Title: Week 9 — Lecture Outline · Midterm Week: The First Half, One Story
Course: Introduction to Statistics (18-Week Generic 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.

1. ❌ "It's a number, so it's quantitative." → ✅ Route numbers, tag numbers, zip codes label. Ask: does arithmetic mean anything?
2. ❌ "The tall bars sit left, so it's skewed left." → ✅ Skew is named for the tail. The tail tells the tale.
3. ❌ "The variance is 16, so the spread is 16 units." → ✅ Variance is squared units — take the root (SD = 4) before you speak.
4. ❌ "r ≈ 0 means no relationship." → ✅ r sees straight lines only — look at the plot (arches hide there).
5. ❌ "P(A | B) is basically P(B | A)." → ✅ Different denominators, different questions. Say the "given" world out loud first.
6. ❌ "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.
7. ❌ "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.
8. ❌ "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.