INTERACTIVE COURSE · 12 LESSONS
Probability & statistics, one question at a time
Four tokens, one marked. How likely are you to pick the marked one? Start there, then work toward what a survey or experiment can actually tell you.
What you will be able to do
Count the right group, read an average without losing the spread, tell a larger sample from a better sample, and explain a comparison without claiming more than the data show.
Count the chances
Out of which possibilities?
Read a set of numbers
What does the summary leave out?
- 04Does the average describe most people?Calculate a mean and a median, and see why they can tell different stories.
- 05Same average, different experienceCompare how spread out the values are, not just their center.
- 06From 20% to 30%: what actually changed?Separate percentage points, relative change, and a combined rate.
Learn from a sample
Who was counted, and how much might it vary?
- 07Who actually answered?Separate the group you care about from the people you actually counted.
- 08Why does a small sample jump around?Understand why larger random samples usually give steadier proportions, not guaranteed exact answers.
- 09An estimate is not an exact addressRead a confidence interval without mistaking it for the spread of individual answers.
Make a fair comparison
What does this difference really tell us?
- 10Better results, or different people?See why a difference alone does not tell you what caused it.
- 11What does a small p-value actually say?Read a p-value as a question under an assumption, not the probability that a claim is true.
- 12Say exactly what the result supportsCombine rates, sampling, comparison design, and uncertainty in one plain-language conclusion.
What this edition does not claim
This is a first course, not a full statistics degree. It leaves calculus, formal proofs, regression, and advanced inference for later. Finishing the exercises records practice, not expertise. These lessons have not yet been tested in a learner study.
Try a problem before opening its solution. A later attempt with no hints is worth revisiting after a delay, not treating as permanent mastery. Local review reminders use a simple one- or three-day interval, not a validated adaptive-learning model.
How do I retain independent judgment when using AI here?
Keep your own answer before consulting an AI candidate. Check sources, calculations, inference and conditions; explain adoption or rejection. Then solve a new-context task independently and apply the checks to this lesson.
Practice the verification workflow and keep a recordMy learning status
Mark statuses manually; visits do not establish mastery. Languages share statuses while lessons keep their own answers. This backup contains statuses only, not answers or notes.