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 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 ...
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 ...
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....
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) ...
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 ...
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...
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...
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...
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 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...
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}...
Determine Normality of Single Observation with Z-Test
Hypothesis Test for a Single Observation Against a Standard Normal Context You observe a single numeric value, x, and want to decide whether it could ...
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...
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...
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,...
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, ...
Analyze Linear Regression Changes with Duplicated Observations
Linear Regression, p-values, and Chi-square with Large Samples Context You are analyzing regression and goodness-of-fit results. Consider what happens...
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...
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 ...