Experimental Demos
This chapter collects interactive demos we are trying out. They are not required course content — they are a sandbox for a format that pairs a StatLens activity (scan it on your phone, or follow along while your instructor projects it) with a few short notes you write in your own words and keep for studying. If you try one, tell us what worked and what didn’t.
The pattern in each demo is the same three moves:
- Predict first — commit a guess before you open the tool. Being a little bit wrong is what makes the right answer stick.
- Do it — scan the code (or open the link) and step through the StatLens activity.
- Explain — write one plain-language conclusion you would actually want in front of you before an exam.
Sampling distributions
Demo: Building a sampling distribution of the sample mean
This guided activity has you draw samples from a right-skewed population and watch the distribution of the sample mean \(\overline{x}\) take shape. It walks you through it step by step — it asks you to predict first, then makes you actually draw the samples, and checks your reasoning along the way.
a) Predict (write it here first). You’ll draw samples of \(n = 10\) from a right-skewed population and plot each sample’s mean, then bump the sample size to \(n = 100\). Before you open anything: what do you expect happens to the center of the sample means as \(n\) grows? To their spread?
b) Do it. Scan the code to open the activity on your phone (your instructor may also project it). Step through all of it — predict, draw a few samples, draw 1000, then freeze and compare \(n = 10\) against \(n = 100\).
Or open the activity in a browser →
c) Explain — keep this for exam study. In your own words, as if explaining to a classmate who missed class: the population was strongly skewed, yet the sampling distribution of \(\overline{x}\) came out centered at \(\mu\) and roughly bell-shaped. Why? And why does a larger \(n\) shrink its spread but not move its center?
The histogram of sample means is the sampling distribution of \(\overline{x}\). Its center sits at the population mean \(\mu\) for every sample size — it does not drift as \(n\) grows. Only the spread changes (\(\sigma/\sqrt{n}\), the standard error), and the shape approaches normal as \(n\) grows — the Central Limit Theorem.