10 Course 10 of 10
Probability and statistics
Statistics summarizes data; probability measures uncertainty. Together they help you read a poll, understand a medical test or decide whether a game is worth playing. Every lesson has examples worked step by step, practice problems with solutions and a quick check at the end.
Before you start: Fractions, percents and exponents; some algebra for the later lessons.
Unit 1 Describing data
- 1 Data, frequency tables and graphs Populations and samples, categorical and quantitative data, frequency and relative frequency tables, and choosing the right graph: bar graphs, pie charts, histograms, dot plots and stem-and-leaf plots. 11 min
- 2 Mean, median and mode Measures of center: the mean, weighted mean, median and mode, computing them from lists and frequency tables, and how outliers affect each one. 12 min
- 3 Measures of spread and box plots Range, quartiles, interquartile range, the five-number summary, box plots, the 1.5 IQR outlier rule, variance and standard deviation. 13 min
Unit 2 Counting
- 4 The counting principle and permutations The fundamental counting principle, factorials, permutations of n objects taken r at a time, and permutations with repeated objects. 12 min
- 5 Combinations and the binomial theorem Combinations of n objects taken r at a time, counting with conditions, Pascal's triangle and the binomial theorem. 12 min
Unit 3 Probability
- 6 Basic probability Sample spaces and events, theoretical probability, complements, using counting in probability, and experimental probability with the law of large numbers. 12 min
- 7 Compound and conditional probability The addition rule, mutually exclusive events, conditional probability from formulas and two-way tables, independent events and the multiplication rule. 13 min
- 8 Tree diagrams, total probability and Bayes' theorem Using tree diagrams for multi-stage experiments, the law of total probability, and Bayes' theorem with spam filters and medical tests. 13 min
Unit 4 Random variables and distributions
- 9 Random variables and expected value Discrete random variables and probability distributions, expected value, variance and standard deviation, fair games and insurance. 13 min
- 10 Binomial and normal distributions Binomial experiments and the binomial probability formula with mean and standard deviation, the normal distribution, the empirical rule and z-scores. 14 min