Statistics

Learn to classify data by type, organize it into frequency tables, and visualize patterns using bar charts, histograms, dotplots, and stemplots — the essential first step in any statistical investigation.

Master the numerical tools that summarize data — mean, median, standard deviation, IQR, z-scores, and boxplots — and learn when each measure is appropriate and what it reveals about a distribution.

Understand the critical difference between observational studies and experiments, master sampling methods that produce trustworthy data, and learn to identify the biases that can invalidate even the most sophisticated analysis.

Build the mathematical framework for reasoning about chance — from sample spaces and basic probability rules through the addition rule, multiplication rule, conditional probability, and independence.

Learn to assign numerical values to random outcomes, compute expected values and variances of discrete random variables, and apply the binomial distribution to model real-world scenarios with fixed numbers of independent trials.

Explore the properties of the normal distribution, apply the empirical rule and z-scores to find probabilities, use the standard normal table for precise calculations, and understand why this single curve appears throughout statistics and nature.

Discover how sample statistics vary from sample to sample, why this variability is predictable, and how the Central Limit Theorem guarantees that sample means and proportions follow approximately normal distributions — the foundation of all statistical inference.

Learn to construct and interpret confidence intervals for means and proportions, understanding how sample size and confidence level control the precision of our estimates about populations.

Master the logic of hypothesis testing — formulating null and alternative hypotheses, calculating p-values, making decisions about statistical significance, and understanding the errors that can occur when drawing conclusions from data.

Extend inference methods to compare two populations — testing whether two means or two proportions differ and constructing confidence intervals for the difference, the core of experimental and observational comparisons.

Explore the relationship between two quantitative variables using least squares regression, learning to fit lines to data, interpret slopes and intercepts, assess model quality through residuals and correlation, and recognize the limits of regression as a predictive tool.

Learn to analyze categorical data using chi-square tests — testing whether observed frequency distributions match expected ones, whether two categorical variables are independent, and whether different populations share the same distribution.

Learn the principles that make experiments the gold standard for establishing causation — randomization, control, replication, and blinding — and explore the major experimental designs used in medicine, agriculture, psychology, and industry.

Synthesize the entire course by conducting complete statistical investigations — from formulating questions and designing data collection to choosing appropriate analyses, drawing conclusions, and communicating results with clarity and intellectual honesty.