctly.
- Explain the waiting-time twist (cs-111) in four sentences to a commuter.
Enrichment (optional):
- Rebuild cs-112's dashboard under three conflicting stakeholder demands; document choices.
- Explain Simpson's reversal with a made-up admission-rate example.
Formative assessment
Exit questions (choose one; answer on a card in 60 seconds):
- When must the median replace the mean? Expected: under skew or outliers — any time a tail can dominate
- What is the percentage maze's core error? Expected: comparing percentages with different bases
- State the inspection paradox in one line. Expected: sampled experiences oversample long waits/stays — the sampling is length-biased
Cards are skimmed before the next lecture; three answers become the framing. Persistent wrong answers route students to the review stations of lecture 16 or to office hours.
Homework and preparation
- Before: skim the four student pages; attempt case 1 on paper.
- After: write a five-line pseudocode solution for any case you did not finish in class; bring one question to the next lecture.
- Enrichment (optional): the stretch question on each case page.
Learning-outcome mapping
- Primary outcomes: LO9, LO8 — Statistical honesty: summaries cross-examined.
- Coverage details: learning outcomes; assessed via the scheduled quizzes, labs, assignments, and term project in the assessment plan.
Differentiation
- Beginners: aim for a correct plan in pseudocode; Python is optional.
- Intermediate: full Python on cases 1–3, plan on case 4.
- Advanced students: finish early, then answer "what breaks at 10x scale?" and present the alternative-approach bullet from the instructor page.
- Everyone: state one assumption out loud before writing anything.