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Statistics Fundamentals

215 questions15 sections

Probability, hypothesis testing, confidence intervals, and the stats DS interviewers ask about.

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Introduction

Statistics is the foundation that keeps ML honest. Data science interviews probe it aggressively because a good model built on a shaky inference is worse than no model at all.

The essentials are: understanding what a p-value actually means (not what most people think), knowing when to bootstrap vs rely on a closed-form CI, reasoning about correlation vs causation, and being able to spot the classic gotchas — Simpson's paradox, multiple testing, sampling bias. This chapter goes through them one by one, interview-style.

The 15 sections

Each section is a short read on one subject, with every answer written out. Work through them in order, or jump to the one you are weakest on.

  1. 01Probability foundationsState the Central Limit Theorem in one sentence.41 questions12 easy19 medium10 hard
  2. 02Common distributionsLog-normal distribution and its uses.5 questions4 medium1 hard
  3. 03Expectation & varianceWhy do we use standard deviation instead of variance in interpretation?3 questions2 easy1 medium
  4. 04Descriptive statistics & EDAMean vs median vs mode — when do you prefer each?24 questions6 easy15 medium3 hard
  5. 05Sampling & central limit theoremWhat is sampling bias and how do you mitigate it?2 questions1 easy1 hard
  6. 06Hypothesis testingWhat is a p-value, precisely?33 questions8 easy18 medium7 hard
  7. 07Non-parametric testsHow many bootstrap resamples do you need, and which statistics does it handle?1 questions1 medium
  8. 08Power, effect size & multiple testingWhat techniques reduce variance in A/B tests?5 questions3 medium2 hard
  9. 09Estimation: MLE, MoM, MAPWhat does a 95% confidence interval mean?18 questions1 easy10 medium7 hard
  10. 10Confidence intervals & bootstrap95% CI for a mean — formula and interpretation.8 questions1 easy3 medium4 hard
  11. 11Regression assumptionsWhat are the Gauss-Markov assumptions for OLS?25 questions1 easy9 medium15 hard
  12. 12Mixed effects & clusteringWhat is a hierarchical Bayesian model?1 questions1 hard
  13. 13Bayesian methodsWhat is the posterior predictive distribution?16 questions3 medium13 hard
  14. 14Causal inference basicsWhy doesn't correlation imply causation?24 questions1 easy3 medium20 hard
  15. 15Experimentation & A/B testingWhat are the pillars of a solid A/B test design?9 questions1 easy2 medium6 hard