📊 Probability & Statistics
Data, graphs, probability, distributions, inference, regression and Bayesian ideas.
98 topics
- Types of Data (Beginner) – Categorical vs numerical, discrete vs continuous.
- Collecting Data and Sampling (Intermediate) – Surveys, experiments and random sampling.
- Bias in Sampling (Intermediate) – Systematic errors that make samples unrepresentative.
- Frequency Tables (Beginner) – Count how often each value occurs.
- Tally Charts and Pictographs (Beginner) – Simple visual summaries of counts.
- Bar Graphs (Beginner) – Compare categories using bars.
- Pie Charts (Beginner) – Show parts of a whole as sectors.
- Line Graphs (Beginner) – Show change over time.
- Histograms (Intermediate) – Bars showing frequency of numerical intervals.
- Dot Plots and Stem-and-Leaf Plots (Intermediate) – Show the shape of small datasets.
- Mean (Intermediate) – The arithmetic average.
- Median (Intermediate) – The middle value of an ordered list.
- Mode (Beginner) – The most frequent value.
- Range (Intermediate) – Difference between maximum and minimum.
- Quartiles and IQR (Advanced) – Quartiles split data into four parts; IQR = Q3 − Q1.
- Box Plots (Advanced) – Five-number summary visualised.
- Outliers (Advanced) – Values beyond 1.5 IQR from the quartiles.
- Variance (Advanced) – Average squared deviation from the mean.
- Standard Deviation (Advanced) – Square root of variance; typical spread.
- Sample vs Population Variance (Advanced) – Divide by n−1 for sample variance.
- Weighted Mean (Advanced) – Average where values have different importance.
- Percentiles and Z-Scores (Advanced) – Position of a value relative to the data.
- Skewness and Kurtosis (Expert) – Measures of asymmetry and tail heaviness.
- Scatter Plots (Intermediate) – Plot pairs of values to see relationships.
- Correlation (Advanced) – Strength of linear relationship from −1 to 1.
- Linear Regression (Advanced) – Best-fit line through data.
- Residuals and R² (Expert) – Error of a fit and proportion of variance explained.
- Correlation vs Causation (Advanced) – Association does not prove one thing causes another.
- Simpson’s Paradox (Expert) – A trend reverses when groups are combined.
- Experiments of Chance (Beginner) – Random processes whose outcomes are uncertain.
- Sample Space and Events (Intermediate) – All outcomes and subsets of interest.
- Basic Probability (Intermediate) – Favourable outcomes over total equally likely outcomes.
- Probability Scale (Beginner) – Values from 0 (impossible) to 1 (certain).
- Complementary Events (Intermediate) – The chance something does not happen.
- Experimental vs Theoretical (Intermediate) – Observed frequency approaches theory with many trials.
- Tree Diagrams (Intermediate) – Map sequential outcomes with branches.
- Counting Principle (Intermediate) – Multiply the number of options at each step.
- Permutations (Advanced) – Ordered arrangements.
- Combinations (Advanced) – Unordered selections.
- Addition Rule (Advanced) – Probability of A or B.
- Mutually Exclusive Events (Advanced) – Events that cannot occur together.
- Conditional Probability (Advanced) – Probability of A given B.
- Independent Events (Advanced) – One event does not affect the other.
- Multiplication Rule (Advanced) – Probability of A and B.
- Law of Total Probability (Expert) – Split an event over a partition.
- Bayes’ Theorem (Expert) – Update beliefs with evidence.
- Medical Tests and Base Rates (Expert) – Why positive results can still be probably false.
- Random Variables (Advanced) – Numerical outcomes of random processes.
- Probability Distributions (Advanced) – Assign probabilities to values of a random variable.
- Expected Value (Advanced) – Long-run average.
- Variance of a Random Variable (Advanced) – Spread of a distribution.
- Linearity of Expectation (Expert) – Expectation of sums is sum of expectations.
- Bernoulli Distribution (Advanced) – A single yes/no trial.
- Binomial Distribution (Advanced) – Number of successes in n independent trials.
- Geometric Distribution (Expert) – Trials until the first success.
- Poisson Distribution (Expert) – Counts of rare events in an interval.
- Hypergeometric Distribution (Expert) – Successes when sampling without replacement.
- Uniform Distribution (Advanced) – All values equally likely.
- Normal Distribution (Advanced) – The bell curve.
- Empirical Rule (68–95–99.7) (Advanced) – Share of data within 1, 2, 3 standard deviations.
- Standard Normal and z-Tables (Advanced) – Look up probabilities for z.
- Exponential Distribution (Expert) – Waiting times between events.
- Continuous Random Variables (Expert) – Use density functions; probability is area.
- Cumulative Distribution Function (Expert) – Probability that X ≤ x.
- Joint and Marginal Distributions (Expert) – Distributions of two variables together and separately.
- Covariance (Expert) – How two variables vary together.
- Law of Large Numbers (Expert) – Sample means converge to the expected value.
- Central Limit Theorem (Expert) – Sums of many variables approach a normal distribution.
- Sampling Distributions (Expert) – Distribution of a statistic across samples.
- Standard Error (Expert) – Standard deviation of a sample mean.
- Confidence Intervals for Means (Expert) – Range likely to contain the true mean.
- Confidence Intervals: Proportions (Expert) – Estimate a population proportion.
- Hypothesis Testing Basics (Expert) – Null vs alternative hypotheses.
- p-Values (Expert) – Probability of results at least as extreme if H₀ is true.
- Type I and Type II Errors (Expert) – False positives and false negatives.
- z-Test (Expert) – Test a mean with known σ.
- t-Test (Expert) – Test means with unknown σ.
- Two-Sample Tests (Expert) – Compare two group means.
- Paired Tests (Expert) – Compare before/after measurements.
- Chi-Square Test (Expert) – Test goodness of fit or independence.
- ANOVA (Expert) – Compare means of three or more groups.
- Nonparametric Tests (Expert) – Tests without distribution assumptions.
- Multiple Regression (Expert) – Predict with several variables.
- Logistic Regression (Expert) – Model probabilities of binary outcomes.
- Maximum Likelihood Estimation (Expert) – Choose parameters maximising the data’s probability.
- Bayesian Inference (Expert) – Combine prior and likelihood into a posterior.
- Bootstrap and Resampling (Expert) – Estimate uncertainty by resampling data.
- Monte Carlo Simulation (Advanced) – Estimate quantities with random experiments.
- Random Walks (Expert) – Sequences of random steps.
- Markov Chains (Expert) – Processes where the future depends only on the present.
- Poisson Process (Expert) – Random events at constant average rate.
- Time Series Basics (Expert) – Trends, seasonality and moving averages.
- Experimental Design (Advanced) – Randomisation, control and blinding.
- Data Ethics and Misleading Graphs (Intermediate) – Truncated axes and cherry-picking distort data.
- Entropy and Information (Expert) – Measure of uncertainty.
- Gambler’s Fallacy (Intermediate) – Past random outcomes do not change future independent ones.
- Birthday Problem (Advanced) – With 23 people the chance of a shared birthday exceeds 50%.
- Monty Hall Problem (Advanced) – Switching doors wins 2/3 of the time.