Statistics And Probability Course

Lesson 1 • Introduction to Statistical Thinking

Defines statistics as a discipline and contrasts descriptive vs. inferential goals. Establishes the mindset needed for data-driven reasoning throughout the course.

Lesson 2 • Organizing and Displaying Data

Teaches frequency tables, histograms, bar charts, and stem-and-leaf plots. Visual organisation reveals patterns before formal analysis begins.

Lesson 3 • Data Collection Methods

Covers surveys, experiments, and observational studies as primary collection strategies. Method choice directly affects validity and generalisability of conclusions.

Lesson 1 • Measures of Central Tendency

Defines mean, median, and mode and explains when each best represents a dataset. Connects choice of measure to data type and distribution shape.

Lesson 2 • Standardisation and Z-Scores

Converts raw scores to z-scores for cross-distribution comparison. Standardisation is a prerequisite for normal distribution work in the next chapter.

Lesson 3 • Measures of Spread and Variability

Introduces range, variance, standard deviation, and IQR as tools for quantifying dispersion. Spread measures complement centre to give a full distributional picture.

Lesson 4 • Five-Number Summary and Box Plots

Constructs five-number summaries and box plots to compare datasets visually. Outlier detection via the IQR fence rule is introduced here.

Lesson 1 • Addition and Multiplication Rules

Derives rules for union and intersection probabilities for mutually exclusive and independent events. These rules form the algebraic toolkit for compound event problems.

Lesson 2 • Counting Techniques

Covers the multiplication rule, permutations, and combinations for counting outcomes. Accurate counting is essential for computing classical probabilities.

Lesson 3 • Conditional Probability

Defines conditional probability and demonstrates how new information updates event likelihood. Conditional reasoning is the gateway to Bayes' theorem.

Lesson 4 • Bayes' Theorem and Its Applications

Derives Bayes' theorem from conditional probability and applies it to diagnostic and classification problems. Students update prior beliefs with observed evidence systematically.

Lesson 1 • Continuous Distributions and the Normal Curve

Introduces probability density functions and the normal distribution's properties. The normal curve is the most widely used model in inferential statistics.

Lesson 2 • Binomial and Geometric Distributions

Models binary-outcome trials with binomial and geometric distributions. Students identify when each applies and compute probabilities and moments.

Lesson 3 • Discrete Random Variables

Defines random variables and probability mass functions for discrete outcomes. Expected value and variance of discrete distributions are derived here.

Lesson 4 • Other Key Continuous Distributions

Surveys uniform, exponential, and t-distributions as complements to the normal model. Each distribution is linked to specific inferential procedures introduced later.

Lesson 1 • Point Estimation and Estimator Properties

Evaluates estimators by bias, consistency, and efficiency criteria. Understanding estimator quality prepares students to interpret confidence intervals correctly.

Lesson 2 • Sampling Distribution of the Proportion

Extends sampling distribution logic to sample proportions and their standard error. Proportion distributions underpin hypothesis tests and intervals for categorical outcomes.

Lesson 3 • Sampling Distribution of the Mean

Derives the mean and standard error of the sample mean distribution. Standard error quantifies estimation precision and feeds directly into confidence intervals.

Lesson 4 • Sampling and Sampling Variability

Explains why repeated samples produce different statistics and defines the sampling distribution concept. Variability in estimates is the core problem that inference solves.

Lesson 1 • Logic of Confidence Intervals

Explains the confidence level, margin of error, and interval interpretation. Correct interpretation prevents the common misconception that the interval contains the parameter with certainty.

Lesson 2 • Intervals for Proportions and Variances

Derives confidence intervals for population proportions and variances using normal and chi-square distributions. These intervals extend estimation to categorical and spread parameters.

Lesson 3 • Bootstrap and Resampling Methods

Introduces bootstrap confidence intervals as a distribution-free alternative to parametric methods. Resampling extends interval estimation to complex statistics without closed-form formulas.

Lesson 4 • Intervals for a Single Mean

Builds z-based and t-based intervals for a population mean under known and unknown variance. Choosing between z and t depends on sample size and variance knowledge.

Lesson 1 • Tests for Means and Proportions

Applies one-sample and two-sample z- and t-tests to means and proportions. Students execute the full test procedure from assumptions through conclusion.

Lesson 2 • Chi-Square Tests

Uses chi-square statistics to test goodness of fit and independence in contingency tables. These tests extend hypothesis testing to categorical data structures.

Lesson 3 • Errors, Power, and Effect Size

Distinguishes Type I and Type II errors and derives statistical power as a function of sample size and effect size. Power analysis guides study design decisions.

Lesson 4 • ANOVA: Comparing Multiple Means

Introduces one-way ANOVA to test equality of three or more group means simultaneously. ANOVA avoids inflated error rates from multiple pairwise t-tests.

Lesson 1 • Regression Diagnostics and Assumptions

Checks linearity, independence, normality, and equal variance through residual plots. Violations of assumptions invalidate inference and must be addressed before reporting.

Lesson 2 • Simple Linear Regression

Derives the least-squares regression line and interprets slope and intercept in context. The regression equation enables prediction and quantifies variable relationships.

Lesson 3 • Introduction to Multiple Regression

Extends simple regression to multiple predictors and introduces adjusted R-squared. Students interpret partial slopes and understand multicollinearity as a model threat.

Lesson 4 • Correlation and Scatter Plots

Quantifies linear association with Pearson's r and visualises it through scatter plots. Correlation is the foundation for understanding regression model fit.