Statistics Lessons

Master statistics with our comprehensive, free lessons. Start from the basics and work your way up to advanced topics at your own pace.

41 lessons 12 categories Free forever

Descriptive Statistics

6 lessons

Summarize and describe data with measures of central tendency and spread

1 beginner 15 minutes

Introduction to Statistics

Learn the fundamentals of statistics, including what statistics is, why it matters, and the key concepts you need to know to get started.

statistics basics introduction data types

2 beginner 20 minutes

Measures of Central Tendency

Master the three main measures of central tendency: mean, median, and mode. Learn when to use each measure and how to calculate them.

mean median mode

3 beginner 25 minutes

Standard Deviation and Variance

Learn to measure data spread using variance and standard deviation. Understand when and how to use these statistics.

standard deviation variance spread

4 beginner 25 minutes

Data Visualization

Master the art of visualizing data: histograms, box plots, scatter plots, bar charts, and more. Learn to choose the right chart for your data.

visualization histogram box plot

5 beginner 20 minutes

Percentiles and Quartiles

Master percentiles, quartiles, and the five-number summary. Learn to interpret relative standing and identify outliers using the IQR method.

percentiles quartiles IQR

6 beginner 20 minutes

Z-Scores and Standardization

Master z-scores to compare values across different distributions. Learn standardization, the empirical rule, and how to use z-tables.

z-score standardization normal distribution

Probability

7 lessons

Understand probability theory, rules, and distributions

1 beginner 25 minutes

Introduction to Probability

Master probability fundamentals. Learn about probability rules, basic calculations, and real-world applications.

probability probability rules events

2 intermediate 22 minutes

Sampling Distributions

Understand sampling distributions and the Central Limit Theorem. Learn why sample means enable statistical inference.

sampling distribution central limit theorem standard error

3 intermediate 25 minutes

Counting Principles and Combinatorics

Master the fundamental counting techniques: multiplication rule, permutations, and combinations. Essential for probability calculations.

counting permutations combinations

4 intermediate 25 minutes

Conditional Probability and Independence

Learn to calculate probabilities when conditions are known. Understand independent vs dependent events and master conditional probability.

conditional probability independence dependent events

5 intermediate 25 minutes

Bayes' Theorem

Master Bayes' theorem to update probabilities with new evidence. Essential for medical diagnosis, machine learning, and decision making.

Bayes theorem posterior probability prior probability

6 intermediate 30 minutes

Discrete Probability Distributions

Master the binomial, Poisson, and other discrete distributions. Learn when to use each and how to calculate probabilities.

binomial Poisson discrete distribution

7 intermediate 30 minutes

Continuous Probability Distributions

Explore continuous distributions beyond the normal: exponential, uniform, and more. Learn probability density functions and their applications.

continuous distribution probability density exponential

Hypothesis Testing

4 lessons

Test claims and draw conclusions from sample data

1 intermediate 20 minutes

Confidence Intervals

Learn how to construct and interpret confidence intervals for population parameters. Understand margin of error and confidence level.

confidence intervals estimation margin of error

2 intermediate 25 minutes

Chi-Square Tests

Learn how to test relationships between categorical variables using chi-square tests of independence and goodness of fit.

chi-square categorical data contingency tables

3 intermediate 22 minutes

One-Sample Tests

Learn to perform one-sample hypothesis tests. Master z-tests, t-tests, and proportion tests for single populations.

z-test one-sample t-test proportion test

4 intermediate 25 minutes

Two-Sample Tests

Learn to compare two groups with hypothesis tests. Master independent t-tests, paired t-tests, and two-proportion tests.

two-sample t-test paired t-test independent samples

Regression

1 lesson

Model relationships between variables and make predictions

1 intermediate 18 minutes

Correlation Analysis

Learn how to measure and interpret the relationship between two variables using correlation coefficients, including Pearson's r.

correlation pearson relationships

Advanced Topics

4 lessons

Explore advanced statistical methods and techniques

1 advanced 25 minutes

Non-Parametric Tests

Learn distribution-free statistical tests for when parametric assumptions fail. Master Mann-Whitney, Wilcoxon, and Kruskal-Wallis tests.

non-parametric Mann-Whitney Wilcoxon

2 advanced 25 minutes

Effect Size and Statistical Power

Go beyond p-values to understand practical significance. Learn effect size measures, power analysis, and sample size planning.

effect size statistical power Cohen's d

3 advanced 30 minutes

Introduction to Bayesian Statistics

Discover Bayesian statistics. Learn about priors, posteriors, likelihood, and how Bayesian inference differs from frequentist methods.

Bayesian posterior prior

4 advanced 30 minutes

Introduction to Time Series Analysis

Learn the fundamentals of time series data. Understand trends, seasonality, stationarity, and basic forecasting techniques.

time series forecasting trend

Inferential Statistics

3 lessons

1 intermediate 30 minutes

Introduction to Hypothesis Testing

Learn the framework for hypothesis testing: null and alternative hypotheses, test statistics, p-values, and drawing conclusions.

hypothesis testing null hypothesis p-value

2 intermediate 30 minutes

T-Tests: Comparing Means

Master one-sample, two-sample, and paired t-tests. Learn when to use each test and how to interpret results.

t-test one-sample t-test two-sample t-test

3 intermediate 30 minutes

ANOVA: Analysis of Variance

Compare means across three or more groups using ANOVA. Learn the F-test, post-hoc analysis, and effect size measures.

ANOVA F-test one-way ANOVA

Probability Distributions

4 lessons

1 intermediate 25 minutes

The Normal Distribution

Understand the most important distribution in statistics. Learn the properties of the bell curve, its parameters, and why it appears everywhere.

normal distribution bell curve Gaussian

2 intermediate 25 minutes

Random Variables

Understand random variables and probability distributions. Learn about discrete vs continuous variables, PMF, PDF, CDF, and expected value.

random variable PMF PDF

3 intermediate 22 minutes

Binomial Distribution

Master the binomial distribution for success/failure experiments. Learn the binomial formula, mean, variance, and applications.

binomial Bernoulli probability distribution

4 intermediate 20 minutes

t-Distribution

Learn about Student's t-distribution, its relationship to the normal distribution, and when to use t instead of z for statistical inference.

t-distribution Student's t degrees of freedom

Regression and Correlation

4 lessons

1 intermediate 25 minutes

Correlation Analysis

Understand correlation coefficients, their interpretation, and limitations. Learn Pearson, Spearman, and point-biserial correlations.

correlation Pearson Spearman

2 intermediate 30 minutes

Simple Linear Regression

Learn to fit and interpret linear regression models. Understand least squares, coefficients, predictions, and model assessment.

linear regression least squares prediction

3 advanced 30 minutes

Multiple Regression

Extend regression to multiple predictors. Learn to interpret coefficients, assess multicollinearity, and build predictive models.

multiple regression multicollinearity adjusted R-squared

4 advanced 30 minutes

Logistic Regression

Learn to predict binary outcomes using logistic regression. Understand odds ratios, maximum likelihood, and model interpretation.

logistic regression binary outcome odds ratio

Foundations

3 lessons

1 beginner 18 minutes

Types of Data

Learn to identify and classify different types of data: categorical vs numerical, discrete vs continuous, and the four scales of measurement.

data types categorical numerical

2 beginner 22 minutes

Data Collection Methods

Master data collection: sampling techniques, surveys, experiments, and observational studies. Learn to design research.

sampling surveys experiments

3 beginner 15 minutes

Summarizing Data with Tables

Learn to organize and summarize data using frequency tables, relative frequency distributions, and cumulative frequency tables.

frequency table relative frequency cumulative frequency

Probability Fundamentals

1 lesson

1 beginner 20 minutes

Probability Rules

Master fundamental probability rules. Learn the addition rule, multiplication rule, complement rule, and complex calculations.

probability addition rule multiplication rule

Sampling and Estimation

3 lessons

1 intermediate 18 minutes

Sampling Methods

Learn different sampling techniques: random, stratified, cluster, and systematic sampling for effective data collection.

sampling random sample stratified

2 intermediate 18 minutes

Point Estimation

Learn about point estimators and their properties. Understand bias, efficiency, consistency, and choosing the best estimator.

estimation bias efficiency

3 intermediate 20 minutes

Sample Size Determination

Learn to calculate required sample size. Understand margin of error, confidence level, power analysis, and planning studies.

sample size margin of error power analysis

Correlation and Regression

1 lesson

1 advanced 25 minutes

Regression Diagnostics

Learn to evaluate regression assumptions and detect problems. Master residual analysis, influence measures, and multicollinearity detection.

regression diagnostics residuals assumptions

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