Title: Week 10 — welcome to the second half: averages behave
Course: Introduction to Statistics (18-Week Generic Edition)

Hi everyone,

The midterm is behind you — nicely done. Whatever your score said, it was a low-stakes checkpoint, and the grade engine remains what it has always been: the weekly work. Now the course turns around. The first half asked how do we describe data? The second half asks what can a sample really tell us? — and this week is the engine room.

Here's the puzzle we open with: a candy bag's label says 200 g, and no bag ever weighs exactly 200 g. Yet the label isn't a lie. This week you'll learn why — individual values wobble a lot, but averages behave: they wobble exactly √n times less, and (this is the astonishing part, the Central Limit Theorem) their wobble follows the bell curve you mastered in Week 8 even when the data don't. By the end of the week you'll compute things like: whether nine adults should side-eye an 1,800-lb elevator placard, and whether a parcel network's bad-looking day is a crisis or just sampling noise.

Three things not to miss: 1. Chapter 10 is your primary reading — the friendly z-table rides again, with two new rulers to use it on. Start there. 2. Data Lab 10 is the course's signature build: you'll hand-crank 30 random penguin samples and watch a bell curve assemble itself out of data you know isn't bell-shaped (Week 8's lab proved it). Statisticians imagine this machine; you'll actually run it. The Discussion ("The Fine Print on 'Average'") wants your initial post two days before the week ends. 3. One habit to install now: before any calculation, ask "one value, or an average?" — then pick the ruler (σ or σ/√n). It's the difference between 31% and 0.62% on the very same question, and your chatbot will get it wrong this week so you can catch it.

Next week we flip the telescope: instead of "given the truth, how do sample means behave?", we'll ask "given ONE sample mean, where is the truth probably hiding?" — your first confidence interval, built directly on this week's standard error.

Open the Start Here / Module Overview page first — it lays out everything in order with due points. See you in the course!