Workshop in Probability and Statistics
About this written course
Original English workshop in introductory data analysis, probability and bounded statistical inference. All datasets are fictional teaching data. This is a self-paced written practice course, not a professional qualification or a substitute for a full statistics curriculum. Earlier completion markers refer to the earlier content and do not establish mastery of this revision.
Level: Foundational undergraduate self-study
Prerequisites
- Arithmetic with fractions and percentages
- Basic algebra and square roots
- A calculator; optional spreadsheet for independent checking
Learning outcomes
- Describe data with appropriate summaries and quality checks
- Calculate joint, conditional and reverse probabilities
- Build simple discrete probability models and sampling arguments
- Interpret one-sample intervals, tests and simple linear relationships with assumptions
Materials in this written edition
- 15 original written lessons with 15 worked examples.
- 45 independent practice questions and 30 exit checks with explanatory answer keys.
- 4 topic self-assessments with 16 questions and marking guidance.
- One integrated 20-point capstone with model answer and rubric.
- Accessible text explanations and labelled learning tables.
Course contents
- Data Literacy and Descriptive Statistics (4 lessons)
- Probability and Conditional Reasoning (4 lessons)
- Counting, Random Variables and Sampling (4 lessons)
- Inference and Statistical Relationships (3 lessons)
New written edition. Earlier course completion is not evidence of completing this revised material. Worked keys are provided for self-checking.
Source references
References support general concepts. Teaching prose, examples and assessments in this edition are original.
- NIST: Confidence limits for the mean. Verification of the one-sample t interval and frequentist coverage interpretation; no copied datasets or examples. Verified 2026-10-03.
- NIST: Relationship between tests and confidence intervals. Verification of matched two-sided testing and interval logic. Verified 2026-10-03.
- OpenStax: Introductory Statistics topic overview. Reference-only confirmation of introductory terminology. No prose, images, examples or exercises reused. Verified 2026-10-03.
- OpenStax: Probability topic overview. Reference-only terminology check; course questions and data are original. Verified 2026-10-03.
- OpenStax: Discrete random variables topic overview. Reference-only scope check; no source content adapted. Verified 2026-10-03.
- OpenStax: Central limit theorem topic overview. Reference-only scope check; no source content adapted. Verified 2026-10-03.
- NIST: Critical values of the Student t distribution. Verification of supplied rounded t quantiles for original exercises. Verified 2026-10-03.
- NIST: Cumulative distribution function of the standard normal distribution. Verification of normal-reference probabilities and critical-value context. Verified 2026-10-03.
- NIST: Linear least squares regression. Verification of elementary least-squares terminology; original data and derivations. Verified 2026-10-03.
What Will I Learn?
- Describe data with appropriate summaries and quality checks
- Calculate joint, conditional and reverse probabilities
- Build simple discrete probability models and sampling arguments
- Interpret one-sample intervals, tests and simple linear relationships with assumptions
Course Content
Data Literacy and Descriptive Statistics
-
Questions, data types and data quality
-
Tables and graphical summaries
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Mean, median and mode
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Variance and standard deviation
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Probability and Statistics: revised knowledge check