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Statistics interview questions

Statistics questions a Data science / ML / AI can be asked, from first job to senior. Open one to see the strongest answer and why it works.

  1. You are summarising customer spend. A few customers spend a hundred times the typical one. Which summary do you report, and why?

    The strongest answer: The median with the spread, because the mean is dragged by the long right tail and describes almost nobody — I show the distribution and mention the mean only with the caveat

    Why it works: Exactly — for skewed distributions the median resists the tail; the shape of the distribution is the real answer.

    • Skewed tail? Report the median.
    • Show the distribution shape.
    • The mean follows the tail.
    • Never delete real customers.

  2. Ice cream sales and drowning rise together. The model uses ice cream to “predict risk.” What do you say?

    The strongest answer: That is a shared-season pattern, not a lever I can pull — I do not recommend banning cones, and I say so

    Why it works: Exactly. Prediction can use a correlate; action needs a mechanism. Interviews want that split.

    • Correlate ≠ intervene.
    • Say when a feature is a proxy.
    • Do not invent causal claims.
    • Do not dress correlation as a risk %.

  3. Your model’s AUC on the test set is 0.82 with a 95% confidence interval of 0.79 to 0.85. What does that interval mean, and what does it not mean?

    The strongest answer: The procedure that produced it captures the true AUC in 95% of repeated samples; it is not a 95% chance the truth is in this interval, and it says nothing about performance on a different population

    Why it works: Right — the confidence is in the procedure, and the interval is about sampling noise on this test set, not about drift or new populations.

    • The confidence is in the procedure.
    • Interval reflects sampling noise.
    • Not a probability of truth.
    • Not a claim about new data.

  4. You tried twenty features and kept the one with p < 0.05 on the same set. What is the honest write-up?

    The strongest answer: I searched and I must say so — that p-value is not a planned test. Confirm on a fresh holdout or treat it as exploratory

    Why it works: Exactly. Search inflates wins. Either pre-specify or confirm on new data — and write the search down.

    • Multiple tries inflate “significance.”
    • Write the search; confirm on new data.
    • Do not report only the winner.
    • Do not adjust after peeking and call it planned.

  5. When is an A/B the wrong next step for a model?

    The strongest answer: When I cannot measure the outcome in time, cannot randomise fairly, or the change is a safety control — I say so instead of running a theatre test

    Why it works: Exactly. Experiments need a measurable outcome and a fair assign. Safety gates are not coin flips.

    • A/B needs a measurable, fair outcome.
    • Do not A/B a safety interlock as theatre.
    • No pre-written lift.
    • Net vs tree does not decide the method.

  6. A linear regression gives ad spend a coefficient of 3.2 on revenue. A stakeholder says “every extra dollar makes 3.2 dollars.” What do you correct?

    The strongest answer: It is the association holding the other included variables fixed, on this data — not a causal return; omitted drivers, collinearity with other spend, and the units and scale of the features all shape that number

    Why it works: Exactly — a coefficient is conditional association with units attached; causal language needs a design (an experiment or a causal model), not a fit.

    • Coefficient: association, other terms fixed.
    • Units and scale matter.
    • Watch collinearity and omitted drivers.
    • Causal claims need a design.

  7. You will try three models and two metrics. How do you stay honest?

    The strongest answer: Write the primary metric and the confirmation set before the hunt — extras are exploratory and labelled that way

    Why it works: Exactly. Pre-specify the exam. Exploration is allowed when it is named.

    • Primary metric and set first.
    • Label extras as exploratory.
    • Do not register after peeking.
    • Do not keep every winner.

  8. You rank products by average rating. A new item with one 5-star review sits above an item rated 4.6 over 2,000 reviews. What do you change?

    The strongest answer: Shrink each item’s average toward a prior — the overall mean — with weight that grows with its review count, so one review barely moves it and 2,000 reviews speak for themselves

    Why it works: Right — a Bayesian average: prior mean plus evidence, weighted by how much evidence there is. Small samples get pulled to the middle.

    • Shrink small samples toward the prior.
    • Weight by evidence count.
    • Bayesian average, not raw mean.
    • Avoid hard cliffs.