Course: Introduction to Statistics (MATH 11) · Silver Oak University (fictional sample) · Prof. Rivera
Module: Week 3 of 16 · Fall 2026 · in-person, two 75-minute sessions
Objective covered: Objective 2 — Summarize and display univariate data: describe its shape, center, and spread.

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. Dates below assume a Tuesday/Thursday session pattern with Week 3 meeting Tue Sep 15 and Thu Sep 17, and end-of-week work due Sunday Sep 20, 11:59 p.m. Adjust the day-of-week and times to match your section.

(A) Module 3 Overview — Start Here

Welcome to Week 3: 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.

Last week you turned a pile of numbers into a picture — a histogram with a shape. This week we go one step further and squeeze the pile down to single numbers: one number for the center (what's typical) and one number for the spread (how tightly the data clusters). The catch is that there's more than one honest way to do it, and choosing wrong can make a number lie. The average person has slightly fewer than two arms — true, and completely useless for picturing a real person. Your job this week is to report the number that tells the truth.

The week's big question

"When we squeeze a whole pile of numbers down to a single number, which number is honest — and what does it hide?"

By Friday you'll be able to take any dataset — incomes, test scores, wait times — and report the one number that tells the truth about the middle and the one number that tells the truth about the spread, and defend why you chose them.

By the end of this week, you can…

Use this as a checklist. If you can do all four out loud, you're ready for the week's graded work.

• [ ] Compute and choose between the mean, median, and mode — and say which one fairly represents a dataset.
• [ ] Explain why the mean chases outliers while the median holds still — and pick the right measure under skew. ("The mean chases the outlier; the median ignores it.")
• [ ] Compute a variance and a standard deviation on a small dataset, and say what the SD means in plain words (roughly, the typical distance from the mean).
• [ ] Build the five-number summary (Min · Q1 · Median · Q3 · Max), compute the IQR (Q3 − Q1), and explain why median + IQR are resistant to outliers while mean + SD are not.

What's due this week, and when

Work these in order — each one gets you ready for the next.

This week's graded set is Quiz 3, Discussion 3, and Assignment 3, plus the weekly Lecture Tutorial.

Heads-up on the AI tutorial and discussion: you'll use a chatbot to draft, and then you judge its work against what we cover in class. Chatbots will happily report "the average income is $80,000" for a block where four of five households earn under $45k — and never warn you the mean is misleading. Catching the missing caveat is the point.

Late policy reminder: 10% off per day late. If life happens, reach out before the deadline — I'd much rather hear from you early.

How to succeed this week

• Lead with the shape, not the formula. Before you pick a "center," ask what the data looks like. Symmetric? Report the mean. Skewed or has an outlier? Report the median. The shape decides the measure — every time.
• Memorize two tiny hooks. "The mean chases the outlier; the median ignores it." And "Center and spread travel as a couple: mean rides with SD, median rides with IQR — don't mix the partners."
• Trust the zero-check on deviations. When you compute a standard deviation, the plain deviations from the mean always add up to zero — that's your built-in arithmetic check before you square them.
• Keep the numbers tiny. Every worked example this week uses five-to-seven friendly values you can do by hand. The point isn't heavy arithmetic; it's which number to report and why.
• Treat the chatbot as a smart intern, not an oracle. It'll compute the mean correctly and still hand you a misleading summary. It drafts; you check whether it told the truth.

You don't need anything from beyond Week 2 for this — just last week's idea of a histogram's shape. Come to class ready to argue about whether the "average" income on a block is honest. See you Tuesday.

(B) Welcome Announcement — Module 3

Release setting: post on the module's start day (offset = 0 days), i.e., Tue Sep 15, 2026 — not before. If your platform won't preserve the scheduled date on import, post this as a draft labeled "Release: Tue Sep 15."

Subject: Week 3 — the number that tells the truth (and the one that lies) 📊

Hi everyone,

Quick one to start: the average person has slightly fewer than two arms. It's mathematically true — and utterly useless for picturing a real human. That's the trap we're disarming this week.

This week — Center & Spread — we tackle the big question: When we squeeze a whole pile of numbers into a single number, which number is honest, and what does it hide? You'll learn to report two numbers that tell the truth — one for the center (mean, median, or mode) and one for the spread (standard deviation or IQR) — and, crucially, how to pick the right ones when the data is lopsided.

Two things not to miss:
1. Lecture Tutorial 3 — work through mean/median/mode, the mean-vs-median showdown under skew, standard deviation, and the five-number summary with one approved chatbot (Gemini, Claude, or ChatGPT), then submit the share link. You'll catch the model handing you a misleading "average." Due Sun Sep 20.
2. Quiz 3, Discussion 3, and Assignment 3 also close Sun Sep 20 — the discussion is a quick AI dialogue about which measure of center is fair for a real dataset, which you summarize and post; start early and leave time to reply to classmates.

A callback to last week: histograms gave us the data's shape. This week the shape earns its keep — it's the very thing that tells you whether to trust the mean or the median. Shape first, then the number.

Open the Start Here / Module Overview page first — it lays out everything in order with due dates. Bring your curiosity (and an opinion about whether the "average income" on a block of mostly modest homes plus one mansion is honest) to class on Tuesday.

See you soon,
Prof. Rivera