Week 10 · Readings & resources

Week 10 — Readings & Resources

Introduction to Statistics Free sample edition

Your primary reading is Chapter 10 (in this module). Everything below is the optional, go-deeper layer — pick what helps, skip the rest.

How to use this page

This page has 11 items (5 readings and 6 videos). Allow 108–126 minutes for everything. Each group points back to the matching chapter section and class-session segment, so use the full menu when you want more practice, or take the quick path below.

Every video here has captions: turn them on with the CC button in the player. The chapter covers the same ideas in text.

Pick-one quick path (17–20 min total)

① Why does a second sample disagree? Sampling variability and sampling distributions

Chapter 10, Section “Sampling variability: why a second sample gives a different answer” · Session 1, Segment 1, “Sampling variability and sampling distributions” · Remember: a statistic changes from sample to sample, while the parameter it estimates stays fixed.

Sampling Distributions: Introduction to the Concept — jbstatistics — a calm, careful introduction that builds the sampling distribution of the sample mean for a tiny population by listing every possible sample, the same move the chapter makes with two dice. (video, 8 min) (captions: creator)
3.5.2 Sampling error — Statistics Canada — a national statistics agency explains why a different sample would give a different estimate and why that variability shrinks as the sample grows; read the opening and the Estimating the sampling error and Sampling variance parts, and skip the coefficient of variation. (reading, 6–9 min)
Sampling Distributions (7.2) — Simple Learning Pro — sorts out three easily confused pictures, the population, one sample, and the sampling distribution, then works two practice questions; pause before each answer and try it yourself. (video, 11 min) (captions: automatic)

② How big is the wobble? The standard error of a sample mean

Chapter 10, Section “Standard deviation versus standard error: two different wobbles” · Session 1, Segment 2, “The standard error of a sample mean” · Remember: the standard deviation describes single values, and the standard error describes how much the sample mean moves.

Standard Deviation vs Standard Error, Clearly Explained!!! — StatQuest with Josh Starmer — under three minutes on the difference between the spread of the data and the spread of the means, the distinction this week's quiz leans on. (video, 3 min) (captions: automatic)
Sampling Distribution of the Mean — Stat Trek — states that the sampling distribution of the mean is centered on the population mean and shows how its standard deviation shrinks as the sample grows; read the shape and standard-deviation parts. The page's formula carries an extra correction factor for small populations; when the population is much larger than the sample, that factor is close to 1 and you get the chapter's version. Stop here before the t-distribution and the how-to-find-probability parts; next week takes up intervals for a mean. (reading, 10–14 min)

③ Why do averages make a bell? The Central Limit Theorem

Chapter 10, Section “The Central Limit Theorem: averages pile into a bell” · Session 2, Segment 3, “The Central Limit Theorem and its rule of thumb” · Remember: the averages from large samples follow an approximately normal model, while the data keep their own shape.

The Central Limit Theorem, Clearly Explained!!! — StatQuest with Josh Starmer — starts from a flat population and a lopsided one, takes many samples, and shows the means piling into a bell either way. This builds on Week 9's work with the normal model. (video, 8 min) (captions: automatic)
But what is the Central Limit Theorem? — 3Blue1Brown — a beautifully animated tour that uses dice sums to show a lopsided distribution turning into a bell; watch from the start to about the 16-minute mark, skip the part on the formula for the bell curve, and come back for the short parts on sample means and underlying assumptions near the end. (video, 31 min) (captions: creator)
Probability Distributions: Central Limit Theorem — Seeing Theory — a free interactive page; in the Central Limit Theorem part, move the two shape sliders to make a lopsided population, set the sample size, press Sample many times, and watch the histogram of sample means; try a small sample size and then a large one, and use it while completing the Week-10 module overview. (reading, 10–15 min)

④ What about shares and polls? The sampling distribution of a proportion

Chapter 10, Section “Proportions: the sampling distribution of p̂” · Session 2, Segment 4, “The sampling distribution of a sample proportion” · Remember: a sample proportion is centered on the population proportion, and a bell fits it when the expected successes and failures are both at least 10.

The Sampling Distribution of the Sample Proportion — jbstatistics — connects the sample proportion to Week 7's binomial count, works out its mean and spread, and shows when a normal model fits; it uses its own version of the large-counts check, and this course's version is both counts at least 10. (video, 10 min) (captions: automatic)
Basic Survey Design: Errors in Statistical Data — Australian Bureau of Statistics — a national statistics agency explains sampling error and the standard error in plain terms, including why a sample must be four times as large to halve the sampling error; read the sampling error and standard error parts, and skim the non-sampling error part for the reminder that a big sample cannot fix a biased one. (reading, 8–12 min)

Optional one-stop reference (free online reference)

1.3.6.6.1. Normal Distribution — NIST/SEMATECH e-Handbook of Statistical Methods — a free government reference; scroll to the part titled Theoretical Justification, Central Limit Theorem, which states that sample means are approximately normal for large samples, centered on the population mean, with standard deviation sigma divided by the square root of the sample size. The handbook writes N for the sample size where this course writes n; skip the formulas and functions above that part. (reading, 3–5 min)

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 reference above in the meantime.

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