Degrees

Statistics and probability

From averages and dice to Bayes, the normal curve, confidence intervals, p-values and regression: the maths for reasoning about data honestly.

Course · 8 lessons · 60 min

Taught inData ScienceArtificial IntelligenceTelecommunications

  1. 1Descriptive statisticsFreeSummarising data with centre and spread: mean, median, variance and standard deviation, why n − 1, and why one outlier can wreck an average.1890s–today · 7 min
  2. 2Probability rules and conditional probabilitySample spaces, the axioms, complements, the addition rule, conditional probability, independence and the law of total probability.1654–1933 · 7 min
  3. 3Bayes' theoremHow to turn P(evidence | cause) into P(cause | evidence), why a 95% accurate test can still be wrong most of the time, and updating beliefs step by step.1763 · 7 min
  4. 4Random variables, expectation and discrete distributionsRandom variables, PMFs and CDFs, expectation and variance, and the two discrete workhorses: the binomial and the Poisson distributions.1713–1898 · 8 min
  5. 5The normal distribution and the central limit theoremThe bell curve, z-scores and the 68–95–99.7 rule, the standard error, and why averages of almost anything end up normally distributed.1733–1810 · 8 min
  6. 6Confidence intervalsEstimating with honest error bars: z and t intervals for a mean, intervals for a proportion, sample size, and what “95% confidence” really means.1908–1937 · 7 min
  7. 7Hypothesis testing and p-valuesNull and alternative hypotheses, test statistics, p-values, type I and II errors and power, and the ways p-values are misread and abused.1925–2016 · 8 min
  8. 8Correlation, causation and linear regressionPearson's r, why correlation is not causation, and fitting a least-squares line: slope, intercept, R² and the limits of prediction.1805–1965 · 8 min