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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Measure Bird Species Segregation
You are a data scientist analyzing bird observations from a forest. The ecology team wants to know whether different bird species are spatially segreg...
Explain Bootstrap and Statistical Inference
Answer the following statistics questions at interview depth: - What is the bootstrap? Describe the resampling procedure, when it is useful, and what ...
Estimate weather’s effect on mental health
Scenario You are studying whether weather (e.g., temperature, precipitation, sunlight, air pressure) affects mental health outcomes (e.g., depression ...
Can bootstrap help reduce variance
An interviewer asks: “Can bootstrap help reduce variance?” Answer this question precisely. Distinguish between: 1) Using the bootstrap to estimate var...
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...
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}...
Explain Bootstrap and Prove Uniformity
You are interviewing for a Data Scientist role. Answer the following statistics-theory prompts: 1. What is the bootstrap, when would you use it, and c...
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...
Compute precision under noisy annotators
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Estimate Population Mean and Conversion Rate Accurately
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Analyze Linear Regression Changes with Duplicated Observations
Linear Regression, P-values, and Chi-square with Large Samples You are analyzing regression and goodness-of-fit results. Consider what happens if ever...
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 ...
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...
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...
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...
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) ...
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....
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, ...
Design human review to estimate model accuracy
Design human review to estimate model accuracy You need to estimate the accuracy of an ML classifier on a population of subjects. You can only afford ...