Statistics & Probability
Every lesson explains the concept, works through examples, and gives you practice problems with full solutions. Work through them in order, or jump to the topic you need.
22 lessons
- Line Plots with FractionsHow to build a line plot from measurements in halves, quarters and eighths, how to read one, and how to use it to answer questions about totals and redistribution.
- Mean, Median and Mode: The Three AveragesHow to find the mean, median and mode of a data set, what each one measures, and how to choose between them when an outlier pulls the mean away from the middle.
- Dot Plots and Histograms: Showing the Shape of DataHow to read and build a dot plot and a histogram, why a histogram's bars touch, how bin width changes what you see, and what a statistical question is.
- Range, Interquartile Range and Mean Absolute DeviationHow to measure how spread out a data set is using range, interquartile range and mean absolute deviation, and why two sets with the same mean can be nothing alike.
- Box Plots: Reading the Five-Number SummaryHow to build a box plot from the five-number summary, what the box and whiskers each show, how to spot skew from the median line, and how to compare two groups.
- Probability: How Likely Is It?What probability means, how to calculate it for equally likely outcomes, why every probability sits between 0 and 1, and how experimental results differ from theory.
- Compound Probability: Two Events at OnceHow to find the probability of two events happening together using organized lists, tables and tree diagrams, and how dependent events differ from independent ones.
- Samples and Populations: Drawing Conclusions from DataWhy a random sample can represent a whole population, what makes a sample biased, how to estimate a population value from one, and how to compare two groups fairly.
- Two-Way Tables: Finding Patterns in Categorical DataHow to build and read a two-way frequency table, how relative frequencies reveal an association between two categories, and why raw counts can mislead.
- Standard Deviation: Measuring Spread Around the MeanWhat standard deviation measures, how to calculate it step by step, why the deviations are squared, and when median and IQR describe the data better.
- The Normal Distribution and the 68-95-99.7 RuleWhat a normal distribution is, how the 68-95-99.7 rule estimates percentages from the mean and standard deviation, how z-scores compare values, and when it fails.
- Residuals and the Correlation CoefficientHow to calculate a residual, what a residual plot reveals about whether a line fits, and how to read the correlation coefficient r for direction and strength.
- Events, Venn Diagrams and the Addition RuleHow to describe events with and, or and not, how a Venn diagram shows them, why the addition rule subtracts the overlap, and what makes two events mutually exclusive.
- Conditional Probability: The Probability of A Given BWhat 'given that' does to a sample space, finding a conditional probability from a table or the formula, why P(A|B) and P(B|A) differ, and the multiplication rule.
- Independent Events: Testing for IndependenceWhat it means for two events to be independent, the two equivalent tests for it, how to decide from a two-way table, and why independent is not mutually exclusive.
- Permutations and CombinationsThe counting principle, factorials, when order matters and when it does not, why a combination divides a permutation by r!, and how to use counts to find probabilities.
- Surveys, Experiments and Observational StudiesWhat each kind of study can and cannot show, where randomization enters, why random selection and random assignment do different jobs, and how confounding works.
- Margin of Error: How Close Is an Estimate?Why two honest samples give different answers, how simulating a thousand samples reveals the spread, where the square-root rule comes from, and how to read a poll.
- Comparing Two Treatments: Is the Difference Real?How reshuffling an experiment's results shows what chance alone can produce, how to judge whether a gap between two groups is significant, and how to read a data report.
- The Binomial Distribution: Exactly k Successes in n TrialsFind the probability of exactly k successes in n independent trials with the binomial formula, see why it works, and answer at least and at most questions.
- Random Variables and Expected ValueHow a random variable turns outcomes into numbers, how to build its probability distribution from theory or from data, and why expected value is the long-run average.
- Expected Value and DecisionsHow to find the expected payoff of a game, compare strategies such as insurance plans, make choices fair with randomness, and read test results with false positives.