Week 10 — Readings & Resources · Sampling Distributions

Course: Introduction to Statistics (MATH 11) · Silver Oak University (fictional sample) · Prof. Rivera
Objective covered: Objective 5 — Use normal and sampling distributions to reason about variability.

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.

This week's load is deliberately light: ~4 short readings + ~3 short videos, grouped by the three ideas from the lecture. Read or watch one item per group and you're ready for the quiz; do all of them and you'll be very comfortable. Total time is roughly 45–55 minutes if you do everything, far less if you pick one per group.

Reading order that matches the lecture: ① sampling variability & the sampling distribution of x̄ → ② the standard error σ/√n → ③ the Central Limit Theorem.

A habit to start now: the one move that runs the whole week is divide σ by √n. As you read, keep asking the two questions: is this about a single value, or about an average? — and if it's an average, did they use the standard error σ/√n, not just σ?

One thing the readings can't replace: in this course we supply the same small z-table as Week 9 (z = 0, ±0.5, ±1, ±1.5, ±2, ±2.5, ±3) inside the tutorial, practice, quiz, and assignment, and we pre-compute the standard error σ/√n with friendly numbers so every problem lands exactly on a table value. So when a reading or video looks up a value in a big z-table, just follow the idea — you'll never have to recall a table value here.

① Sampling Variability & the Sampling Distribution of x̄

Maps to Lecture Segments 2–3. The big idea: a statistic like x̄ is a moving target — a new sample gives a new average — and the histogram of all those averages (its sampling distribution) centers at μ and is far narrower than the spread of individuals.

Reading — "Sampling Distribution of the Sample Mean" (Khan Academy, article)
🔗 https://www.khanacademy.org/math/statistics-probability/sampling-distributions-library/sample-means/a/sampling-distribution-of-the-sample-mean
Why it's assigned: the cleanest plain-language picture of where the sampling distribution of x̄ comes from — draw a sample, get an x̄, repeat — and why its center is μ. Exactly the "one population, many samples, many x̄'s" move from class.
⏱ ~6 min

Reading — "Sampling distributions for sample means" hub (Khan Academy, unit)
🔗 https://www.khanacademy.org/math/statistics-probability/sampling-distributions-library
Why it's assigned: a short, example-driven hub that ties the sampling distribution of x̄ to its center and spread — a good second pass, and it previews the standard error and the CLT you'll meet next.
⏱ ~5–7 min

② The Standard Error · σ/√n

Maps to Lecture Segment 3. The engine of the week: the spread of the averages is the standard error = σ/√n, which is smaller than σ — and shrinks as n grows (quadruple n to halve it).

Reading — "What Is Standard Error? | How to Calculate (Guide with Examples)" (Scribbr)
🔗 https://www.scribbr.com/statistics/standard-error/
Why it's assigned: nails the one formula the whole week turns on — the standard deviation of the sampling distribution is the population σ divided by √n — and warns against the classic mix-up of σ (individuals) with σ/√n (the average). This is the cure for the week's biggest trap.
⏱ ~6 min

③ The Central Limit Theorem

Maps to Lecture Segments 5–6. The miracle: for large n, the sampling distribution of x̄ is approximately normal — whatever the population's shape — so a z-score (using σ/√n) and the table give the probability of any range.

Reading — "Central Limit Theorem | Formula, Definition & Examples" (Scribbr)
🔗 https://www.scribbr.com/statistics/central-limit-theorem/
Why it's assigned: the clearest statement that the means go normal even when the population doesn't, plus the center (μ) and spread (σ/√n) of that bell — the exact three facts we used to compute a probability about x̄.
⏱ ~8 min

Video — "Introduction to the Central Limit Theorem" (jbstatistics)
🔗 https://www.youtube.com/watch?v=Pujol1yC1_A
Why it earns the click: samples from two very different (non-normal) populations and shows the sampling distribution of x̄ becoming a bell as n grows — then works a probability with σ/√n, exactly our three-line ritual.
⏱ ~10 min

Video — "The Central Limit Theorem, Clearly Explained!!!" (StatQuest with Josh Starmer)
🔗 https://www.youtube.com/watch?v=YAlJCEDH2uY
Why it earns the click: the friendliest possible intuition for why averaging produces a bell and why that's the doorway to all of inference — a great first watch if the idea still feels like magic.
⏱ ~8 min

Video — "Central Limit Theorem — Sampling Distribution of Sample Means" (The Organic Chemistry Tutor)
🔗 https://www.youtube.com/watch?v=4YLtvNeRIrg
Why it earns the click: a calm, worked-example tour that computes the standard error σ/√n and finds probabilities about a sample mean step by step — the closest match to the arithmetic in our quiz and assignment. (It's long; just watch the first ~15 minutes for the core moves.)
⏱ ~15 min (of a longer video)

Optional one-stop reference (free online text)

If you'd like one optional reference to skim all term, OpenIntro Statistics keeps its full text and per-section videos free to read online. Chapter 5 ("Foundations for Inference") introduces sampling variability and the Central Limit Theorem — everything in this week — and it leads straight into next week's confidence intervals.
🔗 https://www.openintro.org/book/os/
Why it's here: a reputable, currently-available reference you can return to in later weeks — entirely optional this week. (Its Chapter 4 also has a free online normal distribution calculator if you want to check your by-hand x̄ answers.)

Pick-one quick path (≈15 min total)

In a hurry? Do exactly these three and you'll be ready for the quiz:
1. Read Sampling Distribution of the Sample Mean (group ①).
2. Read What Is Standard Error? (group ②).
3. Watch Introduction to the Central Limit Theorem — jbstatistics (group ③).

Heads-up (links rot): these point to outside sites that occasionally move or rename pages. If a link ever fails, tell Prof. Rivera and use the OpenIntro reference above (Chapter 5) in the meantime.