Week 10 — Readings & Resources · Sampling Distributions & the Central Limit Theorem
Course: Introduction to Statistics (18-week generic edition)
Objective covered: Objective 5 — use normal and sampling distributions to describe how sample statistics behave.
Your primary reading is Chapter 10 (in this module). Everything below is the optional, go-deeper layer.
How to use this page
Everything here is a link to an external resource — open it in your browser, the same way you'd open a YouTube link. Nothing needs to be downloaded, and nothing costs money.
The load is deliberately light: 4 short readings (one of them a play-with-it interactive) + 5 short videos, grouped by the four big ideas of the week. Read or watch one item per group and you're well prepared; do all of them and you'll be very comfortable. Total time is roughly 55–70 minutes if you do everything, far less if you pick one per group.
Order that matches the chapter and lecture: ① the sampling-distribution idea → ② the sample mean's center & spread (SD vs. SE) → ③ the Central Limit Theorem → ④ the sample proportion + see the machine run.
A habit for this week: every time a resource shows a spread, ask which ruler is this — σ for individuals, or σ/√n for averages? That one question sorts out the entire week.
① The Sampling-Distribution Idea
Maps to Chapter 10, Section 1 and Lecture Segment 2. One entry per SAMPLE, not per individual — the distribution your one real x̄ was drawn from.
Reading — Sampling Distribution of the Mean (Online Statistics Education / OnlineStatBook)
🔗 https://onlinestatbook.com/2/sampling_distributions/samp_dist_mean.html
Why it's assigned: a compact, classic walkthrough of the sampling distribution's mean and variance, with simulation pictures comparing small and larger n — the chapter's Section 1–2 story from a second voice.
⏱ ~7 min
Video — Sampling Distributions: Introduction to the Concept (jbstatistics) (video, ~8 min, captioned)
🔗 https://www.youtube.com/watch?v=Zbw-YvELsaM
Why it earns the click: the clearest slow-motion version of the week's core idea — watching a statistic become a random variable with its own distribution.
② The Sample Mean: Center & Standard Error (SD vs. SE)
Maps to Chapter 10, Section 2 and Lecture Segment 3. The two rulers: σ for one value, σ/√n for an average — and quadruple the sample to halve the noise.
Reading — What Is Standard Error? | How to Calculate (Guide with Examples) (Scribbr)
🔗 https://www.scribbr.com/statistics/standard-error/
Why it's assigned: a plain-language treatment of the standard error with a dedicated SD-vs-SE section — the week's #1 vocabulary split, explained twice over.
⏱ ~7 min
Video — The Sampling Distribution of the Sample Mean (jbstatistics) (video, ~12 min, captioned)
🔗 https://www.youtube.com/watch?v=q50GpTdFYyI
Why it earns the click: derives center μ and spread σ/√n carefully and shows what changing n does to the curve — the ÷√n shrink factor, animated.
Video — Sampling distribution of the sample mean (Khan Academy) (video, ~11 min, captioned)
🔗 https://www.youtube.com/watch?v=FXZ2O1Lv-KE
Why it earns the click: builds a sampling distribution from a deliberately weird, non-normal population — so you see the bell emerge from data that has no bell in it.
③ The Central Limit Theorem
Maps to Chapter 10, Sections 3–4 and Lecture Segments 5–6. Whatever the population's shape, sample MEANS go normal as n grows — the CLT fixes shape, never bias.
Reading — Central Limit Theorem | Formula, Definition & Examples (Scribbr)
🔗 https://www.scribbr.com/statistics/central-limit-theorem/
Why it's assigned: states the theorem, its conditions (including the n ≥ 30 rule of thumb), and works two full examples — the closest outside match to the chapter's Section 3.
⏱ ~10 min
Video — The Central Limit Theorem, Clearly Explained!!! (StatQuest with Josh Starmer) (video, ~8 min, captioned)
🔗 https://www.youtube.com/watch?v=YAlJCEDH2uY
Why it earns the click: the friendliest CLT explanation on the internet — uniform and exponential populations both producing bell-shaped means, and why that lets statisticians relax about population shape.
④ The Sample Proportion + See the Machine Run
Maps to Chapter 10, Section 5 and Lecture Segments 7–8. p̂ is a mean in disguise — and the lab's 30-samples build, automated so you can take 5,000.
Interactive — StatKey: Sampling Distribution for a Mean (Lock⁵ / StatKey)
🔗 https://www.lock5stat.com/StatKey/sampling_1_quant/sampling_1_quant.html
Why it's assigned: the week's data lab, motorized — click "Generate 1000 Samples" and watch the dotplot of sample means pile into a bell centered on the true mean. Five minutes here cements the lab forever. (Free, browser-only, no login.)
⏱ ~5–10 min of play
Video — The Sampling Distribution of the Sample Proportion (jbstatistics) (video, ~10 min, captioned)
🔗 https://www.youtube.com/watch?v=fuGwbG9_W1c
Why it earns the click: the p̂ version of the week — center p, the √(p(1−p)/n) standard error, and the np ≥ 10 / n(1−p) ≥ 10 shape check, all with worked numbers.
Optional one-stop reference (free online text)
If you'd like one optional reference to skim, OpenStax Introductory Statistics 2e keeps its full text free to read online. Chapter 7 (The Central Limit Theorem) covers this week end to end — sampling distributions, the CLT for means (and sums, our totals-⟺-means bridge), and practice problems.
🔗 https://openstax.org/books/introductory-statistics-2e/pages/7-introduction
Why it's here: a reputable, currently-available reference you can return to during the inference weeks — entirely optional this week.
Pick-one quick path (≈25 min total)
In a hurry? You've read Chapter 10 — then do exactly these three and you'll be ready for the quiz:
1. Watch The Central Limit Theorem, Clearly Explained!!! (group ③).
2. Read What Is Standard Error? (group ②).
3. Play with StatKey's sampling distribution for five minutes (group ④) — generate 1,000 samples and watch the bell assemble.
Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell your instructor and use the OpenStax reference above in the meantime.