Course overview

Introductory statistics builds a full workflow: collect data carefully, describe patterns, model chance, and draw justified conclusions from samples. You will move from descriptive tools to inference for means and proportions, then finish with relationship modeling and group comparison.

Complete curriculum

Every chapter and lesson

40 lessons total

01
Chapter 1 · 4 lessons
Sampling and Data
Define populations, samples, variables, and study designs while identifying selection and measurement bias.
Why it matters
Inference is only as credible as the data process. Good sampling and clear variable definitions prevent misleading conclusions.
By the end, you will be able to
- Distinguish population parameters from sample statistics.
- Classify variables as categorical or quantitative and identify their measurement context.
- Recognize common sources of bias and describe better sampling plans.
1. 1.1
  Population, sample, and variables
  Set up a statistical study using precise language for who and what is measured.
2. 1.2
  Sampling methods and bias
  Compare random, stratified, cluster, and convenience samples and their risks.
3. 1.3
  Observational studies versus experiments
  Identify when a design supports association only or supports causal claims.
4. 1.4
  Data quality checks
  Screen for missing values, outliers, and wording effects before analysis.
Study chapter 1 in detail
02
Chapter 2 · 4 lessons
Descriptive Statistics
Summarize data with tables, graphs, center, and spread to describe distribution shape and unusual values.
Why it matters
Descriptive statistics turn raw values into an interpretable picture and guide which models and tests are reasonable next.
By the end, you will be able to
- Choose suitable visual summaries for categorical and quantitative variables.
- Compute and interpret mean, median, quartiles, range, and standard deviation.
- Describe distribution shape, skew, and potential outliers in context.
1. 2.1
  Tables and graphs for distributions
  Build frequency tables, bar charts, histograms, and boxplots correctly.
2. 2.2
  Measures of center
  Compare mean and median under symmetric and skewed data patterns.
3. 2.3
  Measures of spread
  Use IQR and standard deviation to quantify variability.
4. 2.4
  Shape and outlier interpretation
  Write clear distribution summaries that include center, spread, shape, and unusual points.
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03
Chapter 3 · 4 lessons
Probability Foundations
Use sample spaces, probability rules, and counting logic to quantify chance in repeatable random processes.
Why it matters
Probability is the engine of statistical inference, because uncertainty about samples is modeled through chance.
By the end, you will be able to
- Apply complement, addition, and multiplication rules to events.
- Distinguish mutually exclusive and independent events.
- Compute event probabilities from tables, tree diagrams, and simple counts.
1. 3.1
  Events and sample spaces
  Represent random outcomes clearly before calculating probabilities.
2. 3.2
  Core probability rules
  Solve multi-event probability problems with addition and multiplication rules.
3. 3.3
  Conditional probability and Bayes
  Update probabilities using given information and reverse conditioning when appropriate.
4. 3.4
  Counting methods for probability
  Use permutations and combinations for finite equally likely outcome spaces.
Study chapter 3 in detail
04
Chapter 4 · 4 lessons
Discrete Random Variables
Define discrete random variables, probability distributions, expected value, and variance, including binomial and geometric models.
Why it matters
Discrete models describe counts and repeated yes-no processes that appear in reliability, quality, and survey settings.
By the end, you will be able to
- Construct and interpret probability mass functions.
- Calculate expected value and standard deviation for a discrete variable.
- Use binomial and geometric models under their assumptions.
1. 4.1
  Random variables and distribution tables
  Translate outcome rules into a valid probability distribution.
2. 4.2
  Expected value and variability
  Compute mean and variance from a discrete distribution.
3. 4.3
  Binomial model
  Identify fixed-trial Bernoulli settings and compute binomial probabilities.
4. 4.4
  Geometric model
  Model the number of trials until first success and interpret long-run behavior.
Study chapter 4 in detail
05
Chapter 5 · 4 lessons
Continuous and Normal Models
Work with density curves and normal models to compute and interpret probabilities for continuous variables.
Why it matters
Many measured quantities are continuous, and normal approximations provide practical probability calculations and benchmarks.
By the end, you will be able to
- Explain the difference between probability at a point and over an interval for continuous data.
- Standardize values with z-scores and interpret relative position.
- Compute normal probabilities and percentiles from model parameters.
1. 5.1
  Continuous random variables
  Interpret area under a density curve as probability.
2. 5.2
  Normal distributions and z-scores
  Convert between raw values and standardized scores.
3. 5.3
  Normal probability calculations
  Find interval probabilities and cutoff values using normal models.
4. 5.4
  Model fit and reasonableness
  Check whether a normal model is plausible from data shape and context.
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06
Chapter 6 · 4 lessons
Central Limit Theorem
Understand sampling distributions and use the central limit theorem to model sample means and sample proportions.
Why it matters
Inference depends on how sample statistics vary across repeated samples, and the CLT explains why normal-based methods often work.
By the end, you will be able to
- Differentiate a population distribution from a sampling distribution.
- Compute standard errors for sample means and proportions under assumptions.
- Use CLT conditions to justify approximate normal inference.
1. 6.1
  Sampling distributions
  Describe the long-run distribution of a statistic across repeated samples.
2. 6.2
  CLT for sample means
  Apply normal approximation to x-bar with known or estimated spread behavior.
3. 6.3
  Sampling distribution of p-hat
  Use success-failure checks and standard error for proportions.
4. 6.4
  Interpreting standard error
  Connect sample size changes to precision changes.
Study chapter 6 in detail
07
Chapter 7 · 4 lessons
Confidence Intervals
Construct and interpret confidence intervals for means and proportions, including margin of error and confidence level tradeoffs.
Why it matters
Confidence intervals report plausible ranges for unknown population values, which is often more informative than a single estimate.
By the end, you will be able to
- Build one-sample confidence intervals for means and proportions under stated conditions.
- Interpret interval meaning correctly in repeated-sampling terms.
- Analyze how confidence level and sample size affect margin of error.
1. 7.1
  Point estimates and margin of error
  Separate center estimate from uncertainty width.
2. 7.2
  Intervals for means
  Construct and read t-based intervals when population spread is unknown.
3. 7.3
  Intervals for proportions
  Construct and interpret one-proportion confidence intervals.
4. 7.4
  Choosing confidence and sample size
  Use design goals to balance precision and certainty.
Study chapter 7 in detail
08
Chapter 8 · 4 lessons
One-Sample Hypothesis Tests
Set up null and alternative hypotheses, compute test statistics and p-values, and make one-sample decisions for means and proportions.
Why it matters
Hypothesis tests provide a structured way to judge whether sample evidence is strong enough to challenge a baseline claim.
By the end, you will be able to
- Write valid null and alternative hypotheses for one-parameter questions.
- Compute and interpret p-values in one-sample z or t tests.
- Distinguish statistical significance from practical importance.
1. 8.1
  Hypothesis testing framework
  Follow a full test workflow from claim to decision.
2. 8.2
  One-sample tests for means
  Run and interpret one-sample t tests with assumptions.
3. 8.3
  One-sample tests for proportions
  Run and interpret one-proportion z tests.
4. 8.4
  Reading p-values and errors
  Explain Type I and Type II errors in context.
Study chapter 8 in detail
09
Chapter 9 · 4 lessons
Two-Sample and Chi-Square Inference
Compare two groups with two-sample methods and analyze categorical associations and fit with chi-square procedures.
Why it matters
Many real questions involve group comparisons or categorical relationships rather than a single mean or proportion.
By the end, you will be able to
- Apply two-sample confidence intervals and tests for means and proportions.
- Use chi-square tests for independence and goodness of fit with expected-count checks.
- Interpret statistically significant differences with careful context language.
1. 9.1
  Two-sample means and proportions
  Choose and run two-sample procedures based on variable type and design.
2. 9.2
  Chi-square for independence
  Evaluate whether two categorical variables are associated.
3. 9.3
  Chi-square goodness of fit
  Compare observed counts to a claimed categorical distribution.
4. 9.4
  Practical interpretation of group differences
  Report direction, size, and uncertainty of detected differences.
Study chapter 9 in detail
10
Chapter 10 · 4 lessons
Regression, Correlation, and Intro ANOVA
Model quantitative relationships with correlation and linear regression, then learn the purpose and structure of one-way ANOVA.
Why it matters
Prediction and comparison tasks often require relationship models, and ANOVA extends mean comparison to more than two groups.
By the end, you will be able to
- Interpret correlation direction and strength without overstating causation.
- Fit and interpret a simple linear regression model including slope and residuals.
- Explain ANOVA as variance-based comparison of multiple group means.
1. 10.1
  Correlation and causation boundaries
  Separate association evidence from causal claims.
2. 10.2
  Simple linear regression basics
  Interpret slope, intercept, prediction, and residual error.
3. 10.3
  Diagnostics and model caution
  Check linearity, outliers, and extrapolation risk.
4. 10.4
  ANOVA first look
  Describe null and alternative ideas for comparing three or more means.
Study chapter 10 in detail

Introductory Statistics

Course overview

Every chapter and lesson

Sampling and Data

Descriptive Statistics

Probability Foundations

Discrete Random Variables

Continuous and Normal Models

Central Limit Theorem

Confidence Intervals

One-Sample Hypothesis Tests

Two-Sample and Chi-Square Inference

Regression, Correlation, and Intro ANOVA

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