Statistics Made Clear
Learn statistics through visual explanations, interactive experiments, and examples worked through one step at a time. Start with averages, graphs, and variation, then build toward sampling, probability, confidence intervals, hypothesis tests, and relationships between variables. Practice choosing a method, checking its assumptions, and explaining what the results do—and do not—support. No calculus or programming required.
Make Sense of Data and What It Means
Statistics helps you answer questions when the numbers don’t tell the whole story. Is a new process actually faster? Does a survey reflect what most people think? How much can you learn from a small sample?
You’ll learn how to work through questions like these, starting with averages and graphs before moving into comparisons, predictions, and uncertainty. We’ll build each idea with examples you can follow, so you understand what you’re calculating, why it’s useful, and what the answer means.
What You’ll Learn
Learn to describe data, compare results, and judge uncertainty.
Understand What a Dataset Shows
Use graphs, averages, and measures of spread to describe a group without hiding its differences.
Learn from Samples
Understand how studies are designed, spot bias, and see why estimates change from one sample to another.
Understand the Uncertainty
Connect probability, confidence intervals, and hypothesis tests with the questions they actually answer.
Compare and Explain
Compare groups, explore relationships, choose an appropriate method, and explain the result and its limits.
Who This Course Is For
This course is for people learning statistics for the first time, returning after a difficult class, or wanting to understand the numbers they encounter at work and in everyday life. Familiarity with fractions, percentages, and simple equations will help; we explain new notation as it appears. You do not need calculus or programming. A basic calculator is useful, and the included activities handle the more involved calculations.
Skills You’ll Develop
The broader competencies and practical skills this guide is designed to build.
Data & Uncertainty
- Statistical Reasoning & Data Interpretation
- Probability & Uncertainty
Data Management & Analysis
- Data Cleaning & Preparation
Data Visualization & Reporting
- Data Visualization
Professional Communication & Research
- Professional Writing & Communication
Numerical & Proportional Reasoning
- Proportional Reasoning
Mathematical Relationships & Change
- Functions & Mathematical Modeling
Guide Sections
Discover how statistics helps us make fair comparisons, learn from samples, and understand patterns.
Identify cases, variables, populations, samples, and the quantity you want to learn.
Choose variable types, define measurements, and handle missing values deliberately.
Understand random sampling, coverage, nonresponse, and why more data may still be biased.
Distinguish association, confounding, random assignment, and the scope of a causal claim.
Build frequency tables, choose denominators, and read categorical graphs.
Read dot plots and histograms without hiding gaps, clusters, or tails.
Understand mean, median, mode, and weighted averages through their meanings.
Measure the middle half, apply an explicit quartile convention, and investigate flagged values.
Build variance from distances, distinguish sample and population formulas, and keep units visible.
Use z-scores and normal models while checking what a distributional assumption means.
Read scatterplots, interpret correlation, and recognize confounding and aggregation problems.
Build a least-squares prediction, interpret residuals, and understand R-squared.
Understand events, complements, joint probabilities, and conditional probabilities.
Use independent trials and the binomial model without confusing expected with guaranteed results.
Distinguish a population distribution, a sample distribution, and a sampling distribution.
Connect standard error to standard deviation and sample size, with explicit conditions.
Move from one estimate to an interval and interpret its confidence level correctly.
Build an approximate interval for a proportion and explore what repeated coverage means.
Learn what bootstrap samples preserve, what they approximate, and what they cannot repair.
Build a null distribution and a p-value from a concrete chance experiment.
Connect a one-sample t test with its interval and distinguish evidence from practical importance.
Build a difference estimate and a Welch interval without assuming equal group variances.
Analyze within-pair differences rather than treating linked observations as separate groups.
Separate pooled null uncertainty from interval uncertainty and report absolute and relative effects.
Calculate expected counts and a Pearson chi-square statistic, and explain what the result tells you.
Recognize false positives, missed effects, multiplicity, and optional stopping.
Understand one-way ANOVA as a ratio of between-group and within-group variation.
Define the target, precision, practical effect, and measurement plan before choosing sample size.
Connect the question, design, calculation, uncertainty, and scope of the claim.
Combine design review, descriptive analysis, a comparison, and a decision in one final study.
Keep the main distinctions and choose a small independent analysis to practice.
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