Google Statistics & Math Interview Questions
Google Statistics & Math interview questions at Google typically blend core probability and inferential statistics with applied experimental design and metric diagnosis. What’s distinctive is the emphasis on real-world thinking: interviewers evaluate not only whether you can compute a p-value or derive a distribution, but whether you can state assumptions, choose the right test or estimator, reason about bias/variance and power, and communicate tradeoffs clearly. Expect both theoretical white‑board style questions and product‑oriented case prompts where you propose analyses, sample sizes, and guardrails for interpretation. ([cleverprep.com](https://www.cleverprep.com/companies/google/data-scientist?utm_source=openai)) For interview preparation focus on fundamentals (distributions, hypothesis testing, confidence intervals, conditional probability and basic linear algebra), applied experimental design and metric interpretation, and practice explaining your choices end‑to‑end. Time yourself on short analytic case studies
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Estimate population singletons from a 10% log
A daily search log has one row per query string. You draw a 10% simple random sample of rows without replacement. Define a “unique query” (singleton) ...
Compute p-values, probabilities, and regularization choices
Answer all parts. A) Hand‑compute a two‑sided p‑value comparing two means using Welch’s t‑test. Sample A: n1=20, mean1=5.2, sd1=1.1. Sample B: n2=24, ...
Assess Fundamental Statistics Knowledge in Data-Science Interviews
Fundamental Statistics (Technical Phone Screen) Context You are given standard statistics tasks commonly used in a data-science interview. Assume all ...
Compute precision under noisy annotators
Two-Annotator Labeling Policy: Precision, Recall, F1, and Generalization You have two independent annotators who review videos and label them as "ille...
Prove OLS invariance to linear transforms
You fit Model 1: y ~ X1 + X2. You also fit Model 2 using Z = [X1 − X2, X1 + X2] = X T where T = [[1,1], [−1,1]] (2×2, invertible). a) Prove that OLS p...
Define and sample a truncated normal
Define the truncated normal Z | a < Z < b for Z ~ N(0,1): write the normalized pdf and cdf. Then design efficient samplers for three cases: (i) a = 1,...
Infer distribution and choose robust statistics
A dataset of n=10,000 session revenues (USD) has: 65% zeros; mean=8.5; median=0; p90=30; p95=120; p99=620. (a) Propose a plausible generative model (e...
Explain mixed models and fixed vs random effects
In an applied DS setting, you are modeling an outcome (e.g., watch time per session, conversion, or rating) across multiple entities (e.g., users, cre...
Infer causal impact without an A/B test
Evaluate Impact of a Shipped Version on Disconnections (No A/B Holdout) Context A new client version was shipped system-wide with the goal of reducing...
Test if one value comes from N(μ,σ²)
Assume the population is N(μ, σ²) with μ and σ known. You observe a single value x = 1.37. Formulate a two-sided hypothesis test H0: X ~ N(μ, σ²) vs H...
Generate values by weighted probabilities
Weighted Random Sampling Generator (Streaming) You are given: - A list of distinct integers values. - A matching list of nonnegative probabilities (we...
Narrow a confidence interval for a mean
You have a simple random sample with n = 100 and sample mean 100. The current 95% CI for the population mean is 100 ± 10, which a PM says is too wide....
Explain and resolve Simpson’s paradox
Define Simpson’s paradox and construct a concrete numeric example where group-wise success rates favor treatment in each subgroup but the aggregate ra...
Analyze data duplication effects in linear regression
OLS With Duplicated Observations: Estimator, Variance, and Inference Pitfalls Context: You have the linear model y = Xβ + ε with full-rank X ∈ ℝ^{n×p}...
Generate Samples from Truncated Normal Distribution
Scenario You draw from a normal distribution but only keep observations that are greater than 1 (i.e., values below 1 are discarded). Assume the origi...
Test a coefficient and explain t-distribution
In OLS, test whether feature j is relevant. a) State H0: β_j = 0 versus H1: β_j ≠ 0 and construct the t‑statistic t_j = b̂_j / se(b̂_j), giving the ex...
Derive MLEs and conditional Normal distributions
Normal and Bivariate Normal: PDFs/CDFs, MLEs, Conditioning, and Unbiased Variance Setup - Let X1, …, Xn be i.i.d. Normal(μ, σ²). - Independently, let ...
Estimate unbiased ad scores with many reviewers
You have 1,000 ads and 100 reviewers; each reviewer rates 100 ads on a 1–10 scale with incomplete overlap. Specify a mixed-effects model to estimate l...
Understand Simpson's Paradox with Simple Examples
Scenario You are a data scientist advising a product team on statistical analysis and experimental design. Tasks 1) Simpson’s paradox - Explain Simpso...
Estimate Population Mean and Conversion Rate Accurately
Statistical Inference: Hypothesis Tests, Confidence Intervals, Sampling Design, and Truncated Normal Estimation Context You are evaluating a set of pr...