Sampling Distributions: Free Course

About this course

A statistic changes from sample to sample. This course explains that variability through sampling distributions of means and proportions, standard error and the central limit theorem. Study the complete public source playlist from Khan Academy in English, with all 11 recordings in the on-site classroom. Original lesson titles, source order and repeated entries are preserved.

Course at a glance

What you’ll learn

• Distinguish population, sample and sampling distributions.
• Interpret standard error and statistic bias.
• Describe sampling distributions of means and proportions.
• Check conditions before using a normal approximation.

Skills you’ll gain

• Sampling distributions
• Standard error
• Central limit theorem
• Statistic bias

Course Overview

The recordings distinguish a population distribution, one observed sample and the distribution of a statistic over repeated samples. Worked examples show why this distinction is essential when calculating probabilities involving sample means or proportions. Standard error describes the variability of a statistic, while bias concerns where its sampling distribution is centered. The normal-condition lessons and central-limit explanations address when a normal approximation is appropriate. Multiple sample-mean and sample-proportion explanations are retained so learners can compare graphical intuition with calculation. Avoid treating a larger sample as a cure for a biased sampling process: variability and representativeness are separate issues.

How to study the course

• Videos 1–2: this part of the source list includes “Sampling distribution example problem” through “Probability of sample proportions example”. Define the question and the observations. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 3–5: this part of the source list includes “Sampling distribution of sample proportion part 1” through “Standard error of the mean”. Check the assumptions behind a method. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 6–8: this part of the source list includes “Central limit theorem” through “Sampling distribution of the sample mean 2”. Connect a calculation with a plain-language interpretation. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 9–11: this part of the source list includes “Sample statistic bias worked example” through “Introduction to sampling distributions”. Describe uncertainty and limits of a conclusion. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.

Who is this for?

This course suits students, analysts and readers who want to understand the specific statistical methods in the course. It also provides a recorded reference for revisiting a topic after an earlier lesson or study attempt. Choose examples appropriate to your background and allow time to work through the method instead of judging understanding only by how familiar the terminology sounds.

Before you start

Basic arithmetic and familiarity with tables and graphs are helpful. More advanced probability or inference topics assume the prerequisite methods shown in the recordings.

Put the lessons into practice

Imagine repeatedly drawing samples from a small population and record the sample mean from each. Sketch the distribution of those means and distinguish it from the original data. Compare two sample sizes, explaining the expected change in variability. For a sample-proportion probability, state and check the approximation conditions before calculating.

This optional study activity is provided by WikiFree for independent practice. Keep your working notes and use the relevant classroom recording to check a step, definition or interpretation. It is not an instructor-marked assignment.

Certificate / Assessment

Watching the public videos and using WikiFree completion tracking does not award a certificate, academic credit, an examination voucher or instructor assessment. Use your practice output to review what you can explain and repeat independently. The recorded lessons provide study material; completion tracking records your progress through that material.

Frequently asked questions

Provider: Khan Academy. Videos play from the Khan Academy channel on YouTube.