University Introductory Statistics Sampling Distributions and the Central Limit Theorem — Unit Notes
Every definition and theorem this unit expects you to know, stated once each and written to be revised from: 2 definitions and 5 theorems, 5 worked examples, 2 diagrams, in 11 printable pages. This page lists what the notes cover. The notes themselves come with the University Introductory Statistics bundle.
Unit notes — in the bundle
Not sold separately. The practice worksheet for this unit is free, with no email and no account.
Sampling Distributions and the Central Limit Theorem — what the notes cover
6 sections, in the order the unit is taught. Each entry below is the title of a definition or a theorem the notes state in full.
What you need
Also in this section: 1 note on method and common errors.
Random samples, statistics and unbiased estimators
- Definition — Random sample, statistic and sampling distribution
- Definition — Unbiased estimator, bias and standard error
Also in this section: 1 worked example, 1 note on method and common errors.
Mean and variance of a sum of independent variables
- Theorem — Mean and variance of a linear combination
Also in this section: 1 worked example, 1 note on method and common errors.
The sampling distribution of the sample mean
- Theorem — Mean and standard error of the sample mean
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
The central limit theorem
- Theorem — The central limit theorem for a sample mean
- Theorem — The total of a random sample
Also in this section: 1 worked example, 1 note on method and common errors, 1 diagram.
The sampling distribution of a sample proportion
- Theorem — Mean and standard error of a sample proportion
Also in this section: 1 worked example, 1 note on method and common errors.
Where the notes are
The notes are one of the documents in the University Introductory Statistics Solutions Bundle, beside the unit test, the challenge problems and every worked answer key. The Sampling Distributions and the Central Limit Theorem practice worksheet is free and stays free.
Every University Introductory Statistics topic — the complete Solutions Bundle
One download, one payment, the whole program. For all 9 University Introductory Statistics units: the worksheet, the reference notes, the challenge set, the unit test and every answer key — these notes included.
- Worked solutions, not answer lists — every step written out
- Covers the whole year's program at this level
- Less than the price of one hour of tutoring — for the entire year's solutions
Practise it, then test yourself
Notes on their own do not make anything stick. This unit has a free, printable practice worksheet, and an end-of-unit test that comes with the bundle.
Sampling Distributions and the Central Limit Theorem practice worksheet About the Sampling Distributions and the Central Limit Theorem unit test