Course 4 of 7 · Beginner

Statisticsand probability, on real data.

Every idea starts from a question about a dataset, and ends with what the number does and does not tell you.

Start with 0.1 Why Statistics Matters for ML, AI and Real DecisionsSee the syllabus
8modules
41lessons planned
41ready to study now
165quiz questions so far

Who Statistics is for and what you will learn

This track is for you if

  • You analyse data and want to know which conclusions actually hold up.
  • You need to read intervals, tests and A/B results with confidence.
  • You want to understand the probability behind loss functions and scores.

By the end you can

  • Summarise a dataset and spot what a summary hides.
  • Reason with conditional probability and Bayes' theorem.
  • Estimate a quantity with an honest interval around it.
  • Know when a difference in results is real.

Before you start

School algebra and basic Python. Code examples use pandas, from the Data Tools track.

Every open lesson is free to read. The opening modules are a free sample: a free account opens all of their material. Pro adds it for the rest of the course.

The syllabus8 modules, each ending in its own finish line.

Every lesson is listed, including the ones still in production, so you can see where the track goes. Open lessons have their parts and key terms free to read, and their quiz free with an account.

  1. Module 0 · 2 lessons · videos in production

    Why Statistics Matters

    Builds to: a Dispatcher Decision Brief
    1. 0.1Why Statistics Matters for ML, AI and Real DecisionsUnderstand what statistics does: describe observed cases and use them carefully to reason about unobserved cases. See why model performance is an estimate about future cases, not a guaranteed score, and why the same reasoning matters outside ML.
    2. 0.2From Question to Evidence to ActionFollow the full statistical workflow once before learning its individual tools.
    Finish lineModule quiz · 12Project: a Dispatcher Decision BriefInterview questionsModule overview: notebooks, cheat sheet
  2. Module 1 · 10 lessons · videos in production

    Describing Data and Reading Statistical Plots

    Builds to: A One-Page Retail Invoice Report
    1. 1.1Histograms and DensitySee the shape of one feature, and read a smooth density without mistaking smoothing for observed data.
    2. 1.2The CDF, Percentiles and QuantilesRead the fraction of data below any value, and the value below any fraction.
    3. 1.3Mean, Median and ModeChoose the right "typical value", and see the mean pulled by one outlier.
    4. 1.4Variance, Standard Deviation and IQRMeasure spread, robustly when the data has outliers.
    5. 1.5Box Plots and Violin PlotsCompare the distributions of several groups side by side.
    6. 1.6Correlation, Confounding and CausationMeasure how two features move together, and know what correlation can never tell you.
    7. 1.7Who Is in the Dataset?See how the sampling frame and missing responses can make a precise-looking summary unrepresentative.
    8. 1.8Categorical Counts, Rates and Bar PlotsCompare categories without confusing a count, a proportion and a mean.
    9. 1.9Scatter, Joint and Density PlotsSee a relationship between two numerical variables, including patterns a single correlation coefficient misses.
    10. 1.10Pair Plots and Correlation Heatmaps (optional)Screen several relationships while keeping the units, groups and sample size visible.
    Finish lineModule quiz · 15Project: A One-Page Retail Invoice ReportInterview questionsModule overview: notebooks, cheat sheet
  3. Module 2 · 4 lessons · videos in production

    EDA, Evidence and Misleading Statistics

    Builds to: A One-Page, Training-Only Credit EDA Report
    1. 2.1EDA Is a Sequence of DecisionsTurn a raw table into a short list of verified observations and the next questions to test.
    2. 2.2How Charts Can MisleadDetect when visual choices change the apparent size or shape of an effect without changing the underlying observations.
    3. 2.3Denominators, Base Rates and Missing GroupsCheck whether the reported numerator and denominator refer to the population the claim is about.
    4. 2.4Project Lab: End-to-End EDA for an ML DecisionProduce a reproducible data report that changes a modelling decision, not a gallery of attractive plots.
    Finish lineModule quiz · 15Project: A One-Page, Training-Only Credit EDA ReportInterview questionsModule overview: notebooks, cheat sheet
  4. Module 3 · 5 lessons · videos in production

    Probability

    Builds to: A One-Page Fraud Review-Queue Brief
    1. 3.1Probability BasicsReason about chance with outcomes, events and the rules that combine them.
    2. 3.2Conditional Probability and IndependenceUpdate a probability given evidence, and tell independent events from mutually exclusive ones.
    3. 3.3Bayes' TheoremTurn "how likely is the evidence given the class" into "how likely is the class given the evidence".
    4. 3.4Random Variables, Expectation and VarianceDescribe an uncertain quantity by its distribution, its average and its spread.
    5. 3.5Monte Carlo Simulation (optional)Approximate an expected outcome when several uncertain inputs interact and the calculation is hard to do by hand.
    Finish lineModule quiz · 15Project: A One-Page Fraud Review-Queue BriefInterview questionsModule overview: notebooks, cheat sheet
  5. Module 4 · 7 lessons · videos in production

    Distributions and Dependence

    Builds to: A One-Page Retail Sampling-and-Value Brief
    1. 4.1Random SamplingDraw reproducible random samples and know when the sampling rule changes what the sample represents.
    2. 4.2Bernoulli and Binomial OutcomesModel one yes/no outcome and the number of successes in a group.
    3. 4.3The Normal DistributionKnow the Gaussian's shape, the 68–95–99.7 rule, and z-scores.
    4. 4.4Residual Shape and the Q-Q Plot (optional)Diagnose the shape of observed data or model residuals without assuming that every ML feature must be normally distributed.
    5. 4.5Long Tails and Log TransformsRecognise long-tailed data and test whether a simple transform helps the model or the interpretation.
    6. 4.6The Multivariate Normal (optional)Extend the Gaussian to several features, and read its contours.
    7. 4.7Dependence Over TimeRecognise when nearby observations are related, so an ordinary random split or row bootstrap gives misleading uncertainty.
    Finish lineModule quiz · 15Project: A One-Page Retail Sampling-and-Value BriefInterview questionsModule overview: notebooks, cheat sheet
  6. Module 5 · 5 lessons · videos in production

    Estimation

    Builds to: A One-Page Retail Uncertainty Brief
    1. 5.1Samples, Sampling Distributions and the Central Limit TheoremSee how an estimate changes across samples, without requiring a formal central-limit-theorem proof.
    2. 5.2Maximum Likelihood EstimationChoose the probability that best explains observed yes/no outcomes, then connect it to logistic-regression log loss.
    3. 5.3Confidence IntervalsReport an estimate with its uncertainty, and say what the interval does and does not mean.
    4. 5.4The BootstrapGet an interval for any statistic by resampling the data you have.
    5. 5.5Bayesian Estimation and Credible Intervals (optional)Update uncertainty about an unknown rate as new outcomes arrive, and distinguish a credible interval from a confidence interval.
    Finish lineModule quiz · 15Project: A One-Page Retail Uncertainty BriefInterview questionsModule overview: notebooks, cheat sheet
  7. Module 6 · 4 lessons · videos in production

    Hypothesis Testing

    1. 6.1Hypothesis Testing and the p-ValueTest a claim against chance, and read a p-value correctly.Written walkthrough
    2. 6.2Permutation and Resampling TestsTest a difference by shuffling labels under an exchangeability null, without assuming a parametric outcome distribution.
    3. 6.3Using Tests WellAvoid the ways hypothesis testing misleads in practice.
    4. 6.4Designing and Reading an A/B TestDecide whether a new deployed model improves an outcome that matters to users, not merely an offline score.
  8. Module 7 · 4 lessons · videos in production

    Information Theory and Probabilistic Scores

    1. 7.1Entropy (optional)Measure uncertainty in bits, and see why a pure node has zero entropy.
    2. 7.2Cross-Entropy and Log LossSee log loss as the average surprise of the true labels under the model's probabilities.
    3. 7.3KL Divergence (optional)Measure how different two distributions are, and why the direction matters.
    4. 7.4Mutual Information (optional)Detect a feature-target dependency that correlation may miss, while remembering that dependency is not causation.

How Statistics is taughtone lesson, opened up.

Lessons in this track are built the same way. Here is Stats 3.3 as its outline lists it: what it builds on, its parts in order, and everything around it in its module.

Stats 3.3

Bayes' Theorem

Turn "how likely is the evidence given the class" into "how likely is the class given the evidence".

The lesson, part by part
  1. The result we need to explain
  2. All the ways a flag can occur
  3. Build Bayes' theorem from those counts
  4. Change only the starting rate
  5. Update when new evidence arrives
  6. Check the assumption and run the update
  7. Use the reasoning independently

Key term · posteriorProbability after incorporating the stated evidence: 8.33% after one flag

After the lesson
  • A 5-question quiz, marked the moment you answer
  • Practice at levels A to C, with values to check against
  • Where the idea is used in real work
  • Common mistakes: the error you will see, why, and the fix
In its module · 3. Probability
  • 4 notebooks to run the examples yourself
  • 26 interview questions with model answers
  • The module project: A One-Page Fraud Review-Queue Brief, set with no template
Open the lesson See the module

What's inside a lessonin Statistics, published so far.

Counted from this track's published lessons. A part still being written is left out until it is published.

  1. Learn

    The lesson

    Short parts, each with its key terms, and a free video where one is recorded.

    41 lessonsNo account
  2. Check yourself

    Quiz

    Multiple-choice questions on the lesson, marked the moment you answer.

    33 lessonsFree account
  3. Practise

    Assignments

    Exercises to do yourself, starting from the lesson's own challenge.

    33 lessonsPro
  4. Apply it

    Real-world applications

    Where each idea is used in real work, from data analysis to production models.

    33 lessonsPro
  5. Avoid

    Common mistakes, and the fix

    The error you will actually see, why it happens, and how to fix it.

    33 lessonsPro
  6. Prepare

    Interview questions

    Questions an interviewer asks about each module, with model answers.

    151 questionsPro
  7. Build

    Projects and notebooks

    Module projects, set as a problem with no template and checked by a notebook, and notebooks to run the examples yourself.

    6 projects, 28 notebooksPro

What you will build6 module projects, each set with no template.

Each project is a problem to solve on your own, then checked against test values or a notebook.

Start free, go further with Pro

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  • Practice problems for every lesson, levels A to C, with values to check
  • Self-checking notebooks that mark your answers as you go
  • Module projects, cheat sheets, common mistakes and interview answers
  • A certificate for every course you complete
  • Weekly live sessions with Gaurav
  • Everything in Free

Worked articles on Statistics

All Statistics resources

Where Statistics is used

All AI applications

Questions about Statistics

Why does machine learning need statistics?

To describe data before modelling it, to know how sure a result is, and to understand the loss functions models are trained on.

Other courses

See the machine learning path