Week 10 — Sampling Distributions & the Central Limit Theorem

Welcome to your Week 10 Start Here page.

Why this matters

A hospital quality team asks whether this month's higher average wait is a real change or ordinary wobble, and a polling team asks how a survey of about 1,000 voters can speak for millions. Both questions are about how much an average or a share shifts from one sample to the next.

In plain language

When you take a random sample and compute an average or a percentage, a second sample would give a slightly different number. This week is about that wobble, which statisticians call sampling variability (the change in a sample's summary from one sample to the next). You will learn how big the wobble typically is and how it shrinks as samples grow. You will also meet the Central Limit Theorem (the reason averages of many values tend to pile into a bell shape), which is why a well-drawn poll of about a thousand people can tell you something about millions.

• Already covered: Week 1 separated a parameter from a statistic; Week 9 gave you the normal model.
• This week: sampling distributions, the standard error, and the Central Limit Theorem.
• How they connect: a sample mean is a random variable whose distribution is close to Week 9's normal model.
• Where we're going next: Week 11 builds confidence intervals for a mean.

Focus

If you drew a fresh random sample, how much would its average or its share change, and why do averages pile into a bell?

By the end of this module, you should be able to:

• [ ] explain why a sample mean changes from sample to sample
• [ ] find the standard error of a sample mean and tell it apart from the standard deviation of single values
• [ ] use the Central Limit Theorem and its rule of thumb
• [ ] describe the sampling distribution of a sample proportion

To-do

Plan your week

1. Read Chapter 10 (about 50 minutes), then the lecture and slides.
2. Work the lecture tutorial (60–90 minutes) and the practice set (about 20 minutes).
3. Do the Data Lab (about 90 minutes), the discussion, and the assignment.
4. Take the quiz.

This week's checkpoint: find the standard error of an average of 30 fair-die rolls and say which 30-roll averages would be surprising.

You've got this

Take it in order, and ask your instructor early if a step snags.

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