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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.

Start lesson 1 Only addition, subtraction, multiplication, and division

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.

01

Count the chances

Out of which possibilities?

  1. 01One out of fourTurn a count into a probability, without treating it as a promise.
  2. 02Does the first draw change the second?Notice whether a draw changes the next chance before multiplying probabilities.
  3. 03Which group are you counting in?Find the right total when the question gives you a condition.
02

Read a set of numbers

What does the summary leave out?

  1. 04Does the average describe most people?Calculate a mean and a median, and see why they can tell different stories.
  2. 05Same average, different experienceCompare how spread out the values are, not just their center.
  3. 06From 20% to 30%: what actually changed?Separate percentage points, relative change, and a combined rate.
03

Learn from a sample

Who was counted, and how much might it vary?

  1. 07Who actually answered?Separate the group you care about from the people you actually counted.
  2. 08Why does a small sample jump around?Understand why larger random samples usually give steadier proportions, not guaranteed exact answers.
  3. 09An estimate is not an exact addressRead a confidence interval without mistaking it for the spread of individual answers.
04

Make a fair comparison

What does this difference really tell us?

  1. 10Better results, or different people?See why a difference alone does not tell you what caused it.
  2. 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.
  3. 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.