Google Data Scientist Statistics & Math Interview Questions
Practice the exact questions companies are asking right now.
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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 ...
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...
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 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}...
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...
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...
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 ...
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) ...
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...
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 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...
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...
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...
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...
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...
Determine Impact of New Chat-Notification on User Engagement
Scenario A product team wants to determine whether a new chat-notification design increases daily active users (DAU) in Google Workspace Chat. Task De...
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...
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,...