Week 9 · Lecture outline

Week 9 — Lecture Outline · Midterm Week: The First Half, One Story

Introduction to Statistics Generic evergreen edition

Course: Introduction to Statistics (18-week generic edition)
Objectives covered: Objectives 1–4 in full and Objective 5's normal-distribution portion — the Weeks 1–8 scope, reviewed and then examined.
SLOs touched: A (reason quantitatively from data) · B (communicate results to a non-technical audience)
Meeting pattern: planned as 2 sessions × ~75 min. Session 1 = the cumulative review (segments 1–5). Session 2 = the midterm itself plus a short post-exam hand-off.

Week at a Glance


The week's big question	"Can you walk up to any number in the wild — a rating, a rate, a bell curve — and run the right Weeks 1–8 move on it, start to finish?"
By the end of the week, students can…	(1) place every Weeks 1–8 tool on one connected map (get data → picture it → summarize it → relate it → weigh chance → model it); (2) execute the classic moves quickly and correctly under mild time pressure; (3) name and dodge the eight classic traps; (4) sit the 50-question midterm with calm and a plan.
The exam	50 questions × 2 points = 100 · covers Weeks 1–8 · Midterm group (5%) · closed to AI · calculator fine; one page of notes if you permit it; any z-table values an item needs are printed in the item.
Materials	review deck (Deck 9), the Week 9 study guide, practice exam, exam-prep tutorial, and the debrief discussion — plus each week's chapter for targeted re-reading
Timing note	Session 1 ≈ 75 min of review (segments 1–5). Session 2 ≈ 75 min: administer the exam (~60) + margins and a debrief hand-off.

Segment 1 — Opening: The Map of the First Half (12 min) · Session 1 opens

Hook. "Eight weeks ago I promised you'd be able to interrogate any statistic you meet. Today we prove it. One story, eight weeks, five moves — and then you show a 50-question exam what you've got."

Draw the map on the board, left to right, and have students call out what lives in each box (the deck's map slides mirror this):

GET the data honestly (W1) — population vs. sample, parameter vs. statistic (P→P, S→S), NOIR, sampling methods, bias, observation vs. experiment. The week that decides whether any later number deserves trust.
PICTURE it (W2) — frequency and relative frequency, histograms and friends, shape words, the graphs that lie.
SUMMARIZE it (W3) — mean/median/mode, SD and IQR, five-number summary and fences, z-scores as relative standing.
RELATE it (W4) — scatterplots and r, two-way tables, marginal vs. conditional, the handshake that isn't a push.
WEIGH the chance (W5–6) — probability rules, conditional probability, random variables, E(X) and SD(X), linear transformations.
MODEL it (W7–8) — the binomial (B·I·N·S, the formula, np and √(np(1−p))) and the normal (68–95–99.7, z, the friendly table, both directions).

Land the line: "The midterm is not eight little exams. It's one story asked fifty ways: where did the number come from, and what does it mean?"

Segment 2 — Rapid-Fire Classification Drills (18 min)

Format. Fingers-vote or mini-whiteboards, 20–30 seconds each, answer said aloud immediately — momentum over ceremony. (These drills also live in the exam-prep tutorial, so absent students still get the reps.)

Round A — "Which tool?" (students name the move, not the answer)
1. "Typical rent in a right-skewed market?" → median (resistant).
2. "How unusual is this one battery... er, this one measurement, relative to its group?" → z-score.
3. "Percent of an approximately normal pile below a cutoff?" → z → table left-tail area.
4. "How many of 20 independent yes/no trials succeed, on average?" → binomial mean np.
5. "Do these two categorical variables travel together?" → compare conditional distributions.
6. "Is this claim causal?" → ask: was anything randomly assigned?

Round B — quick numbers (every answer verified in the Week 9 math script)
1. "14 of 56 farm-stand customers bought jam. Relative frequency?" → 14 ÷ 56 = 0.25.
2. "P(a car-wash customer adds wax) = 0.62. P(does not add wax)?" → 1 − 0.62 = 0.38.
3. "Score 82, group mean 70, SD 8. z?" → (82 − 70) ÷ 8 = 1.5.
4. "Ordered categories, unmeasurable gaps — the level?" → ordinal.
5. "Histogram's thin tail stretches toward the low values — the shape word?" → skewed left (the tail tells the tale).

Coaching note: wrong votes are gold — ask the room which trap the wrong answer fell into, then re-vote a cousin question.

Segment 3 — Two Worked Integration Examples (20 min)

Why integration: weekly quizzes asked one-week questions; the midterm's synthesis items chain weeks together. Model that chaining out loud, every step shown.

Integration Example 1 — one small dataset, three weeks of moves (W1 → W2 → W3).

A dog park logs five visit lengths (minutes): 10, 15, 20, 25, 80.
- W1 move: visit length in minutes — quantitative, ratio level (zero means none). These five visits are a sample; the park's question is about all visits (the population).
- W2 move: four values bunch low, one sits far high → skewed right with a possible high outlier. A dot plot would show the gap instantly.
- W3 move: mean = (10 + 15 + 20 + 25 + 80) ÷ 5 = 150 ÷ 5 = 30; median = 20. The mean chases the tail — one 80-minute epic drags it 10 minutes above the median — so report the median as typical.
The chain, said plainly: classify → picture → choose the honest summary. Three weeks, one fluid move.

Integration Example 2 — chance to model (W5/W7 → W8).

An arcade game wins a token on each play with probability 0.5, plays independent. A player runs 64 plays.
- W7 move: X = tokens won is binomial (B·I·N·S ✓): mean = np = 64 × 0.5 = 32; SD = √(64 × 0.5 × 0.5) = √16 = 4.
- W8 move: with n this large the count's histogram is approximately bell-shaped, so the empirical rule prices a session: about 95% of 64-play sessions land within 2 SDs — 24 to 40 tokens.
- One more step (forward normal): how unusual is a 40-token session? z = (40 − 32) ÷ 4 = 2.0 → beyond 40 lies about 1 − 0.9772 = 0.0228 ≈ 2.3% of sessions (course z-table).
The chain, said plainly: check the setting → compute np and √(np(1−p)) → let the bell turn the SD into percentages. That is exactly how the two synthesis items on the exam think.

Segment 4 — Misconception Clinic: The Eight Classic Traps (15 min)

Format. Put each trap up as a confident wrong sentence; the room's job is to (a) veto it and (b) state the cure in one line. These are the traps the exam's distractors are built from — say that out loud; it converts anxiety into strategy.

❌ "It's a number, so it's quantitative." → ✅ Route numbers, tag numbers, zip codes label. Ask: does arithmetic mean anything?
❌ "The tall bars sit left, so it's skewed left." → ✅ Skew is named for the tail. The tail tells the tale.
❌ "The variance is 16, so the spread is 16 units." → ✅ Variance is squared units — take the root (SD = 4) before you speak.
❌ "r ≈ 0 means no relationship." → ✅ r sees straight lines only — look at the plot (arches hide there).
❌ "P(A | B) is basically P(B | A)." → ✅ Different denominators, different questions. Say the "given" world out loud first.
❌ "E(X) = 0.95, so most purchases give about one extra token." → ✅ E(X) is what you'd average, not what you'd expect — it needn't be a possible value.
❌ "P(exactly 2 of 4) = p²(1−p)²." → ✅ Count the ways: × C(4, 2). Forgetting the ways factor is the most common binomial error.
❌ "About 95% of any dataset sits within 2 SDs." → ✅ The empirical rule's password: IF bell-shaped. Check the shape first.

Callback: every one of these appeared in a weekly outline with its cure — the clinic is pure recall, not new content.

Segment 5 — Exam Logistics + Q&A (10 min) · Session 1 closes (~75)

Say the logistics slowly (deck slide mirrors it):

50 questions, 2 points each, 100 points, 5% of the grade. Covers Weeks 1–8. One attempt, time-bound (plan ~60 minutes — a little over a minute per item).
Closed to AI — this one is all you. Calculator fine. One page of notes if your instructor permits it (announce your policy now). Any z-table value an item needs is printed inside the item — nothing to memorize beyond 68–95–99.7.
Strategy, honestly: answer everything (no penalty for wrong answers); flag and return rather than stall; read "at least" vs. "exactly" like a lawyer; for table questions, find the "among ___" group first; sketch-and-shade before any z lookup.
Perspective: the midterm is a checkpoint, not a verdict — 5%. The weekly work remains the grade engine. Walk in curious about what held.

Q&A: take remaining questions; steer "will X be on it?" answers back to the map — if it's on the Weeks 1–8 map, it's fair; the study guide lists the map completely.

Hand-off (say it explicitly): "Before Session 2: work the study guide, take the practice exam at least once closed-book (unlimited attempts, zero shared items with the real thing), and run the exam-prep tutorial — it diagnoses you, drills your weak spots, and it's this week's graded tutorial."

Session 2 — Administering the Midterm (~75 min)

Before students arrive: confirm the exam is published, one attempt, shuffle on, time limit set (~60 min), and — if you allow the notes page — that students know it. Have two or three spare calculators.

Administration notes:

Open (5 min): settle, remind: closed to AI, calculator fine, permitted notes out, needed table values are printed in the items. "Answer everything; flag and return."
During (~60 min): proctor lightly. Announce time at the halfway mark and with 10 minutes left. For content questions during the exam, answer only clarifications of wording — never the statistics.
Collect / close (5–10 min): as submissions land, point students at the debrief discussion (initial post due two days before the week ends): "While it's fresh — which topics held, which wobbled? That conversation, with your chatbot, is graded and genuinely useful: it writes your second-half study plan."

Post-exam debrief plan (2 minutes of talk, then let them go):

Normalize: "However that felt, it's 5%. What it bought you is information."
Preview: scores release after everyone sits it; the debrief discussion turns each student's item-level wobbles into a Weeks 10–18 plan.
Tease Week 10 warmly: "The second half asks one question the first half couldn't: how far can a sample be trusted? The answer starts with the most useful fact in statistics — averages behave."

Instructor FAQ — Exam-Week Stumbles

Situation	Quick cure
"Is the midterm hard?" panic in Session 1	Reframe: 5%, checkpoint, and every item is a fresh variant of moves they've already been graded on for eight weeks. The practice exam proves it — send them there.
Students want to cram the night before	The bundle is the cram, structured: study guide (diagnose) → practice exam (rehearse) → tutorial (drill the misses). One honest pass beats three re-reads.
"Do we memorize the z-table?"	No — only 68–95–99.7. Every needed table value is printed inside its item, exactly as the weekly materials promised.
"Can we use AI on the practice exam?"	Yes — practice and the tutorial are AI-open. Only the midterm itself (like the quizzes) is closed. Encourage practicing at least one attempt AI-free for realism.
A student misses the exam window	Standard make-up policy: documented emergencies, contact before the deadline where possible. The exam stays low-stakes; don't let one miss spiral.
"Will there be trick questions?"	No — but distractors are built from the eight classic traps, and say so openly: knowing the traps is the study strategy.
Students finish the exam in 25 minutes	Fine — but remind the room at the start: fast finishers should re-check the "at least / exactly" items and any table-denominator items, the two places speed bites.
"My practice score was low — am I doomed?"	Opposite: the practice exam found the wobbles while they're free. Route each miss to its week's chapter section and the tutorial drill; retake until clean.

Scope flag

This outline reviews and examines only Weeks 1–8 (Objectives 1–4 plus Objective 5's normal portion). No new content is introduced; the two integration examples chain previously taught moves. Session 2 assumes your platform's standard quiz proctoring — adapt the timing notes to your own delivery mode.