Course: Introduction to Statistics (18-week generic edition)
Module: Week 3 of 18 · planned around two ~75-minute sessions
Objective covered: Objective 2 — Summarize and display univariate data.

This file holds two pieces: (A) the Module 3 Overview page ("Start Here") and (B) the Welcome Announcement that drips out when the module opens. All timing is relative — "start of Week 3," "end of Week 3" — and maps onto real dates when the adopting instructor sets the term calendar.

(A) Module 3 Overview — Start Here

Welcome to Week 3: Numerical Summaries — Center & Spread

This is your home base for the week. Read it first, then work the checklist below from top to bottom. Everything you need is linked inside the module.

You've been trusting "averages" all week — a maps app's average commute, an area's average rent, a class average. This week you find out what that word hides. Last week you turned piles of numbers into pictures; now we compress each picture into two or three honest numbers: one for center (where's the middle?), one for spread (how much do values wander?) — and we learn the exact moment an average starts lying.

The week's big question

"Can one number honestly stand in for a hundred numbers — and which number should it be?"

By the end of the week you'll compute all the classic summaries — and, more importantly, you'll know which one to trust for any dataset: mean or median, SD or IQR, and a formal rule (not a feeling) for calling something an outlier.

By the end of this week, you can…

Use this as a checklist. If you can do all five out loud, you're ready for the quiz.

• [ ] Compute and choose among the mean, median, and mode — and say which one a dataset deserves (mean = balance point, median = middle person, mode = most common).
• [ ] Explain resistance — why one wild value drags the mean (and SD) but barely touches the median (and IQR), and why the mean chases the tail in skewed data.
• [ ] Compute a standard deviation by hand — the full recipe: deviations → square → add → ÷(n−1) → root — and read it as the typical distance from the mean.
• [ ] Build a five-number summary, find the IQR, and apply the 1.5×IQR rule — fences, flags, and the boxplot that draws it all.
• [ ] Compute a z-score — (value − mean) ÷ SD — and use it to compare values from completely different scales.

What to do this week, in order

The table below lists the week's items in working order, with what each is worth and when it's due.

Heads-up on the AI work: this is the first heavy computation week, and it exposes a classic chatbot flaw — asked for a standard deviation, chatbots routinely divide by n instead of n − 1. On the dataset 6, 6, 8, 10, 10 the wrong divisor gives ≈1.79; the right answer is exactly 2. You'll catch this exact error in the tutorial and the lab. The chatbot drafts, you judge.

Late policy reminder: 10% off per day late. If life happens, reach out to your instructor before the deadline — early is always easier.

How to succeed this week

• Memorize the two pairing hooks. Mean = balance point, median = middle person, mode = most common — and the mean travels with the SD; the median travels with the IQR. Half the week's judgment calls fall out of those two lines.
• Respect the recipe. Every SD computation is the same six steps, and the deviations must sum to zero before you square — that free check catches most arithmetic slips.
• Sort before you slice. Medians and quartiles are positions; positions only exist in sorted data.
• Flag with a rule, not a feeling. Compute the 1.5×IQR fences before calling anything an outlier — then investigate (typo or truth?), never silently delete.
• Keep units honest. Variance comes out in squared units (dollars², points²); the SD brings it back to reality. If your "spread" can't be said in the data's own units, you stopped one square root too early.

You already know how to read a distribution's shape — this week you get to measure it. Come to the first session with an "average" from your own life that you're not sure you believe.

(B) Welcome Announcement — Module 3

Release setting: drips at the start of Week 3 (offset = 0 days from module start) — not before. If your platform won't preserve the scheduled release on import, post it as a draft labeled "Release: start of Week 3."

Subject: Welcome to Week 3 — the week the average goes on trial

Hi everyone,

Nice work last week — you turned raw numbers into histograms and learned to read a distribution's shape, including the graphs designed to fool you. Keep that skepticism handy, because this week's target is even more common than a bad graph: the "average."

This week — Numerical Summaries: Center & Spread — we tackle the big question: Can one number honestly stand in for a hundred numbers — and which number should it be? You'll learn all three centers (mean, median, mode), the spread measures that give a center its meaning (standard deviation, IQR), a formal rule for flagging outliers, and the z-score — the trick that lets you compare a commute time to a grocery bill.

Three things not to miss:
1. Chapter 3 is your primary reading — start there. The moment a single crash-day commute drags a mean from 20 to 32 minutes while the median doesn't budge is the whole week in one example.
2. Data Lab 3 hands you the penguins again — this time you'll summarize each species' body mass and then sabotage your own data with a 9,999-gram typo to watch, live, which summaries survive. Due at the end of Week 3.
3. The Discussion ("The Average That Misled Me") wants your initial post two days before the week ends — pick a real average from your life and put it on trial.

One heads-up: this is the first real computation week, and your chatbot will get some of it wrong — there's a divide-by-the-wrong-number error most of them make on standard deviations. Catching it is literally part of this week's work. The tool drafts; you judge.

Open the Start Here / Module Overview page first — it lays out everything in order with due points. Bring a healthy distrust of the word "average."

See you in the course!