Title: Week 3 Overview — Start Here
Course: Introduction to Statistics (18-Week Generic Edition)

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.

# | Do this | Type | Due
1 | Read Chapter 3 — the module's primary reading | Chapter (ungraded prep) | Early in the week
2 | Skim the slides (Deck 3) and the Week 3 lecture outline; browse the Readings & Resources links that interest you | Prep (ungraded) | Alongside class
3 | Lecture Tutorial 3 — work through centers, spread, five-number summaries, and z-scores with your chatbot, then submit the share link + Completion Summary | Tutorial · graded (Lecture tutorials, 20% group) | End of Week 3
4 | Practice exercises — quick reps with the AI coach | Practice · ungraded | Before the quiz (recommended)
5 | Data Lab 3 — "Sabotage the Penguins: Center & Spread by Species" — summarize real penguin masses by species, then inject a 9,999-gram typo and watch which summaries survive | Data lab · graded (Data labs, 15% group) | End of Week 3
6 | Quiz 3 — mean/median/mode, SD, five-number summaries, the outlier rule, z-scores | Quiz · graded (Quizzes, 15% group) · closed to AI | End of Week 3
7 | Discussion 3 — "The Average That Misled Me" — put a real average from your life on trial with your chatbot, post the AI summary + chat link, then reply to two classmates | Discussion · graded (Discussions, 15% group) | Initial post two days before week's end; replies by end of Week 3
8 | Assignment 3 — "Pick the Honest Number" — four AI-coached problems; submit the report (score on line 1) + chat link | Assignment · graded (Assignments, 25% group) | End of Week 3

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.