James's Math Hub

Track 6 of 6

James's favorite

Statistics & Probability

From summarizing data all the way to hypothesis testing: descriptive stats, study design, probability and Bayes' theorem, random variables, the binomial and normal distributions, the Central Limit Theorem, confidence intervals, and significance tests. The math behind science, polls, and AI.

13 lessons · ~155 min total · 26-question quiz

Lessons

  1. 01

    Descriptive Statistics

    Mean, median, mode, range, variance, and standard deviation.

  2. 02

    Data Displays & Distribution Shape

    Histograms, box plots, quartiles, the IQR, and spotting skew and outliers.

  3. 03

    Sampling & Study Design

    Populations vs samples, random sampling methods, bias, and experiments vs observational studies.

  4. 04

    Probability Basics

    Sample spaces, independence, conditional probability, expected value.

  5. 05

    Conditional Probability & Bayes' Theorem

    Updating probabilities when you learn something new — and why base rates matter.

  6. 06

    Random Variables & Expected Value

    Probability distributions, expected value, and the variance of a random variable.

  7. 07

    The Normal Distribution

    The bell curve, the 68-95-99.7 rule, and z-scores.

  8. 08

    Permutations & Combinations

    Counting arrangements when order matters — and when it doesn't.

  9. 09

    The Binomial Distribution

    Counting successes in n independent trials, with a clean formula for mean and spread.

  10. 10

    Sampling Distributions & the Central Limit Theorem

    Why sample means are predictable — the engine behind all of inference.

  11. 11

    Confidence Intervals

    Estimating a parameter with a margin of error — and what 'confidence' really means.

  12. 12

    Hypothesis Testing

    Null vs alternative, test statistics, p-values, and the two ways to be wrong.

  13. 13

    Linear Regression & Correlation

    Best-fit lines, the correlation coefficient, and the causation trap.

Section quiz

26 questions covering the lessons above. Instant feedback on each, full review at the end.

Start the quiz