1. Explain the Central Limit Theorem and why it matters.
Sample means approach normality as n grows, enabling inference regardless of population shape.
Statistics & Probability interview questions and answers for data analysts and data scientists
Statistics interview questions for data roles cover experimentation, inference, and the reasoning behind an A/B test, the round that separates a data scientist from a dashboard builder. Real questions with worked answers below.
How the Statistics round is run, and what it scores
What the round actually tests
Whether you can reason under uncertainty and say so plainly. Statistics rounds are less about deriving anything than about definitions you can state without hedging, assumptions you volunteer before being asked, and what you would do when an assumption fails. The interviewer is usually checking whether you can be trusted to read an experiment result correctly.
This is the round that most often separates a data scientist from a dashboard builder, and it is scored heavily on explanation. Several large companies ask you to explain a confidence interval or a p-value to a non-technical stakeholder as a question in its own right.
The questions that repeat
What a p-value is, and what it is not. What 95% means in a confidence interval. Type I against Type II error and which is more expensive here. The Central Limit Theorem and why it lets you use a normal approximation on skewed data. Power, and what raises it. Sample size for an A/B test. Multiple comparisons and why twenty metrics produce a winner by accident.
Then the applied half: design an A/B test for this feature, this test ran for three days and the lift is 12%, do you ship it, the treatment group has more users than control, what happened. The applied questions are where the definitions get used, and where memorized answers come apart.
What interviewers score
The definition, then the assumption, then the failure mode. In that order. A candidate who says a p-value is the probability of data this extreme if the null were true, and then adds that it says nothing about effect size, has answered the question and the follow-up at once.
They also score restraint. Reporting an interval rather than a bare p-value, refusing to call a result significant when the interval includes trivial values, and saying a three-day test cannot be read because of novelty and weekly seasonality, all read as judgment rather than caution.
How to prepare, and in what order
Rebuild the core from the questions interviewers ask rather than from a textbook chapter order: p-value, confidence interval, Type I and II error, power, sample size, the CLT, and multiple comparisons. That set covers most of what is asked, and each one has a standard wrong answer you should be able to name.
Then practice the explanations at two levels, one for a fellow analyst and one for a product manager, because you will be asked for the second and graded on it. Say the numbers out loud. Most of the failures in this round are fluency failures, not knowledge failures.
Where candidates lose it
Saying a p-value is the probability the null hypothesis is true, which is the single most common wrong answer in the round. Saying there is a 95% probability the true value lies in this particular interval, which is a credible interval, not a confidence interval. Reading two overlapping confidence intervals as no significant difference. And treating p = 0.06 as no effect rather than as weaker evidence than 0.04.
26 Statistics questions
Probability and distributions
2. What is the law of large numbers, and how is it different from the Central Limit Theorem?
The law of large numbers says the sample mean converges to the true mean as n grows. The CLT says how it gets there: the sampling distribution of the mean becomes normal with spread sigma over root n.
3. Explain Bayes' theorem with a real example.
Posterior is proportional to prior times likelihood. A 99% accurate test for a 1 in 1,000 condition still gives a positive result that is wrong about 90% of the time, because the false positives from the healthy majority outnumber the true positives.
4. Explain expected value with a simple example, and why it is not the same as the likely outcome.
Expected value is the probability-weighted average of the outcomes. A ticket that pays 1,000 with probability 0.001 has an expected value of 1, a number you never actually win. It is the long-run average per play, not what happens on any one play.
5. How do you check whether data is normally distributed, and when does it matter?
Look first: a histogram and a Q-Q plot show skew and tails better than any test. Shapiro Wilk and similar tests reject everything at large n. It matters for small-sample t-tests and regression inference, and much less for means at large n because of the CLT.
Hypothesis testing and inference
6. Explain p-value in plain language.
Probability of observing data as extreme as this, assuming the null hypothesis is true.
7. What is the difference between Type I and Type II error?
Type I is a false positive (rejecting a true null), Type II is a false negative (failing to reject a false null).
8. What is a one-tailed vs two-tailed test, and when is one-tailed defensible?
Two-tailed asks whether there is any difference in either direction, one-tailed asks about one direction only and puts all of alpha there. One-tailed is defensible only when the other direction is impossible or irrelevant by design, decided before the data.
9. Explain statistical power and what increases it.
Power is the probability of detecting an effect that is really there, one minus the Type II error rate. It rises with sample size, effect size and a higher alpha, and falls with variance. 80% is the usual target.
10. What is the difference between statistical and practical significance?
Statistical significance says an effect is unlikely to be noise. Practical significance says it is big enough to matter. With enough data a 0.01% lift is significant, and it is still not worth shipping. Report the effect size with its interval, not just the p-value.
11. What is a confidence interval, and what does 95% actually mean?
A range built from the sample by a procedure that would contain the true value in 95% of repeated samples. It is a statement about the procedure, not a 95% probability that this particular interval holds the truth.
12. Explain confidence intervals vs credible intervals.
A confidence interval is frequentist coverage over repeated samples, a credible interval is Bayesian probability given the data.
13. When would you use a t-test vs a chi-square test?
A t-test compares means of a continuous variable, a chi-square test checks association between categorical variables.
14. What is the difference between parametric and non-parametric tests, and when do you choose each?
Parametric tests assume a distribution for the data or its errors, like the t-test assuming roughly normal means. Non-parametric tests like Mann Whitney or a permutation test work on ranks or resampling. Choose non-parametric for small skewed samples, ordinal data or heavy outliers.
15. What is the bootstrap, and when would you use it instead of a formula?
Resample the data with replacement many times, recompute the statistic each time, and read the spread off those results. Use it when there is no clean formula for the standard error: medians, ratios, percentiles, or a metric per user with heavy tails.
16. How do you correct for multiple comparisons?
Testing twenty metrics at alpha 0.05 gives a 64% chance of at least one false positive. Bonferroni divides alpha by the number of tests and is safe but conservative. Benjamini Hochberg controls the false discovery rate and keeps more real findings.
17. What is p-hacking and how do you avoid it?
Pre-register hypotheses, correct for multiple comparisons, fix sample size in advance.
Experiments and causal inference
18. How do you determine sample size for an A/B test?
Use power analysis: baseline rate, MDE, alpha, power (0.8) to compute n per arm.
19. How long should an A/B test run, and what are novelty and seasonality effects?
Run for the sample size the power calculation requires and for whole weeks, at least one and usually two, so weekday and weekend behavior are both covered. Novelty effects fade as users get used to a change, so check whether the lift holds for later cohorts before you trust it.
20. Explain regression to the mean, and how it fools an analysis.
Extreme measurements are partly luck, so the next measurement of the same thing tends to be closer to average. Pick the worst-performing stores, intervene, and they improve on their own. The fix is a control group selected the same way.
21. What is the difference between correlation and causation, and how do you get closer to causation without an experiment?
Correlation is co-movement, causation needs a counterfactual. Without a randomized test you approximate one with a natural experiment, difference in differences, regression discontinuity, matching or instrumental variables, each with assumptions you must state.
22. What is Simpson's paradox?
A trend within groups reverses when groups are combined due to a confounder.
Regression and modeling
23. What are the assumptions of linear regression, and how do you check them?
Linear relationship, independent errors, constant error variance, normal errors for inference, and no severe multicollinearity. Check with residual plots, a Durbin Watson or autocorrelation plot, a scale location plot, a Q-Q plot, and VIF.
24. How do you interpret a regression coefficient, and when is that interpretation wrong?
A one-unit increase in the feature is associated with a coefficient-sized change in the outcome, holding the other features fixed. Wrong when features cannot move independently, when the relationship is nonlinear, when the outcome is logged or logistic, or when you read it as causal.
25. How do you detect and handle multicollinearity?
Check VIF and correlations, then drop or combine features, or use regularization or PCA.
26. Explain the bias-variance tradeoff.
Bias is underfitting error, variance is overfitting error, and the goal is the lowest total generalization error.